sem4 termo tuto tsh

Tutorial 1:1

Tutorial1: Property Tables SSP2113: Thermodynamics

1.

(a) Refer Table A4 (Temperature table),

T=50oC Psat.=12.352 kPa, v(4.16 m

3/kg)<vg=12.026 m

3/kg,Saturated mixture

(b) Refer Table A5 (Pressure table), P=200kPaT=120.21oC, vg=0.88578m

3/kg, (saturated vapor)

(c) T=250oC > 100

oC (>boiling water) Refer Table A6 (P=0.4MPa, T=250

oC)v=0.5952 m

3/kg, superheated

water

(d) Refer Table A4 (Temperature table), T=110oC, v=143.38 m

3/kgSaturated liquid

Summary:

T, °C P, kPa v, m3

/ kg Phase description

50 12.352 4.16 Saturated mixture

120.21 200 0.8858 Saturated vapor

250 400 0.5952 Superheated vapor

110 143.38 0.001052 Saturated liquid

2.

(a) The quality is given to be x = 0.7, which implies that 70 percent of the mass is in the vapor phase and the

remaining 30 percent is in the liquid phase. Therefore, we have saturated liquid-vapor mixture at a pressure

of 200 kPa. Then the temperature must be the saturation temperature at the given pressure:

T = Tsat @ 200 kPa= 120.21°C (Table A-5)

At 200 kPa, we also read from Table A-5 that hf = 504.71 kJ/kg

andhfg = 2201.6 kJ/kg. Then the average enthalpy of the mixture is

h = hf + xhfg

= 504.71 kJ/kg + (0.7)(2201.6 kJ/kg)

= 2045.83 kJ/kg <hg (saturated mixture)

(b) Refer Table A4 (Temperature table), T=140oCP=361.53kPa

The quality is determined from

ANSWER

UNIVERSITI TEKNOLOGI MALAYSIA

FAKULTI SAINS

JABATAN FIZIK

Tutorial 1:2

5646.03.2144

16.5891800

fg

f

h

hhx Saturated mixture

(c) x=0 meant at Saturated liquid, Refer Table A5, P=950kPa T=177.66oC, h=752.74 kJ/kg

(d) Refer Table A6; P=0.8MPa, Tsat.=350oCh=3162.2 kJ/kgSuperheated vapor

Summary:

T, °C P, kPa h, kJ / kg x Phase description

120.21 200 2045.8 0.7 Saturated mixture

140 361.53 1800 0.565 Saturated mixture

177.66 950 752.74 0.0 Saturated liquid

350.0 800 3162.2 - - - Superheated vapor

3.

Tutorial 1:3

4.

5.

6.

7.

Tutorial 1:4

8.

9.

(a)

(b)

(c)

10.

1


1. Complete this table for H2O:

T °C P, kPa v, m3/kg Phase description

50 4.16

200 Saturated vapor

250 400

110 143.38

2. Complete this table for H2O:

T °C P, kPa h, kJ/kg x Phase description

200 0.7

140 1800

950 0.0

800 3162.2

3. One kilogram of water fills a 0.140 m3 rigid container at an initial pressure of 1.8 MPa. The container is

then cooled to 40°C. Determine the initial temperature and final pressure of the water.

4. One kilogram of R-134a fills a 0.14-m3 weighted piston-cylinder device at a temperature of -26.4°C. The

container is now heated until the temperature is 100°C. Determine the final volume of the R-134a. Answer:

0.3014 m3

5. One kilogram of water vapor at 200 kPa fills the 1.1989 m3 left chamber of a partitioned system shown in

Fig. 1. The right chamber has twice the volume of the left and is initially evacuated. Determine the pressure

of the water after the partition has been removed and enough heat has been transferred so that the

temperature of the water is 3°C.

Fig. 1

6. Ten kilograms of R-134a fill a 1.595 m3 weighted piston-cylinder device at a temperature of -26.4

oC. The

container is now heated until the temperature is 100°C. Determine the final volume of the R-134a.

7. One kilogram of water fills a container whose volume is 0.13 m3. The pressure in the container is 750 kPa.

Calculate the total internal energy and enthalpy in the container. Answers: 1654 kJ, 1751 kJ

8. 10 kg of R-134a at 300 kPa fills a rigid container whose volume is 14 L. Determine the temperature and

total enthalpy in the container. The container is now heated until the pressure is 600 kPa. Determine the

temperature and total enthalpy when the heating is completed.


FAKULTI SAINS

JABATAN FIZIK

2

9. A piston-cylinder device contains 0.1 m3 of liquid water and 0.9 m

3 of water vapor in equilibrium at 800

kPa. Heat is transferred at constant pressure until the temperature reaches 350°C.

(a) What is the initial temperature of the water?

(b) Determine the total mass of the water.

(c) Calculate the final volume.

(d) Show the process on a P-v diagram with respect to saturation lines.

10. Superheated water vapor at l.4 MPa and 250°C is allowed to cool at constant volume until the temperature

drops to 120°C. At the final state, determine

(a) the pressure,

(b) the quality, and

(c) the enthalpy.

(d) Also, show the process on a T-v diagram with respect to saturation lines.

Answers: (a) 198.7 kPa, (b) 0.1825, (c) 905.7 kJ/kg

1

Tutorial2:EQUATION OF STATE SSP2113: Thermodynamics

2A: Ideal Gas Equation of State

1. A spherical balloons with a diameter of 6 m is filled with helium at 20°C and 200 kPa. Determine the

mole number and the mass of the helium in the balloon. Given the universal gas constant is Ru= 8.314

kPa.m3

/kmol.K. The molar mass of helium is 4.0 kg/kmol. Answers: 9.28 kmol. 37.15 kg

2. The pressure in an automobile tire depends on the temperature of the air in the tire. When the air

temperature is 25°C, the pressure gauge reads 210 kPa: If the volume of the tire is 0.025 m3, determine

the pressure rise in the tire when the air temperature in the tire rises to 50°C. Also, determine the

amount of air that must be bled off to restore pressure to its original value at this temperature. Assume

the atmospheric pressure is 100 kPa. The gas constant of air is R = 0.287 kPa.m3

/kg.K

3. A 1 m3 tank containing air at 25

oC and 500 kPa is connected through a valve to another tank

containing 5 kg of air at 35oC and 200 kPa. Now the valve is opened, and the entire system is allowed

to reach thermal equilibrium with the surroundings, which are at 20°C. Given the gas constant of air is

R = 0.287 kPa.m3

/kg.K. Determine the volume of the second tank and the final equilibrium pressure of

air. Answers: 2.21 m3, 284.1 kPa

4. A mass of 10-g of oxygen fill a weighted piston cylinder device at 20 kPa and 100°C. The device is

now cooled until the temperature is 0°C. Given the gas constant of oxygen is R = 0.2598 kJ/kg⋅K.

Determine the change of the volume of the device during this cooling.

5. A mass of 0.1 kg of helium fills a 0.2 m3 rigid vessel at 350 kPa. The vessel is heated until the pressure

is 700 kPa. Calculate the temperature change of helium (in K) as a result of this heating. Given the gas

constant of helium is R = 2.0769 kJ/kg⋅K. Answers: 337°C, 337 K

6. Argon in the amount of 0.2 kg fills a 0.2m3 piston cylinder device at 400 kPa. The piston is now

moved by changing the weights until the volume is twice its original size. During this process, argon's

temperature is maintained constant. Given the gas constant of argon is R = 0.2081 kJ/kg⋅K. Determine

the final pressure in the device.

2B: Compressibility Factor

7. Determine the specific volume of superheated water vapor at 10 MPa and 400°C, using (a) the ideal-

gas equation, (b) the generalized compressibility chart, and (c) the steam tables. Also determine the

error involved in the first two cases. Answers: (a) 0.03106 m3/kg, 17.6 percent; (b) 0.02609 m

3/kg, 1.2

percent; (c) 0.02644 m3/kg

8. Determine the specific volume of refrigerant-134a vapor at 0.9 MPa and 70°C based on (a) the ideal-

gas equation, (b) the generalized compressibility chart, and (c) data from tables. Also, determine the

error involved in the first two cases.

9. Determine the specific volume of nitrogen gas at 10 MPa and 150 K based on (a) the ideal-gas

equation and (b) the generalized compressibility chart. Compare these results with the experimental

value of 0.002388 m3/kg, and determine the error involved in each case. Answers: (a) 0.004452 m

3/kg,

86.4 percent; (b) 0.002404 m3/kg, 0.7 percent

10. Determine the specific volume of superheated water vapor at 3.5 MPa and 450°C based on (a) the

ideal-gas equation, (b) the generalized compressibility chart, and (c) the steam tables. Determine the

error involved in the first two cases.

11. Ethane in a rigid vessel is to be heated from 350 kPa and 40°C until its temperature is 315°C. What is

the final pressure of the ethane as predicted by the compressibility chart?


FAKULTI SAINS

JABATAN FIZIK

2

12. Ethylene is heated at constant pressure from 5 MPa and 20°C to 200°C. Using the compressibility

chart, determine the change in the ethylene's specific volume as a result of this heating. Answer:

0.0172 m3/kg

13. Saturated water vapor at 350°C is heated at constant pressure until its volume has doubled. Determine

the final temperature using the ideal gas equation of state, the compressibility charts, and the steam

tables.

14. Methane at 8 MPa and 300 K is heated at constant pressure until its volume has increased by 50

percent. Determine the final temperature using the ideal gas equation of state and the compressibility

factor. Which of these two results is more accurate?

15. What is the percentage of error involved in treating carbon dioxide at 3 MPa and 10°C as an ideal gas?

Answer: 25 percent

16. Carbon dioxide gas enters a pipe at 3 MPa and 500 K at a rate of 2 kg/s. CO2 is cooled at constant

pressure as it flows in the pipe and the temperature of CO2 drops to 450 K at the exit. Determine the

volume flow rate and the density of carbon dioxide at the inlet and the volume flow rate at the exit of

the pipe using (a) the ideal-gas equation and (b) the generalized compressibility chart. Also, determine

(c) the error involved in the first case.

2C: Other Equations of State

17. Methane is heated in a rigid container from 100 kPa and 20°C to 400°C. Determine the final pressure

of the methane treating it as (a) an ideal gas and (b) a Benedict-Webb-Rubin gas.

18. Carbon monoxide is heated in a rigid container from 101 kPa and 21°C to 427°C. Determine the final

pressure of the carbon monoxide treating it as (a) an ideal gas and (b) a Benedict- Webb-Rubin gas.

19. 1-kg of carbon dioxide is compressed from 1 MPa and 200°C to 3 MPa in a piston-cylinder device

arranged to execute a polytropic process for which PV1.2

= constant. Determine the final temperature

treating the carbon dioxide as (a) an ideal gas and (b) a van der Waals gas.

20. Refrigerant-134a at 0.7 MPa has a specific volume of 0.033322 m3/kg. Determine the temperature of

the refrigerant based on (a) the ideal-gas equation, (b) the van der Waals equation, and (c) the

refrigerant tables.

21. Nitrogen at 150 K has a specific volume of 0.041884 m3/kg. Determine the pressure of the nitrogen,

using (a) the ideal-gas equation and (b) the Beattie-Bridgeman equation. Compare your results to the

experimental value of 1000 kPa. Answers: (a) 1063 kPa, (b) 1000.4 kPa

22. What are the first eight virial coefficients of a Benedict-Webb-Rubin gas? Hint: Expand the

exponential term in a power series expansion.

23. Oxygen is maintained at 4 MPa and 20°C. Compare the specific volume of the oxygen under this

condition as predicted by (a) the ideal gas equation of state, (b) the Beattie-Bridgeman equation of

state, and (c) with the compressibility factor.

2D: Specific Heats, U, and h of Ideal Gases

24. What is the change in the internal energy, in kJ/kg, of air as its temperature changes from 50 to 100°C?

Is there any difference if the temperature were to change from 0 to 50°C?

25. The temperature of 2 kg of neon is increased from 20°C to 180°C. Calculate the change in the total

internal energy of the neon, in kJ. Would the internal energy change be any different if the neon were

replaced with argon?

26. Calculate the change in the enthalpy of argon, in kJ/kg, when it is cooled from 400 to 100°C. If neon

had undergone this same change of temperature, would its enthalpy change have been any different?

27. Neon is compressed from 100 kPa and 20°C to 500 kPa in an isothermal compressor. Determine the

change in the specific volume and specific enthalpy of neon caused by this compression.

28. Determine the internal energy change u of hydrogen, in kJ/kg, as it is heated from 200 to 800 K,

using (a) the empirical specific heat equation as a function of temperature (TableA-2c), (b) the cv value

at the average temperature (TableA-2b), and (c) the cv value at room temperature (Table A-2a).

1--PM"

'"~r~ I 12..0..'1::' o. :1.1':} f./••..PI 't/~. tcT" Jr c-

f-..; :.~uY I

( 1>":. Mr\:~ 1-?'V2, ~ (~ ~-r)'2 ('J_~)C(), ),'7 fl..,,~.Itt1hf;l; It..) (S 0tL)•.. '\ t ~ ('-P~- .,.~~,~

~ -:.. 1\1) I"" 1\1\1- ": j,ly, t ~()eo 10·lyt '!i~ -II\r~ l~ )~ (to.~,)~J.I.:}. )("IJ) fL.

'1.2-f :. C JO\>~'" )(t. 0 ",,3) _ =.r.lWlj~ ~., lCf( ( 0."1';).. Itp., .rh'(t,;:/,(t.) (J.. C, ",c-•

'\J ':. "", of '\J '\. = ,,() ..f,J •2...1 ).. '1 . J../ h1!-

'V,

.•.

~

~, :: ~ yt.T,. ~ (0.016) (0. lJ'tip.J OrJO I-;)...11) ':! o.olfl.,1p, ~ /VI'

('\»"- ~ ~ fl-T1.:. (o,orD) (6 ,.2.-rtfo' ) (0'" '-7J )~ o. oIry'') .-

p", ~

c,v:,. '\J" - 'V,::.. -0· 0'1 ~~•

o~-0.1 kj \ ~..uJ().1. ~} - ~

1)\J l~t; 1 , 1w~

ftlLt. ~ ,t. 0 ':K'1 kJ.) I ~.IC.. .

fN = #VI. (LT9 7i ~ PI 'V, _ = Crr0 (c..f.;) (o..l.I~,l)_: ~~tv\ fL ( 0-' l-j) (~.()~'9 tc..A .IhYkJ.tL)

"', =- 'V'\.L~ T.•.~7, Cb)f'\h- tvo.(LT) %. O~rt) (J-w-) ~ '7~ rcISO -- -

6.T::.. T,,- - 7, ~ '1--\1 - j1'}-~ 1r';f- ~- ~

, I

-- ..•... - - .-.-, l'~-I..••

~ -~~~y\

G. ~C). 0 r 1!J

--

Tutorial 2B:1

Tutorial-2B:Compressibility Factor SSP2113: Thermodynamics

7.

The gas constant, the critical pressure, and the critical temperature of water are, from Table A-1,

R = 0.4615 kPa·m3

/kg·K, Tcr

= 647.1 K, Pcr

= 22.06 MPa

(a) From the ideal gas equation of state,

(b) From the compressibility chart (Fig. A-15),

(c) From the superheated steam table (Table A-6),

8.

The gas constant, the critical pressure, and the critical temperature of refrigerant-134a are, from Table A-1,

R = 0.08149 kPa·m3

/kg·K, Tcr

= 374.2 K, Pcr

= 4.059 MPa



(c) From the superheated refrigerant table (Table A-13), R-134a 0.9 MPa 70°C

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 2B:2

9.

The gas constant, the critical pressure, and the critical temperature of nitrogen are, from Table A-1,

R = 0.2968 kPa·m3

/kg·K, Tcr

= 126.2 K, Pcr

= 3.39 MPa



10.


R = 0.4615 kPa·m3

/kg·K, Tcr

= 647.1 K, Pcr

= 22.06 MPa




11.

The gas constant, the critical pressure, and the critical temperature of ethane are, from Table A-1,

R = 0.2765 kPa·m3

/kg·K, Tcr

= 305.5 K, Pcr

= 4.48 MPa

From the compressibility chart at the initial state (Fig. A-15),

The specific volume does not change during the process.

Tutorial 2B:3

12.


R = 0.2964 kPa·m3

/kg·K, Tcr

= 282.4 K, Pcr

= 5.12 MPa

From the compressibility chart at the initial and final states (Fig. A-15),

The specific volume change

13.


R = 0.4615 kPa·m3

/kg·K, Tcr

= 647.1 K, Pcr

= 22.06 MPa

(a) From the ideal gas equation,

(b) The pressure of the steam is

From the compressibility chart at the initial state (Fig. A-15)

Tutorial 2B:4

(c) From the superheated steam table,

14.

The gas constant, the critical pressure, and the critical temperature of methane are, from Table A-1,

R = 0.5182 kPa·m3

/kg·K, Tcr

= 191.1 K, Pcr

= 4.64 MPa

From the ideal gas equation,


At the final state,

15.

The critical pressure, and the critical temperature of CO2 are, from Table A-1,

From the compressibility chart (Fig. A-15),

Tutorial 2B:5

Then the error involved in treating CO

2 as an ideal gas is

16.

The gas constant, the critical pressure, and the critical temperature of CO2 are (Table A-1)

R = 0.1889 kPa·m3

/kg·K, Tcr

= 304.2 K, Pcr

= 7.39 MPa


(b) From the compressibility chart

Tutorial 2C:1

Tutorial-2C:Other Equations of State SSP2113: Thermodynamics

17.


The specific molar volume of the methane is

(b) The specific molar volume of the methane is v1=24.36 m3/kg

Using the coefficients of Table 3-4 for methane and the given data, the Benedict-Webb-Rubin equation of state for state 2

gives

18.

The gas constant and molar mass of CO are (Table A-1)

R = 0.2968 kPa·m3

/kg·K, M = 28.011 kg/kmol


(b) The specific molar volume of the CO in SI units

Using the coefficients of Table 3-4 for CO, the Benedict-Webb-Rubin equation of state for state 2 gives

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 2C:2

19. The gas constant, molar mass, critical pressure, and critical temperature of carbon dioxide are (Table A-1)

R = 0.1889 kPa·m3

/kg·K, M = 44.01 kg/kmol, Tcr

= 304.2 K, Pcr

= 7.39 MPa

(a) The specific volume at the initial state is

According to process specification,

The final temperature

(b) The van der Waals constants for carbon dioxide are determined from

Applying the van der Waals equation to the initial state,

Solving this equation by trial-error: According to process specification,

Applying the van der Waals equation to the final state

20. The gas constant, critical pressure, and critical temperature of R-134a are (Table A-1)

R = 0.08149 kPa·m3

/kg·K, Tcr

= 374.2 K, Pcr

= 4059 kPa


(b) The van der Waals constants for the refrigerant are determined from

(c) From the superheated refrigerant table (Table A-13),

Tutorial 2C:3

21. The gas constant and molar mass of nitrogen are (Table A-1)

R = 0.2968 kPa·m3

/kg·K and M = 28.013 kg/kmol (a) From the ideal gas equation of state,

(b) The constants in the Beattie-Bridgeman equation are

22. The Benedict-Webb-Rubin equation of state

Expanding the last term in a series

Substituting this into the Benedict-Webb-Rubin equation of state and rearranging

The virial equation of state

Comparing the Benedict-Webb-Rubin equation of state to the virial equation of state, the virial coefficients

Tutorial 2C:4

23. The properties of oxygen are (Table A-1)

R = 0.2598 kPa·m3


= 154.8 K, Pcr

= 5.08 MPa


(b) The constants in the Beattie-Bridgeman equation

Substituting these coefficients into the Beattie-Bridgeman equation

and solving using an equation

(c) From the compressibility chart (Fig. A-15),

Tutorial 2D:1

Tutorial-2D: Specific Heats, U, and h of Ideal Gases SSP2113: Thermodynamics

24. At specified conditions, air behaves as an ideal gas.

The constant-volume specific heat of air at room temperature is cv = 0.718 kJ/kg⋅K (Table A-2a).

Using the specific heat at constant volume,

Δu= cvΔT = (0.718 kJ/kg ⋅K)(100 -50)K = 35.9 kJ/kg

if we consider the variation of specific heat with temperature and use thespecific heat values from

Table A-2b, we have cv = 0.721 kJ/kg⋅K at 75°C and cv = 0.718 kJ/kg⋅K at 25°C.

Then,

Δu1= cv ΔT = (0.721 kJ/kg ⋅K)(100 − 50)K = 36.05 kJ/kg


The two results differ from each other by about 0.4%.

25. The constant-volume specific heats of neon and argon are 0.6179 kJ/kg⋅K and 0.3122 kJ/kg⋅K,respectively

(Table A-2a).

The internal energy changes are

Δuneon= cvΔT = (0.6179 kJ/kg ⋅K)(180 − 20)K = 98.9 kJ/kg

Δuargon= cvΔT = (0.3122 kJ/kg ⋅K)(180 − 20)K = 50.0 kJ/kg

26. At specified conditions, neon and argon behave as an ideal gas.

The constant-pressure specific heats of argon and neon are 0.5203 kJ/kg⋅K and 1.0299 kJ/kg⋅K,respectively

(Table A-2a).

The enthalpy changes are

Δhargon= cpΔT= (0.5203 kJ/kg ⋅K)(400 −100)K = 156.1kJ/kg

Δhneon= cpΔT= (1.0299 kJ/kg ⋅K)(400 −100)K = 309.0 kJ/kg

27. The gas constant of neon is R = 0.4119 kJ/kg⋅K and the constant-pressure specific heat of neon is 1.0299

kJ/kg⋅K (Table A-2a).

Compressor inlet, the specific volume is

Compressor exit,

The change in the specific volume caused by the compressor is

Δv=v2- v1= 0.2414 −1.207 = −0.966m3 /kg

Since the process is isothermal,

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 2D:2

28. (a) Using the empirical relation for c p (T) from Table A-2c and relating it to cv (T) ,

where

(b) Using a constant cpvalue from Table A-2b at the average temperature of 500 K,

(c) Using a constant cpvalue from Table A-2a at room temperature,

Tutorial 3:1

Tutorial3: ENERGY TRANSFER SSP2113: Thermodynamics

1. The gas constant of helium is R = 2.0769 kJ/kg⋅K (Table A-1). The initial specific volume is

Using the ideal gas equation,

Since the pressure stays constant,

and the work integral expression gives

2. No work is done during the process 2-3 sincethe area under process line is zero.

the work done isequal to the area under the process line 1-2:

3. The work done is equal to the area under theprocess line 1-2:

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 3:2

4. The gas constant for nitrogen is 0.2968 kJ/kg.K (Table A-2).

5. The properties of nitrogen are R = 0.2968 kJ/kg.K , k = 1.4(Table A-2a)

6. The pressure remains constant during this process, the specific volumes at the initialand the final states are

(Table A-4 through A-6)

The positive sign indicates that work is done by the system

Tutorial 3:3




8. The gas constant of air is R = 0.287 kJ/kg.K (Table A-1).

The negative sign indicates that work is done on the system

9. At state 1:

At state 2:


Tutorial 3:4

10.


11. The gas constant for nitrogen is R = 0.2968 kJ/kg.K (Table A-2a) The boundary work for this polytropic process

The negative sign indicates that work is done onthe system

12. (a) The term 10 /v

2 must have pressure unitssince it is added to P.

Thus the quantity 10 must have the unit kPa·m6/kmol

2.

(b) The boundary work for this process


13.

Tutorial 3:5

14. The properties of nitrogen are R = 0.2968 kJ/kg.K ,k = 1.4 (Table A-2a).

15. The properties of air are R = 0.287 kJ/kg.K ,k = 1.4 (Table A-2a). isothermal expansion process

polytropic compression process:

constant pressure compression process:

net work for the cycle is the sum of the works for each process

16. The initial state is saturated mixture at 90°C. Thepressure and the specific volume at this state are (Table A-4),

The final specific volume at 800 kPa and 250°C is (Table A-6)

the work done is equal to the area under the process line 1-2:

Tutorial 3:6

17. The initial state is saturated mixture at 1 MPa. Thespecific volume at this state is (Table A-5),

The final state is saturated liquid at 100°C (Table A-4)


The negative sign shows that the work is done on the system in the amount of 5.34 kJ.

18. For a polytropic expansion or compression process,

For an ideal gas,

Combining these equations

1

Tutorial−3: ENERGY TRANSFER SSP2113: Thermodynamics

1. The volume of 1 kg of helium in a piston-cylinder deviceis initially 5 m3. Now helium is

compressed to 3 m3while its pressure is maintained constant at 200 kPa. Determine the initial

and final temperatures of helium as well as the work required to compress it in kJ.

2. Calculate the total work, in kJ, for process 1-3 shown in Fig. 1 when the system consists of 2

kg of nitrogen.

FIGURE 1 3. Calculate the total work, in kJ, produced by the process of Fig. 2.

FIGURE 2 4. A piston-cylinder device initially contains 0.07 m

3 of nitrogen gas at 130 kPa and 120°C. The

nitrogen is now expanded polytropically to a state of 100 kPa and 100°C. Determine the

boundary work done during this process.

5. A piston-cylinder device initially contains 0.07 m3 of nitrogen gas at 130 kPa and 120°C. The

nitrogen is now expanded to a pressure of 100 kPapolytropically with a polytropic exponent

whose value is equal to the specific heat ratio (called isentropic expansion). Determine the

final temperature and the boundary work done during this process.

6. A mass of 5 kg of saturated water vapor at 300 kPa is heated at constant pressure until the

temperature reaches 200°C. Calculate the work done by the steam during this process.

Answer: 165.9 kJ

7. A frictionless piston-cylinder device initially contains 200 L of saturated liquid refrigerant-

134a. The piston is free to move, and its mass is such that it maintains a pressure of 900 kPa

on the refrigerant. The refrigerant is now heated until its temperature rises to 700C. Calculate

the work done during this process. Answer: 5571 kJ


FAKULTI SAINS

JABATAN FIZIK

2

8. A mass of 2.4 kg of air at 150 kPa and 12°C is contained in a gas-tight, frictionless piston-

cylinder device. The air is now compressed to a final pressure of 600 kPa. During the

process, heat is transferred from the air such that the temperature inside the cylinder remains

constant. Calculate the work input during this process. Answer: 272 kJ

9. During an expansion process, the pressure of a gas changes from 100 to 700 kPa according to

the relation P= aV + b, where a = 1220 kPa/m3 and b is a constant. If the initial volume of the

gas is 0.2 m3, calculate the work done during the process. Answer: 197 kJ

10. During some actual expansion and compression processes in piston-cylinder devices, the

gases have been observed to satisfy the relationship PVn= C, where nand C are constants.

Calculate the work done when a gas expands from ISO kPa and 0.03 m3 to a final volume of

0.2 m3 for the case of n = 1.3.

11. A frictionless piston-cylinder device contains 2 kg of nitrogen at 100 kPa and 300 K.

Nitrogen is now compressed slowly according to the relation PV1.4

= constant until it reaches

a final temperature of 360 K. Calculate the work input during this process. Answer: 89 kJ

12. The equation of state of a gas is given as v(P + 10/v2) = RuT where the units of v and

Parem3/kmol and kPa, respectively. Now 0.5 kmol of this gas is expanded in a quasi-

equilibrium manner from 2 to 4 m3 at a constant temperature of 300 K. Determine (a) the unit

of the quantity 10 in the equation and (b) the work done during this isothermal expansion

process.

13. Carbon dioxide contained in a piston-cylinder device iscompressed from 0.3 to 0.1 m3.

During the process, the pressure and volume are related by P = aV-2

, where a = 8 kPa·m6.

Calculate the work done on the carbon dioxide during this process. Answer: 53.3 kJ

14. A piston-cylinder device initially contains 0.25 kg of nitrogen gas at 130 kPa and 120°C. The

nitrogen is now expanded isothermally to a pressure of 100 kPa. Determine the boundary

work done during this process. Answer: 7.65 kJ

15. A piston-cylinder device contains 0.15 kg of air initially at 2 MPa and 350°C. The air is first

expanded isothermally to 500 kPa, then compressed polytropically with a polytropic

exponent of 1.2 to the initial pressure, and finally compressed at the constant pressure to the

initial state. Determine the boundary work for each process and the net work of the cycle.

16. 1-kg of water that is initially at 90°C with a quality of 10 percent occupies a spring-loaded

piston-cylinder device, such as that in Fig. 3. This device is now heated until the pressure

rises to 800 kPa and the temperature is 250°C. Determine the total work produced during this

process, in kJ. Answer: 24.5 kJ

FIGURE 3

17. 0.5-kg water that is initially at 1MPa and 10 percent quality occupies a spring-loaded piston-

cylinder device. This device is now cooled until the water is a saturated liquid at 100°C.

Calculate the total work produced during this process in kJ.

18. Argon is compressed in a polytropic process with n = 1.2 from 120 kPa and 30°C to 1200

kPa in a piston-cylinder device. Determine the final temperature of the argon.

1

Tutorial−4: FIRST LAW & MASS FLOW SSP2113: Thermodynamics

1. A vessel contains an ideal gas at pressure 150 kPa. When the gas is heated it expands at

constant pressure until the temperature increases by 100 K. The amount of heat absorbed by

the gas is 4.36 kJ. However, if the gas at its initial condition is heated at constant volume

until the temperature increases by 100 K, the amount of heat absorbed is 3.11 kJ. Determine

(a) the value of , (b) the work done by the gas when it expands at constant pressure, (c) the

change in volume of the gas when the gas is heated at constant pressure and the temperature

rises by 100 K.

2. A vessel contains an ideal gas in condition A, as shown in Figure 1. When the condition of

the gas changes from A to that of B, the gas system undergoes a heat transfer of 10.5 kJ.

When the gas in condition B changes to condition C, there is a heat transfer of 3.2 kJ.

Calculate (a) the work done in the process ABC, (b) the change in the internal energy of the

gas in the process ABC, (c) the work done in the process ADC, (d) the total amount of heat

transferred in the process ADC.

3. Air is contained in a cylinder by a frictionless gas-tight piston. (a) Calculate the work done

by the air as it expands from a volume of 0.015 m3 to a volume of 0.027 m

3 at a constant

pressure of 2.0 105 Pa. (b) Determine the final pressure of the air if it starts from the same

initial conditions as in (a) and expanding by the same amount, the change occurs (i)

isothermally, (ii) adiabatically. (Given for air is 1.40)

4. A vessel contains an ideal gas of volume 2.0 cm3 at pressure 100 kPa and temperature 25 C.

The gas expands adiabatically until the volume becomes 4.0 cm3. After that, it is compressed

isothermally until the volume becomes 3.0 cm3. (a) Calculate the pressure and the

temperature of the gas in the final condition. (b) Sketch and label a graph of gas pressure (P)

against gas volume (V) to show how the pressure and volume changes when the condition of

the gas changes from the initial condition to final condition. (Given for gas is 1.67)

5. A quantity of ideal gas whose ratio of molar heat capacities is 5/3 has a temperature of 300

K, volume of 64 103 m

3 and pressure of 243 kPa. It is made to undergo the following three

changes in order:

1: adiabatic compression to a volume 27 103 m

3,

2 : isothermal expansion to 64 103 m

3 ,

3 : a return to its original state.


FAKULTI SAINS

JABATAN FIZIK

2

(a) Calculate the pressure on completion of process 1 and the temperature at which the

process 2 occurs. (b) Describe the process 3, (c) Sketch and label a graph of pressure against

volume for the changes described.

6. Air enters a nozzle steadily at 2.21 kg/m3 and 40 m/s and leaves at 0.762 kg/m

3 and 180 m/s.

If the inlet area of the nozzle is 90 cm2, determine (a) the mass flow rate through the nozzle,

and (b) the exit area of the nozzle. Answers: (a) 0.796 kg/s (b) 58 cm2

7. A pump increases the water pressure from 70 kPa at the inlet to 700 kPa at the outlet. Water

enters this pump at 15oC through a 1 cm diameter opening and exits through a 1.5 cm

diameter opening. Determine the velocity of the water at the inlet and outlet when the mass

flow rate through the pump is 0.5 kg/s. Will these velocities change significantly if the inlet

temperature is raised to 40°C?

FIGURE 2 8. A hair dryer is basically a duct of constant diameter in which a few layers of electric resistors

are placed. A small fan pulls the air in and forces it through the resistors where it is heated. If

the density of air is 1.20 kg/m3 at the inlet and 1.05 kg/m

3 at the exit, determine the percent

increase in the velocity of air as it flows through the dryer.

9. Refrigerant-134a enters a 28-cm diameter pipe steadily at 200 kPa and 20°C with a velocity

of 5 m/s. The refrigerant gains heat as it flows and leaves the pipe at 180 kPa and 40°C.

Determine (a) the volume flow rate of the refrigerant at the inlet, (b) the mass flow rate of the

refrigerant, and (c) the velocity and volume flow rate at the exit.

10. Air flows steadily in a pipe at 300 kPa, 77oC, and 25 m/s at a rate of 18 kg/min. Determine

(a) the diameter of the pipe, (b) the rate of flow energy, (c) the rate of energy transport by

mass, and (d) the error involved in part (c) if the kinetic energy is neglected.

11. A water pump increases the water pressure from 75 kPa to 350 kPa. Determine the flow

work, in kJ/kg, required by the pump.

12. Air at 4.18 kg/m3 enters a nozzle that has an inlet-to exit area ratio of 2:1 with a velocity of

120 m/s and leaves with a velocity of 380 m/s. Determine the density of air at the exit.

Answer: 2.64 kg/m3

13. Steam at 3 MPa and 400°C enters an adiabatic nozzle steadily with a velocity of 40 m/s and

leaves at 2.5 MPa and 300 m/s. Determine (a) the exit temperature and (b) the ratio of the

inlet to exit area A1/A2.

14. Air enters a gas turbine at 1000 kPa and 350°C and leaves at 100 kPa and 40°C. Determine

the inlet and outlet volume flow rates when the mass flow rate through this turbine is 2 kg/s.

15. A heat exchanger is to cool ethylene glycol (cp = 2.56 kJ/kg.oC) flowing at a rate of 2 kg/s

from 80°C to 40°C by water (cp = 4.18 kJ/kg.oC) that enters at 20°C and leaves at 55°C.

Determine (a) the rate of heat transfer and (b) the mass flow rate of water.

Tutorial 5:1

Tutorial-5: SECOND LAW THERMODYNAMICS SSP2113: Thermodynamic

ANSWER 1.

In reality the amount of heat rejected - be lower (lost to the surrounding air) through the pipes and other components.

2.

3.

4.

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 5:2

5.

6.

7.

8.

9.

Tutorial 5:3

10.

11.

12.

(a)

(b)


1. A 600-MW steam power plant, which is cooled by a nearby river, has a thermal efficiency of

40 percent. Determine the rate of heat transfer to the river water. Will the actual heat transfer

rate be higher or lower than this value? Why?

2. A heat engine that pumps water out of an underground mine accepts 500 kJ of heat and

produces 200 kJ of work. How much heat does it reject, in kJ?

3. A heat engine with a thermal efficiency of 40 percent rejects 1000 kJ/kg of heat. How much

heat does it receive? Answer: 1667 kJ/kg

4. A steam power plant with a power output of 150 MW consumes coal at a rate of 60 tons/h. If

the heating value of the coal is 30,000 kJ/kg, determine the overall efficiency of this plant.

Answer: 30.0 percent

5. An automobile engine consumes fuel at a rate of 28 L/h and delivers 60 kW of power to the

wheels. If the fuel has a heating value of 44,000 kJ/kg and a density of 0.8 g/cm3, determine

the efficiency of this engine. Answer: 21.9 percent

6. A household refrigerator with a COP of 1.2 removes heat from the refrigerated space at a rate

of 60 kJ/min. Determine (a) the electric power consumed by the refrigerator and (b) the rate

of heat transfer to the kitchen air. Answers: (a) 0.83 kW, (b) 110 kJ/min

7. A commercial heat pump removes 10,000 kJ/h from the source, rejects 15,090 kJ/h to the

sink, and requires 1.5 kW of power. What is this heat pump's coefficient of performance?

8. A refrigerator used for cooling food in a grocery store is to produce a 10,000 kJ/h cooling

effect, and it has a coefficient of performance of 1.35. How many kilowatts of power will this

refrigerator require to operate? Answer: 2.06 kW

9. A heat pump has a COP of 1.7. Determine the heat transferred to and from this heat pump

when 50 kJ of work is supplied.

10. A food refrigerator is to provide a 15,000 kJ/h cooling effect while rejecting 22,000 kJ/h of

heat. Calculate the COP of this refrigerator. Answer: 2.14

11. A heat pump is used to maintain a house at a constant temperature of 23°C. The house is

losing heat to the outside air through the walls and the windows at a rate of 60,000 kJ/h while

the energy generated within the house from people, lights, and appliances amounts to 4000

kJ/h. For a COP of 2.5, determine the required power input to the heat pump. Answer: 6.22

kW

12. Refrigerant -134a enters the condenser of a residential heat pump at 800 kPa and 35°C at a

rate of 0.018 kg/s and leaves at 800 kPa as a saturated liquid. If the compressor consumes 1.2

kW of power, determine (a) the COP of the heat pump and (b) the rate of heat absorption

from the outside air.


FAKULTI SAINS

JABATAN FIZIK

Tutorial 6:1

Tutorial-6: CARNOT CYCLE, PRINCIPLE & HEAT ENGINE SSP2113: Thermodynamic

1.

2.

3.

4.

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 6:2

5.

the claim is FALSE

6.

7.

8.

Tutorial 6:3

9.

10.

11.

12.

of 1

Tutorial-6: CARNOT CYCLE PRINCIPLE & HEAT ENGINESSP2113: Thermodynamic

1. From a work-production perspective, which is more valuable: (a) thermal energy reservoirs

at 675 K and 325 K or (b) thermal energy reservoirs at 625 K and 275 K?

2. You are an engineer in an electric-generation station. Youknow that the flames in the boiler

reach a temperature of 1200 K and that cooling water at 300 K is available from a nearby

river. What is the maximum efficiency your plant will ever achieve?

3. A heat engine operates between a source at 550°C and a sink at 25°C. If heat is supplied to

the heat engine at a steady rate of 1200 kJ/min, determine the maximum power output of this

heat engine.

4. A completely reversible heat engine operates with a source at 800 K and a sink at 280 K. At

what rate must heat be supplied to this engine, in kJ/h, for it to produce 4 kW of power?

Answer: 22,150 kJ/h

5. An experimentalist claims that, based on his measurements, a heat engine receives 300 kJ of

heat from a source of 500 K, converts 160 kJ of it to work, and rejects the rest as waste heat

to a sink at 300 K. Are these measurements reasonable? Why?

6. Determine the minimum work per unit of heat transfer from the source reservoir that is

required to drive a heat pump with thermal energy reservoirs at 460 K and 535 K.

7. A thermodynamicist claims to have developed a heat engine with 50 percent thermal

efficiency when operating with thermal energy reservoirs at 700 K and 280 K. Is this claim

valid?

8. A completely reversible refrigerator is driven by a 10kW compressor and operates with

thermal energy reservoirs at 250 K and 300 K. Calculate the rate of cooling provided by this

refrigerator. Answer: 50 kW

9. A refrigerator is to remove heat from the cooled space at a rate of 300 kJ/min to maintain its

.temperature at -8°C. If the air surrounding the refrigerator is at 25°C, determine the

minimum power input required for this refrigerator. Answer: 0.623 kW

10. A Carnot refrigerator operates in a room in which the temperature is 25°C. The refrigerator

consumes 500 W of power when operating and has a COP of 4.5. Determine (a) the rate of

heat removal from the refrigerated space and (b) the temperature of the refrigerated space.

Answers: (a) 135 kJ/min, (b) -29.2°C

11. A heat pump is used to heat a house and maintain it at 24°C. On a winter day when the

outdoor air temperature is -5°C, the house is estimated to lose heat at a rate of 80,000 kJ/h.

Determine the minimum power required to operate this heat pump.

12. A completely reversible heat pump has a COP of 1.6 and a sink temperature of 300 K.

Calculate (a) the temperature of the source and (b) the rate of heat transfer to the sink when

1.5 kW of power is supplied to this heat pump.


FAKULTI SAINS

JABATAN FIZIK

Tutorial 7:1

Tutorial−7: ENTROPY SSP2113: Thermodynamic

1. Assumptions

1 This is a steady-flow process since there is no change with time.

2 Kinetic and potentialenergy changes are negligible.

3 Air is an ideal gas.

4 The process involves no internal irreversibilitiessuch as friction, and thus it is an isothermal, internally

reversible process.

2.

entropy - increased, transfer of heat - possible 3.

violates the increase in entropy principle the entropy is decreasing

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 7:2

4.

rate is positive (i.e., the entropy increases as time passes),this transfer of heat is possible

5.

net rate of entropy change is zero as it must be in order to satisfy the second law

6.

heat pump is completely reversible

Tutorial 7:3

7.

8.

entropy increases, a refrigerator with COP = 4 is possible.

refrigerator can no longer be possible.

9.

positive-satisfies the increase in entropy principle

1

Tutorial−7: ENTROPY SSP2113: Thermodynamic 1. Air is compressed by a 12 kW compressor from P1 to P2. The air temperature is maintained constant at 25

oC

during this process as a result of heat transfer to the surrounding medium at 10oC. Determine the rate of entropy

change of the air. State the assumptions made in solving this problem. Answer: -0.0403 kW/K

2. Heat in the amount of 100 kJ is transferred directly from a hot reservoir at 1200 K to a cold reservoir at 600 K.

Calculate the entropy change of the two reservoirs and determine if the increase of entropy principle is satisfied.

Figure 1

3. In the Question 2, assume that the heat is transferred from the cold reservoir to the hot reservoir contrary to the

Clausius statement of the second law. Prove that this violates the increase of entropy principle-as it must

according to Clausius.

4. Heat is transferred at a rate of 2 kW from a hot reservoir at 800 K to a cold reservoir at 300 K. Calculate the rate

at which the entropy of the two reservoirs changes and determines if the second law is satisfied. Answer:

0.00417 kW/K

5. A completely reversible air conditioner provides 36,000 kJ/h of cooling for a space maintained at 20°C while

rejecting heat to the environmental air at 45°C. Calculate the rate at which the entropies of the two reservoirs

change and verify that this air conditioner satisfies the increase of entropy principle.

6. A completely reversible heat pump produces heat at a rate of 100 kW to warm a house maintained at 21°C. The

exterior air, which is at 10°C, serves as the source. Calculate the rate of entropy change of the two reservoirs

and determine if this heat pump satisfies the second law according to the increase of entropy principle.

7. Refrigerant-134a enters the coils of the evaporator of a refrigeration system as a saturated liquid-vapor mixture

at a pressure of 160 kPa. The refrigerant absorbs 180 kJ of heat from the cooled space, which is maintained at -

5°C, and leaves as saturated vapor at the same pressure. Determine (a) the entropy change of the refrigerant, (b)

the entropy change of the cooled space, and (c) the total entropy change for this process.

8. A refrigerator with a coefficient of performance of 4 transfers heat from a cold region at -20°C to a hot region at

30°C. Calculate the total entropy change of the regions when 1 kJ of heat is transferred from the cold region. Is

the second law satisfied? Will this refrigerator still satisfy the second law if its coefficient of performance is 6?

Figure2 9. A proposed heat pump design creates a heating effect of 25 kW while using 5 kW of electrical power. The

thermal energy reservoirs are at 300 K and 260 K. Is this possible according to the increase of entropy

principle?


FAKULTI SAINS

JABATAN FIZIK

Tutorial 8:1


1.

2.

3.

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 8:2

4.

5.

6.

ΔU + Wb= ΔH

(a)

(b)

Tutorial 8:3

7.

8. (a)

(b)

(c)

9.

Tutorial 8:4

10.

.

11.

12.

Tutorial 8:5

13.

14.

1


1. Determine the total heat transfer for the reversible process 1-3 shown in Fig. 1.

FIGURE 1

2. Determine the total heat transfer for the reversible process 1-2 shown in Fig. 2.

FIGURE 2

3. A 25-kg iron block initially at 350°C is quenched in an insulated tank that contains 100 kg of

water at 18°Cshown in Fig. 3. Assumingthe water that vaporizes during the process

condensesback in the tank,determine the total entropy change duringthis process. The

specific heat of water at 25°C is cp= 4.18 kJ/kg.oC. The specific heat of iron at

roomtemperature is cp= 0.45 kJ/kg.oC.

FIGURE 3

4. Which of the two gases-helium or nitrogen-experiences the greatest entropy change as its

state is changed from 2000 kPa and 427°C to 200 kPa and 27°C? The properties of helium

are cp= 5.1926 kJ/kg⋅K, R = 2.0769 kJ/kg⋅K


FAKULTI SAINS

JABATAN FIZIK

2

5. Which of the two gases-neon or air-has the lowest final temperature as it is expanded

isentropically from 1000 kPa and 500°C to 100 kPa in a piston-cylinder device? The specific

heat ratios of neon and air at room temperature are k = 1.667 and k = 1.4, respectively

6. An insulated piston-cylinder device initially contains 300 L of air at 120 kPa and 17°Cshown

in Fig. 4. Air is now heated for 15 min by a 200-W resistance heater placed inside the

cylinder. The pressure of air is maintained constant during this process. Determine the

entropy change of air, assuming (a) constant specific heats and (h) variable specific heats.

The gas constant of air is R = 0.287 kJ/kg.K

FIGURE 4

7. An insulated rigid tank contains 4 kg of argon gas at 450 kPa and 30°Cshown in Fig. 5. A

valve is now opened, and argon is allowed to escape until the pressure inside drops to 200

kPa. Assuming the argon remaining inside the tank has undergone a reversible, adiabatic

process, determine the final mass in the tank. The specific heat ratio of argon is k = 1.667.

Answer: 2.46 kg

FIGURE 5

8. A container filled with 45 kg of liquid water at 95°C is placed in a 90-m3 room that is

initially at 12°Cshown in Fig. 6. Thermal equilibrium is established after a while as a result

of heat transfer between the water and the air in the room. Using constant specific heats,

determine (a) the final equilibrium temperature, (b) the amount of heat transfer between the

water and the air in the room, and (c) the entropy generation. Assume the room is well sealed

and heavily insulated. The properties of air at room temperature are R = 0.287 kPa.m3/kg.K,

cp= 1.005 kJ/kg.K, cv = 0.718 kJ/kg.K. The specific heat of water at room temperature is cw=

4.18 kJ/kg.K

FIGURE 6

3

9. An ideal gas at 100 kPa and 27oC enters a steady-flow compressor. The gas is compressed to

400 kPa, and 10 percent of the mass that entered the compressor is removed for some other

use. The remaining 90 percent of the inlet gas is compressed to 600 kPa before leaving the

compressor. The entire compression process is assumed to be reversible and adiabatic. The

power supplied to the compressor is measured to be 32 kW. If the ideal gas has constant

specific heats such that cv = 0.8 kJ/kg.K and cp = l.l kJ/kg.K, (a) sketch the compression

process on a T-s diagram, (b) determine the temperature of the gas at the two compressor

exits, in K, and (c) determine the mass flow rate of the gas into the compressor, in kg/s.

10. Argon gas enters an adiabatic turbine at 800°C and 1.5 MPa at a rate of 80 kg/min and

exhausts at 200 kPa. If the power output of the turbine is 370 kW, determine the isentropic

efficiency of the turbine. The specific heat ratio of argon is k = 1.667. The constant pressure

specific heat of argon is cp= .5203 kJ/kg.K

11. Nitrogen is compressed by an adiabatic compressor from 100 kPa and 17°C to 600 kPa and

227°C.Calculate the entropy generation for this process, in kJ/kg-K. The specific heat of

nitrogen at the average temperature of (17+227)/2=122°C = 395 K is cp=1.044 kJ/kg⋅K

12. The inner and outer surfaces of a 5-m x 7-m brick Regenerator wall of thickness 20 cm are

maintained at temperatures of 20 oC and 5°C, respectively. If the rate of heat transfer through

the wall is 1890 W, determine the rate of entropy generation within the wall.

13. A 1000-W iron is left on the ironing board with its base exposed to the air at 20°Cshown in

Fig. 7. If the surface temperature is 400°C, determine the rate of entropy generation during

this process in steady operation. How much of this entropy generation occurs within the iron?

FIGURE 7

14. A frictionless piston-cylinder device contains saturated liquid water at 175-kPa

pressureshown in Fig. 8. Now 400 kJ of heat is transferred to water from a source at 500°C,

and part of the liquid vaporizes at constant pressure. Determine the total entropy generated

during this process, in kJ/K.

FIGURE 8

Tutorial 9:1

Tutorial−9: EXERGY SSP2113: Thermodynamic

1.

The minimum number of windmills

2. Potential energy it possesses, Exergy = PE = mgh

3. (a) The reversible power

(b) The irreversibility rate

(c) The second law efficiency is determined from its definition,

4. Air:

The entropy change

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 9:2

The air’s specific volumes at the given state and dead state

The specific closed system exergy of the air is then

The total exergy available, Φ = m = (1.730 kg)(83.06 kJ/kg) = 144 kJ

Helium:

helium system has a greater potential for the production of work

5. Ideal-gas entropy change relation,

Tutorial 9:3

6. (a)

(b)

7. (a)

from Table A-17,

(b)

Tutorial 9:4

Alternative

8.

minimum power input - for compression process.

9. (a)

Tutorial 9:5

(b)

10. (a) The mass flow rate

The power input

the actual power

(b) The given isothermal efficiency

(c) An energy balance

The mass flow rate

11. (a)

Tutorial 9:6

An energy balance

(b) The specific exergy changes

The exergy destruction

(c) The second-law efficiency

,

12.

entropy balance

entropy generation

X destroyed = ToSgen= (278 K)(7.098 kJ/K) = 1973 kJ

1


1. The electric power needs of a community are to be met by windmills with 10-m-diameter

rotors. The windmills are to be located where the wind is blowing steadily at an average

velocity of 8 m/s. Determine the minimum number of windmills that need to be installed if

the required power output is 600 kW. The gas constant of air is 0.287 kPa.m3/kg.K

2. One method of meeting the extra electric power demand at peak periods is to pump some

water from a large body of water (such as a lake) to a water reservoir at a higher elevation at

times of low demand and to generate electricity at times of high demand by letting this water

run down and rotate a turbine (i.e., convert the electric energy to potential energy and then

back to electric energy). For an energy storage capacity of 5 x 106 kWh, determine the

minimum amount of water that needs to be stored at an average elevation (relative to the

ground level) of 75 m. Answer: 2.45 x 1010

kg

FIGURE 1

3. A heat engine receives heat from a source at 1500 K at a rate of 700 kJ/s, and it rejects the

waste heat to a medium at 320 K. The measured power output of the heat engine is 320 kW,

and the environment temperature is 25°C. Determine (a) the reversible power, (b) the rate of

irreversibility, and (c) the second-law efficiency of this heat engine. Answers: (a) 550.7

kW,(b) 230.7 kW, (c) 58.1 percent

4. Which is a more valuable resource for work production in a closed system 0.3 m3 of air at

700 kPa and 150°C or 0.6 m3 of helium at 550 kPa and 95°C? Take To = 25°C and Po = 100

kPa. The properties of air at room temperature are cp= 1.005 kJ/kg·K, cv= 0.718 kJ/kg·K, k =

1.4, and R = 0.287 kJ/kg·K. For helium, cp= 5.1926 kJ/kg·K, cv= 3.1156 kJ/kg·K, k = 1.667,

and R = 2.0769 kJ/kg·K.

5. A mass of 8 kg of helium undergoes a process from an initial state of 3 m3/kg and 15°C to a

final state of 0.5 m3/kg and 80°C. Assuming the surroundings to be at 25°C and 100 kPa,

determine the increase in the useful work potential of the helium during this process. The gas

constant of helium is R = 2.0769 kJ/kg.K. The constant volume specific heat of helium is cv =

3.1156 kJ/kg.K.

6. An iron block of unknown mass at 85°C is dropped into an insulated tank that contains 100 L

of water at 20°C. At the same time, a paddle wheel driven by a 200-W motor is activated to

stir the water. It is observed that thermal equilibrium is established after 20 min with a final

temperature of 24°C. Assuming the surroundings to be at 20oe, determine (a) the mass of the


FAKULTI SAINS

JABATAN FIZIK

2

iron block and (b) the exergy destroyed during this process. The density and specific heat of

water at 25oC are ρ = 997 kg/m3 and cp= 4.18 kJ/kg.

oF. The specific heat of iron at room

temperature (the only value available in the tables) is cp= 0.45 kJ/kg.oC. Answers: (a) 52.0

kg, (b) 375 kJ

FIGURE 2

7. Air enters a nozzle steadily at 300 kPa and 87°C with a velocity of 50 m/s and exits at 95 kPa

and 300 m/s. The heat loss from the nozzle to the surrounding medium at 17°C is estimated

to be 4 kJ/kg. Determine (a) the exit temperature and (b) the exergy destroyed during this

process. The gas constant of air is R = 0.287 kJ/kg.K. The properties of air at the nozzleinlet

are (Table A-17) T1=360K h1=360.58kJ/kg, s1o=1.88543 kJ/kg.K. Answers: (a) 39.5

oC, (b)

58.4 kJ/kg

8. Air is compressed by a compressor from 95 kPa and 27°C to 600 kPa and 277°C at a rate of

0.06 kg/s. Neglecting the changes in kinetic and potential energies and assuming the

surroundings to be at 25°C, determine the reversible power input for this process. The gas

constant of air is R = 0.287 kJ/kg.K. From the air table (Table A-17)

Answer: 13.7 kW

9. A well-insulated shell-and-tube heat exchanger is used to heat water (cp = 4.18 kJ/kg.oC) in

the tubes from 20 to 70°C at a rate of 4.5 kg/s. Heat is supplied by hot oil (cp = 2.30 kJ/kg.oC)

that enters the shell side at 170°C at a rate of 10 kg/s. Disregarding any heat loss from the

heat exchanger, determine (a) the exit temperature of oil and (b) the rate of exergy

destruction in the heat exchanger. Take To = 25°C. The specific heats of water and oil are

given to be 4.18 and 2.3 kJ/kg.oC, respectively.

FIGURE 3

10. Air enters a compressor at ambient conditions of 100 kPa and 20°C at a rate of 4.5 m3/s with

a low velocity, and exits at 900 kPa, 60°C, and 80 m/s. The compressor is cooled by cooling

water that experiences a temperature rise of 10°C. The isothermal efficiency of the

compressor is 70 percent. The gas constant of air is R = 0.287 kJ/kg.K and the specific heat

of air at room is cp= 1.005 kJ/kg.K. the specific heat of water at room temperature is cw= 4.18

kJ/kg.K. Determine (a) the actual and reversible power inputs, (b) the second-law efficiency,

and (c) the mass flow rate of the cooling water.

3

11. Hot exhaust gases leaving an internal combustion engine at 400°C and 150 kPa at a rate of

0.8 kg/s is to be used to produce saturated steam at 200°C in an insulated heat exchanger.

Water enters the heat exchanger at the ambient temperature of 20°C, and the exhaust gases

leave the heat exchanger at 350°C. The gas constant of air is R = 0.287 kJkg.K. The specific

heat of air at the average temperature of exhaust gases (650 K) is cp= 1.063 kJ/kg.K.

Determine (a) the rate of steam production, (b) the rate of exergy destruction in the heat

exchanger, and (c) the second-law efficiency of the heat exchanger.

FIGURE 4

12. The inner and outer surfaces of a 0.5-cm-thick, 2-m x 2-m window glass in winter are 10°C

and 3°C, respectively. If the rate of heat loss through the window is 4.4 kJ/s, determine the

amount of heat loss, in kJ, through the glass over a period of 5 h. Also, determine the exergy

destruction associated with this process. Take To = 5°C.

Tutorial 10:1

Tutorial – 10 : GAS POWER CYCLES SSP2113: Thermodynamic 1. maximum efficiency

efficiency of 55 percent is possible.

2. (a)

(b)

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 10:2

3. (a)

(b)

(c)

4. (a)

Tutorial 10:3

(b)

5. (a)

(b)

Tutorial 10:4

6.

7. (a)

(b)

(c)

(d)

8.

Tutorial 10:5

9.

10. (a)

(b)

(c)

(d)

11. (a)

Tutorial 10:6

(b)

(c)

(d)

(e)

Tutorial 10:7

12.

13.

14.

1

Tutorial - 10: GAS POWER CYCLES SSP2113: Thermodynamic

1. Can any ideal gas power cycle have a thermal efficiency greater than 55 percent when using

thermal energy reservoirs at 627°C and 17°C?

2. An air-standard cycle is executed in a closed system and is composed of the following four

processes:

1-2 Isentropic compression from 100 kPa and 27°C to I MPa

2-3 P = constant heat addition in amount of 2800 kJ/kg

3-4 v = constant heat rejection to 100 kPa

4-1 P = constant heat rejection to initial state

(a) Show the cycle on P-v and T-s diagrams. (b) Calculate the maximum temperature in the

cycle. (c) Determine the thermal efficiency. Assume constant specific heats at room

temperatureare cp= 1.005 kJ/kg.K, cv = 0.718 kJ/kg·K, and k= 1.4. Answers: (b) 3360 K, (c)

21.0 percent

3. An air-standard cycle is executed in a closed system with 0.004 kg of air and consists of the

following three processes:

1-2 Isentropic compression from 100 kPa and 27°C to 1 MPa

2-3 P = constant heat addition in the amount of 2.76 kJ

3-1 P = c1v + c2 heat rejection to initial state (c1 and c2 are constants)

(a) Show the cycle on P-v and T-s diagrams. (b) Calculate the heat rejected. (c) Determine

the thermal efficiency. Assume constant specific heats at room temperatureare cp= 1.005

kJ/kg.K, cv = 0.718 kJ/kg·K, and k= 1.4. Answers: (b) 1.679 kJ, (c) 39.2 percent

4. An air-standard cycle with variable specific heats is executed in a closed system with 0.003

kg of air and consists of the following three processes:

1-2 v = constant heat addition from 95 kPa and 17°C to 380 kPa

2-3 Isentropic expansion to 95 kPa

3-1 P = constant heat rejection to initial state

The properties of air are given in Table A-17(a) Show the cycle on P-v and T-s diagrams. (b)

Calculate the net work per cycle, in kJ. (c) Determine the thermal efficiency.

5. Repeat Question 4, using constant specific heats at room temperatureare cp= 1.005 kJ/kg.K,

cv = 0.718 kJ/kg·K, and k = 1.4.

6. Consider a Carnot cycle executed in a closed system with 0.003 kg of air. The temperature

limits of the cycle are 300 and 900 K, and the minimum and maximum pressures that occur

during the cycle are 20 and 2000 kPa. Assuming constant specific heatscp= 1.005 kJ/kg.K, cv

= 0.718 kJ/kg·K, R =0.287 kJ/kg.K, and k = 1.4, determine the net work output per cycle.

7. Consider a Carnot cycle executed in a closed system /takes in air at 100 kPa and 20°C, and is

repeated 1000 times with air as the working fluid. The maximum pressure in the cycle is 800

kPa while the maximum temperature is 750 K. If the entropy increase during the isothermal

heat rejection process is 0.25 kJ/kg.K and the net work output is 100 kJ/kg, determine (a) the

minimum pressure in the cycle, (b) the heat rejection from the cycle, and (c) the thermal

efficiency of the cycle. (d) If an actual heat engine cycle operates between the same

temperature limits and produces 5200 kW of power for an air flow rate of 90 kg/s, determine


FAKULTI SAINS

JABATAN FIZIK

2

the second law efficiency of this cycle. The properties of air at room temperatures are R =

0.287 kJ/kg.K and k = 1.4.

8. An Ideal gas Carnot cycle uses as: as the working fluid, receives heat from. a heat reservoir

at 107oC, is repeated 1500 times per minute, and has a compression ratio of 12. The

compression ratio is defined as the volume ratio during the compression process. Determine

the maximum temperature of the low-temperature heat reservoir, the cycle's thermal

efficiency, and the amount of heat that must be supplied per cycle if this device is to produce

500 kW of power. The properties of air at room temperature are cp= 1.005 kJ/kg.K, cv =

0.718 kJ/kg·K, and k= 1.4 Answers: 481 K, 63.0 percent, 31.8 kJ

9. An ideal Otto cycle has a compression ratio of 12, takes in air at 100 kPa and 20°C, and is

repeated 1000 times per minute. Using constant specific heats at room temperature,

determine the thermal efficiency of this cycle and the rate of heat input if the cycle is to

produce 200 kW of power.The properties of air at room temperature are cp= 1.005 kJ/kg.K,

cv = 0.718 kJ/kg·K, and k= 1.4.

10. The compression ratio of an air-standard Otto cycle is 9.5. Prior to the isentropic

compression process, the air is at 100 kPa, 35oC, and 600 cm. The temperature at the end of

the isentropic expansion process is 800 K. Using specific heat values at room temperature,

determine (a) the highest temperature and pressure in the cycle; (b) the amount of heat

transferred in, in kJ; (c) the thermal efficiency; and (d) the mean effective pressure (MEP).

The properties of air at room temperature are cp= 1.005 kJ/kg·K, cv = 0.718 kJ/kg·K, R

=0.287 kJ/kg·K, and k = 1.4. Answers: (a) 1969 K, 6072 kPa, (b) 0.59 kJ, (c) 59.4 percent,

(d) 652 kPa

11. A four-cylinder, four-stroke, 2.2-L gasoline engine operates on the Otto cycle with a

compression ratio of 10. The air is at 100 kPa and 60°C at the beginning of the compression

process, and the maximum pressure in the cycle is 8 MPa. The compression and expansion

processes may be modeled as polytropic with a polytropic constant of 1.3. Using constant

specific heats at 850 K, determine (a) the temperature at the end of the expansion process, (b)

the net work output and the thermal efficiency, (c) the mean effective pressure, (d) the engine

speed for a net power output of 70 kW, and (e) the specitic fuel consumption, in g/kWh,

defined as the ratio of the mass of the fuel consumed to the net work produced. The air-fuel

ratio, defined as the amount of air divided by the amount of fuel intake is 16. The properties

of air at 850 K are cp= 1.110 kJ/kg·K, cv = 0.823 kJ/kg·K, R = 0.287 kJ/kg·K, and k = 1.349.

12. Determine the mean effective pressure (MEP) of an ideal Otto cycle that uses air as the

working fluid; its state at the beginning of the compression is 96 kPa and 17°C; its

temperature at the end of the combustion is 817°C; and its compression ratio is 9. Use

constant specific heats at room temperature. The properties of air at room temperature are R

= 0.287 kPa·m3/kg.K, cp= 1.005 kJ/kg·K, cv = 0.718 kJ/kg·K, and k = 1.4

13. Determine the rate of heat addition and rejection for the Otto cycle of Question 12, when it

produces 105 kW and the cycle is repeated 1400 times per minute. The properties of air at

room temperature are R = 0.287 kPa·m3/kg.K (Table A-1), cp= 1.005kJ/kg·K, cv = 0.718

kJ/kg·K, and k = 1.4.

14. An ideal Otto cycle has a compression ratio of 7. At the beginning of the compression

process, P1 = 90 kPa, T1 = 27°C, and V1 = 0.004 m3. The maximum cycle temperature is

1127°C. For each repetition of the cycle, calculate the heat rejection and the net work

production. Also calculate the thermal efficiency and mean effective pressure for this cycle.

Use constant specific heats at room temperature. The properties of air at room temperature

are R = 0.287 kJ/kg.K, cp= 1.005 kJ/kg·K, cv =0.718 kJ/kg·K, and k = 1.4.Answers: 1.03 kJ,

1.21 kJ, 54.1 percent, 354 kPa.

Tutorial 11:1

Tutorial-11: REFRIGERATION CYCLES SSP2113: Thermodynamic

1.

(a)

TH

= 30°C = 303 K

TL

= Tsat @ 160 kPa

= -15.60°C = 257.4 K (Refer Table A-12),

COP -Carnot refrigerator

(b) Refer Table A-11,

(c) The net work input is determined from

2.

(a) Refer Table A-13;TH

= Tsat @ 0.6 MPa

= 21.55°C = 294.6 K and TL

= Tsat @ 0.2 MPa

= -10.09°C = 262.9 K.

(b) Process 4-1 : isentropic

(c) s

3= s

g @ 0.6 MPa= 0.92177 kJ/kg·K,

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 11:2

3. Refer the refrigerant tables (Tables A-11, A-12, and A-13),

Mass flow rate

Power requirement

COP of the refrigerator

4. Refer refrigerant tables (Tables A-12 and A-13),

Rate of heat removal

(b) Rate of heat rejection

(c) COP of the refrigerator

Tutorial 11:3

5. (a) The properties of refrigerant-134a are (Tables A-11 through A-13)

The isentropic efficiency

(b) The rate of heat

(c) The power input and the COP

(d) The ideal vapor-compression cycle

Tutorial 11:4

6. From the air table (Table A-17),

Then the rate of refrigeration

(b) The net power input

(c) The COP

7. (a) From the isentropic relations,

(b) The COP

(c) The mass flow rate

Tutorial 11:5

8.

(a) the isentropic relations,

The temperature at state 4

T4 = 281.3 K.

energy balance on the regenerator

effectiveness of the regenerator

(b) The refrigeration load

(c)

(d)

Tutorial 11:6

9.

10.

The mass flow rate

The rate of heat addition to the cycle

The rate of heat rejection

11.

claim is possible, but not probable.

Tutorial 11:7

12. (a)

(b)

(c)

13.

14. (a)

(b)

(c)

Tutorial 11:8

15. (a)

(b)

(c)

1


1. A steady-flow Carnot refrigeration cycle uses refrigerant-134a as the working fluid. The refrigerant changes from

saturated vapor to saturated liquid at 30°C in the condenser as it rejects heat. The evaporator pressure is 160 kPa.

Show the cycle on a T-s diagram relative to saturation lines, and determine (a) the coefficient of performance, (b) the

amount of heat absorbed from the refrigerated space, and (c) the net work input. Answers: (a) 5.64, (b) 147 kJ/kg, (c)

26.1 kJ/kg

2. Refrigerant-134a enters the condenser of a steady flow Carnot refrigerator as a saturated vapor at 0.6 MPa, and it

leaves with a quality of 0.05. The heat absorption from the refrigerated space takes place at a pressure of 0.2 MPa.

Show the cycle on a T-s diagram relative to saturation lines, and determine (a) the coefficient of performance, (b) the

quality at the beginning of the heat-absorption process, and (c) the net work input.

3. An ideal vapor-compression refrigeration cycle that uses refrigerant-134a as its working fluid maintains a condenser

at 1000 kPa and the evaporator at 4°C. Determine this system's COP and the amount of power required to servicea

400 kW cooling load. Answers: 6.46, 61.9 kW

FIGURE 1

4. A refrigerator uses refrigerant-134a as the working fluid and operates on an ideal vapor-compression refrigeration

cycle between 0.12 and 0.7 MPa. The mass flow rate of the refrigerant is 0.05 kg/so Show the cycle on a T-s diagram

with respect to saturation lines. Determine (a) the rate of heat removal from the refrigerated space and the power

input to the compressor, (b) the rate of heat rejection to the environment. and (c) the coefficient of performance.

Answers: (a) 7.41 kW, 1.83 kW, (b) 9.23 kW, (c) 4.06

5. Refrigerant-134a enters the condenser of a residential heat pump at 800 kPa and 55°C at a rate of 0.018 kg/s and

leaves at 750 kPa sub-cooled by 3°C. The refrigerant enters the compressor at 200 kPa superheated by 4°C.

Determine (a) the isentropic efficiency of the compressor, (b) the rate of heat supplied to the heated room, and (c) the

COP of the heat pump. Also, determine (d) the COP and the rate of heat supplied to the heated room if this heat pump

operated on the ideal vapor-compression cycle between the pressure limits of 200 and 800 kPa.


FAKULTI SAINS

JABATAN FIZIK

2

FIGURE 2 6. Air enters the compressor of an ideal gas refrigeration cycle at 12°C and 50 kPa and the turbine at 47°C and 250 kPa.

The mass flow rate of air through the cycle is 0.08 kg/so Assuming variable specific heats for air, determine (a) the

rate of refrigeration, (b) the net power input, and (c) the coefficient of performance. Answers: (a) 6.67 kW, (b) 3.88

kW, (c) 1.72

7. A gas refrigeration cycle with a pressure ratio of 3 uses helium as the working fluid. The temperature of the helium is

-10°C at the compressor inlet and 50°C at the turbine inlet. Assuming isentropic efficiencies of 80 percent for both

the turbine and the compressor, determine (a) the minimum temperature in the cycle, (b) the coefficient of

performance, and (c) the mass f10w rate of the helium for a refrigeration rate of 18 kW. The properties of helium are

cp = 5.1926 kJ/kg·K and k = 1.667

8. A gas refrigeration system using air as the working fluid has a pressure ratio of 5. Air enters the compressor at O°C.

The high-pressure air is cooled to 35°C by rejecting heat to the surroundings. The refrigerant leaves the turbine at -

80°C and then it absorbs heat from the refrigerated space before entering the regenerator. The mass flow rate of air is

0.4 kg/so Assuming isentropic efficiencies of 80 percent for the compressor and 85 percent for the turbine and using

constant specific heats at room temperature, determine (a) the effectiveness of the regenerator, (b) the rate of heat

removal from the refrigerated space, and (c) the COP of the cycle. Also, determine (d) the refrigeration load and the

COP if this system operated on the simple gas refrigeration cycJe. Use the same compressor inlet temperature as

given, the same turbine inlet temperature as calculated, and the same compressor and turbine efficiencies. The

properties of air at room temperature are cp = 1.005 kJ/kg·K and k = 1.4. Answers: (a) 0.434, (b) 21.4 kW, (c) 0.478,

(d) 24.7 kW, 0.599

FIGURE 3

9. An ideal gas refrigeration cycle uses air as the working fluid. The air is at 35 kPa and -23°C as it enters the

compressor with a compression ratio of 4. The temperature at the turbine entrance is 37°C. Determine this cycle's

COP. Use constant specific heats at room temperature. The properties of air at room temperature are cp

= 1.005

kJ/kg·K and k = 1.4

3

10. An ideal gas refrigeration system operates with air as the working. Air is at 100 kPa and 20°C before compression,

and 500 kPa and 30°C before expansion. The system is to provide 15 kW of cooling. Calculate the rate at which air is

circulated in this system, as well as the rates of heat addition and rejection. Use constant specific heats at room

temperature. The properties of air at room temperature are cp

= 1.005 kJ/kg·K and k = 1.4.

11. An absorption refrigeration system that receives heat from a source at 130°C and maintains the refrigerated space at -

5°C is claimed to have a COP of 2. If the environment temperature is 27°C, can this claim be valid? Justify your

answer.

12. A reversible absorption refrigerator consists of a reversible heat engine and a reversible refrigerator. The system

removes heat from a cooled space at –10oC at a rate of 22 kW. The refrigerator operates in an environment at 25°C. If

the heat is supplied to the cycle by condensing saturated steam at 200°C, determine (a) the rate at which the steam

condenses and (b) the power input to the reversible refrigerator. (c) If the COP of an actual absorption chiller at the

same temperature limits has a COP of 0.7, determine the second law efficiency of this chiller. The enthalpy of

vaporization of water at 200°C is hfg

= 1939.8 kJ/kg. Answers: (a) 0.00408 kg/s, (b) 2.93 kW, (c) 0.252

FIGURE 4

13. A thermoelectric refrigerator is powered by a 12-V car battery that draws 3 A of current when running. The

refrigerator resembles a small ice chest and is claimed to cool nine canned drinks, 0.350-L each, from 25 to 3°e in 12

h. Determine the average COP of this refrigerator. The properties of canned drinks are the same as those of water at

room temperature, ρ = 1 kg/L and cp = 4.18 kJ/kg·°C.

FIGURE 5

14. Thermoelectric coolers that plug into the cigarette lighter of a car are commonly available. One such cooler is

claimed to cool a 350-g drink from 26 to 3°C or to heat a cup of coffee from 24 to 54°C in about 15 min in a well-

insulated cup holder. Assuming an average cop of 0.2 in the cooling mode, determine (a) the average rate of heat

removal from the drink, (b) the average rate of heat supply to the coffee, and (c) the electric power drawn from the

battery of the car, all in W.The properties of canned drinks are the same as those of water at room temperature, cp

=

4.18 kJ/kg.°C.

15. Consider a regenerative gas refrigeration cycle using helium as the working fluid. Helium enters the compressor at

100 kPa and -10°C and is compressed to 300 kPa. Helium is then cooled to 20°C by water. It then enters the

regenerator where it is cooled further before it enters the turbine. Helium leaves the refrigerated space at -25°C and

enters the regenerator. Assuming both the turbine and the compressor to be isentropic, determine (a) the temperature

of the helium at the turbine inlet, (h) the coefficient of performanceof the cycle, and (c) the net power input required

for a mass flow rate of 0.45 kg/s. The properties of helium are cp = 5.1926 kJ/kg·K and k = 1.667.

Tutorial 1:1


1.

(a) Refer Table A4 (Temperature table),

T=50oC Psat.=12.352 kPa, v(4.16 m

3/kg)<vg=12.026 m

3/kg,Saturated mixture

(b) Refer Table A5 (Pressure table), P=200kPaT=120.21oC, vg=0.88578m

3/kg, (saturated vapor)

(c) T=250oC > 100

oC (>boiling water) Refer Table A6 (P=0.4MPa, T=250

oC)v=0.5952 m

3/kg, superheated

water

(d) Refer Table A4 (Temperature table), T=110oC, v=143.38 m

3/kgSaturated liquid

Summary:

T, °C P, kPa v, m3

/ kg Phase description

50 12.352 4.16 Saturated mixture

120.21 200 0.8858 Saturated vapor

250 400 0.5952 Superheated vapor

110 143.38 0.001052 Saturated liquid

2.

(a) The quality is given to be x = 0.7, which implies that 70 percent of the mass is in the vapor phase and the

remaining 30 percent is in the liquid phase. Therefore, we have saturated liquid-vapor mixture at a pressure

of 200 kPa. Then the temperature must be the saturation temperature at the given pressure:

T = Tsat @ 200 kPa= 120.21°C (Table A-5)

At 200 kPa, we also read from Table A-5 that hf = 504.71 kJ/kg

andhfg = 2201.6 kJ/kg. Then the average enthalpy of the mixture is

h = hf + xhfg

= 504.71 kJ/kg + (0.7)(2201.6 kJ/kg)

= 2045.83 kJ/kg <hg (saturated mixture)

(b) Refer Table A4 (Temperature table), T=140oCP=361.53kPa

The quality is determined from

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 1:2

5646.03.2144

16.5891800

fg

f

h

hhx Saturated mixture

(c) x=0 meant at Saturated liquid, Refer Table A5, P=950kPa T=177.66oC, h=752.74 kJ/kg

(d) Refer Table A6; P=0.8MPa, Tsat.=350oCh=3162.2 kJ/kgSuperheated vapor

Summary:

T, °C P, kPa h, kJ / kg x Phase description

120.21 200 2045.8 0.7 Saturated mixture

140 361.53 1800 0.565 Saturated mixture

177.66 950 752.74 0.0 Saturated liquid

350.0 800 3162.2 - - - Superheated vapor

3.

Tutorial 1:3

4.

5.

6.

7.

Tutorial 1:4

8.

9.

(a)

(b)

(c)

10.

1--PM"

'"~r~ I 12..0..'1::' o. :1.1':} f./••..PI 't/~. tcT" Jr c-

f-..; :.~uY I

( 1>":. Mr\:~ 1-?'V2, ~ (~ ~-r)'2 ('J_~)C(), ),'7 fl..,,~.Itt1hf;l; It..) (S 0tL)•.. '\ t ~ ('-P~- .,.~~,~

~ -:.. 1\1) I"" 1\1\1- ": j,ly, t ~()eo 10·lyt '!i~ -II\r~ l~ )~ (to.~,)~J.I.:}. )("IJ) fL.

'1.2-f :. C JO\>~'" )(t. 0 ",,3) _ =.r.lWlj~ ~., lCf( ( 0."1';).. Itp., .rh'(t,;:/,(t.) (J.. C, ",c-•

'\J ':. "", of '\J '\. = ,,() ..f,J •2...1 ).. '1 . J../ h1!-

'V,

.•.

~

~, :: ~ yt.T,. ~ (0.016) (0. lJ'tip.J OrJO I-;)...11) ':! o.olfl.,1p, ~ /VI'

('\»"- ~ ~ fl-T1.:. (o,orD) (6 ,.2.-rtfo' ) (0'" '-7J )~ o. oIry'') .-

p", ~

c,v:,. '\J" - 'V,::.. -0· 0'1 ~~•

o~-0.1 kj \ ~..uJ().1. ~} - ~

1)\J l~t; 1 , 1w~

ftlLt. ~ ,t. 0 ':K'1 kJ.) I ~.IC.. .

fN = #VI. (LT9 7i ~ PI 'V, _ = Crr0 (c..f.;) (o..l.I~,l)_: ~~tv\ fL ( 0-' l-j) (~.()~'9 tc..A .IhYkJ.tL)

"', =- 'V'\.L~ T.•.~7, Cb)f'\h- tvo.(LT) %. O~rt) (J-w-) ~ '7~ rcISO -- -

6.T::.. T,,- - 7, ~ '1--\1 - j1'}-~ 1r';f- ~- ~

, I

-- ..•... - - .-.-, l'~-I..••

~ -~~~y\

G. ~C). 0 r 1!J

--

Tutorial 2B:1

Tutorial-2B:Compressibility Factor SSP2113: Thermodynamics

7.


R = 0.4615 kPa·m3

/kg·K, Tcr

= 647.1 K, Pcr

= 22.06 MPa




8.

The gas constant, the critical pressure, and the critical temperature of refrigerant-134a are, from Table A-1,

R = 0.08149 kPa·m3

/kg·K, Tcr

= 374.2 K, Pcr

= 4.059 MPa



(c) From the superheated refrigerant table (Table A-13), R-134a 0.9 MPa 70°C

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 2B:2

9.

The gas constant, the critical pressure, and the critical temperature of nitrogen are, from Table A-1,

R = 0.2968 kPa·m3

/kg·K, Tcr

= 126.2 K, Pcr

= 3.39 MPa



10.


R = 0.4615 kPa·m3

/kg·K, Tcr

= 647.1 K, Pcr

= 22.06 MPa




11.


R = 0.2765 kPa·m3

/kg·K, Tcr

= 305.5 K, Pcr

= 4.48 MPa


The specific volume does not change during the process.

Tutorial 2B:3

12.


R = 0.2964 kPa·m3

/kg·K, Tcr

= 282.4 K, Pcr

= 5.12 MPa

From the compressibility chart at the initial and final states (Fig. A-15),

The specific volume change

13.


R = 0.4615 kPa·m3

/kg·K, Tcr

= 647.1 K, Pcr

= 22.06 MPa

(a) From the ideal gas equation,

(b) The pressure of the steam is

From the compressibility chart at the initial state (Fig. A-15)

Tutorial 2B:4

(c) From the superheated steam table,

14.

The gas constant, the critical pressure, and the critical temperature of methane are, from Table A-1,

R = 0.5182 kPa·m3

/kg·K, Tcr

= 191.1 K, Pcr

= 4.64 MPa

From the ideal gas equation,


At the final state,

15.

The critical pressure, and the critical temperature of CO2 are, from Table A-1,

From the compressibility chart (Fig. A-15),

Tutorial 2B:5

Then the error involved in treating CO

2 as an ideal gas is

16.

The gas constant, the critical pressure, and the critical temperature of CO2 are (Table A-1)

R = 0.1889 kPa·m3

/kg·K, Tcr

= 304.2 K, Pcr

= 7.39 MPa


(b) From the compressibility chart

Tutorial 2C:1

Tutorial-2C:Other Equations of State SSP2113: Thermodynamics

17.


The specific molar volume of the methane is

(b) The specific molar volume of the methane is v1=24.36 m3/kg

Using the coefficients of Table 3-4 for methane and the given data, the Benedict-Webb-Rubin equation of state for state 2

gives

18.

The gas constant and molar mass of CO are (Table A-1)

R = 0.2968 kPa·m3

/kg·K, M = 28.011 kg/kmol


(b) The specific molar volume of the CO in SI units

Using the coefficients of Table 3-4 for CO, the Benedict-Webb-Rubin equation of state for state 2 gives

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 2C:2

19. The gas constant, molar mass, critical pressure, and critical temperature of carbon dioxide are (Table A-1)

R = 0.1889 kPa·m3


= 304.2 K, Pcr

= 7.39 MPa

(a) The specific volume at the initial state is

According to process specification,

The final temperature

(b) The van der Waals constants for carbon dioxide are determined from

Applying the van der Waals equation to the initial state,

Solving this equation by trial-error: According to process specification,

Applying the van der Waals equation to the final state

20. The gas constant, critical pressure, and critical temperature of R-134a are (Table A-1)

R = 0.08149 kPa·m3

/kg·K, Tcr

= 374.2 K, Pcr

= 4059 kPa


(b) The van der Waals constants for the refrigerant are determined from

(c) From the superheated refrigerant table (Table A-13),

Tutorial 2C:3

21. The gas constant and molar mass of nitrogen are (Table A-1)

R = 0.2968 kPa·m3

/kg·K and M = 28.013 kg/kmol (a) From the ideal gas equation of state,

(b) The constants in the Beattie-Bridgeman equation are

22. The Benedict-Webb-Rubin equation of state

Expanding the last term in a series

Substituting this into the Benedict-Webb-Rubin equation of state and rearranging

The virial equation of state

Comparing the Benedict-Webb-Rubin equation of state to the virial equation of state, the virial coefficients

Tutorial 2C:4

23. The properties of oxygen are (Table A-1)

R = 0.2598 kPa·m3


= 154.8 K, Pcr

= 5.08 MPa


(b) The constants in the Beattie-Bridgeman equation

Substituting these coefficients into the Beattie-Bridgeman equation

and solving using an equation

(c) From the compressibility chart (Fig. A-15),

Tutorial 2D:1

Tutorial-2D: Specific Heats, U, and h of Ideal Gases SSP2113: Thermodynamics

24. At specified conditions, air behaves as an ideal gas.

The constant-volume specific heat of air at room temperature is cv = 0.718 kJ/kg⋅K (Table A-2a).

Using the specific heat at constant volume,

Δu= cvΔT = (0.718 kJ/kg ⋅K)(100 -50)K = 35.9 kJ/kg

if we consider the variation of specific heat with temperature and use thespecific heat values from

Table A-2b, we have cv = 0.721 kJ/kg⋅K at 75°C and cv = 0.718 kJ/kg⋅K at 25°C.

Then,



The two results differ from each other by about 0.4%.

25. The constant-volume specific heats of neon and argon are 0.6179 kJ/kg⋅K and 0.3122 kJ/kg⋅K,respectively

(Table A-2a).

The internal energy changes are

Δuneon= cvΔT = (0.6179 kJ/kg ⋅K)(180 − 20)K = 98.9 kJ/kg

Δuargon= cvΔT = (0.3122 kJ/kg ⋅K)(180 − 20)K = 50.0 kJ/kg

26. At specified conditions, neon and argon behave as an ideal gas.

The constant-pressure specific heats of argon and neon are 0.5203 kJ/kg⋅K and 1.0299 kJ/kg⋅K,respectively

(Table A-2a).

The enthalpy changes are

Δhargon= cpΔT= (0.5203 kJ/kg ⋅K)(400 −100)K = 156.1kJ/kg

Δhneon= cpΔT= (1.0299 kJ/kg ⋅K)(400 −100)K = 309.0 kJ/kg

27. The gas constant of neon is R = 0.4119 kJ/kg⋅K and the constant-pressure specific heat of neon is 1.0299

kJ/kg⋅K (Table A-2a).

Compressor inlet, the specific volume is

Compressor exit,

The change in the specific volume caused by the compressor is

Δv=v2- v1= 0.2414 −1.207 = −0.966m3 /kg

Since the process is isothermal,

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 2D:2

28. (a) Using the empirical relation for c p (T) from Table A-2c and relating it to cv (T) ,

where

(b) Using a constant cpvalue from Table A-2b at the average temperature of 500 K,

(c) Using a constant cpvalue from Table A-2a at room temperature,

Tutorial 3:1

Tutorial3: ENERGY TRANSFER SSP2113: Thermodynamics

1. The gas constant of helium is R = 2.0769 kJ/kg⋅K (Table A-1). The initial specific volume is

Using the ideal gas equation,

Since the pressure stays constant,

and the work integral expression gives

2. No work is done during the process 2-3 sincethe area under process line is zero.

the work done isequal to the area under the process line 1-2:

3. The work done is equal to the area under theprocess line 1-2:

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 3:2

4. The gas constant for nitrogen is 0.2968 kJ/kg.K (Table A-2).

5. The properties of nitrogen are R = 0.2968 kJ/kg.K , k = 1.4(Table A-2a)




Tutorial 3:3




8. The gas constant of air is R = 0.287 kJ/kg.K (Table A-1).

The negative sign indicates that work is done on the system

9. At state 1:

At state 2:


Tutorial 3:4

10.


11. The gas constant for nitrogen is R = 0.2968 kJ/kg.K (Table A-2a) The boundary work for this polytropic process

The negative sign indicates that work is done onthe system

12. (a) The term 10 /v

2 must have pressure unitssince it is added to P.

Thus the quantity 10 must have the unit kPa·m6/kmol

2.

(b) The boundary work for this process


13.

Tutorial 3:5

14. The properties of nitrogen are R = 0.2968 kJ/kg.K ,k = 1.4 (Table A-2a).

15. The properties of air are R = 0.287 kJ/kg.K ,k = 1.4 (Table A-2a). isothermal expansion process

polytropic compression process:

constant pressure compression process:

net work for the cycle is the sum of the works for each process

16. The initial state is saturated mixture at 90°C. Thepressure and the specific volume at this state are (Table A-4),

The final specific volume at 800 kPa and 250°C is (Table A-6)


Tutorial 3:6

17. The initial state is saturated mixture at 1 MPa. Thespecific volume at this state is (Table A-5),

The final state is saturated liquid at 100°C (Table A-4)


The negative sign shows that the work is done on the system in the amount of 5.34 kJ.

18. For a polytropic expansion or compression process,

For an ideal gas,

Combining these equations

1

Tutorial−4: FIRST LAW & MASS FLOW SSP2113: Thermodynamics

1. A vessel contains an ideal gas at pressure 150 kPa. When the gas is heated it expands at

constant pressure until the temperature increases by 100 K. The amount of heat absorbed by

the gas is 4.36 kJ. However, if the gas at its initial condition is heated at constant volume

until the temperature increases by 100 K, the amount of heat absorbed is 3.11 kJ. Determine

(a) the value of , (b) the work done by the gas when it expands at constant pressure, (c) the

change in volume of the gas when the gas is heated at constant pressure and the temperature

rises by 100 K.

2. A vessel contains an ideal gas in condition A, as shown in Figure 1. When the condition of

the gas changes from A to that of B, the gas system undergoes a heat transfer of 10.5 kJ.

When the gas in condition B changes to condition C, there is a heat transfer of 3.2 kJ.

Calculate (a) the work done in the process ABC, (b) the change in the internal energy of the

gas in the process ABC, (c) the work done in the process ADC, (d) the total amount of heat

transferred in the process ADC.

3. Air is contained in a cylinder by a frictionless gas-tight piston. (a) Calculate the work done

by the air as it expands from a volume of 0.015 m3 to a volume of 0.027 m

3 at a constant

pressure of 2.0 105 Pa. (b) Determine the final pressure of the air if it starts from the same

initial conditions as in (a) and expanding by the same amount, the change occurs (i)

isothermally, (ii) adiabatically. (Given for air is 1.40)

4. A vessel contains an ideal gas of volume 2.0 cm3 at pressure 100 kPa and temperature 25 C.

The gas expands adiabatically until the volume becomes 4.0 cm3. After that, it is compressed

isothermally until the volume becomes 3.0 cm3. (a) Calculate the pressure and the

temperature of the gas in the final condition. (b) Sketch and label a graph of gas pressure (P)

against gas volume (V) to show how the pressure and volume changes when the condition of

the gas changes from the initial condition to final condition. (Given for gas is 1.67)

5. A quantity of ideal gas whose ratio of molar heat capacities is 5/3 has a temperature of 300

K, volume of 64 103 m

3 and pressure of 243 kPa. It is made to undergo the following three

changes in order:

1: adiabatic compression to a volume 27 103 m

3,

2 : isothermal expansion to 64 103 m

3 ,

3 : a return to its original state.


FAKULTI SAINS

JABATAN FIZIK

2

(a) Calculate the pressure on completion of process 1 and the temperature at which the

process 2 occurs. (b) Describe the process 3, (c) Sketch and label a graph of pressure against

volume for the changes described.

6. Air enters a nozzle steadily at 2.21 kg/m3 and 40 m/s and leaves at 0.762 kg/m

3 and 180 m/s.

If the inlet area of the nozzle is 90 cm2, determine (a) the mass flow rate through the nozzle,

and (b) the exit area of the nozzle. Answers: (a) 0.796 kg/s (b) 58 cm2

7. A pump increases the water pressure from 70 kPa at the inlet to 700 kPa at the outlet. Water

enters this pump at 15oC through a 1 cm diameter opening and exits through a 1.5 cm

diameter opening. Determine the velocity of the water at the inlet and outlet when the mass

flow rate through the pump is 0.5 kg/s. Will these velocities change significantly if the inlet

temperature is raised to 40°C?

FIGURE 2 8. A hair dryer is basically a duct of constant diameter in which a few layers of electric resistors

are placed. A small fan pulls the air in and forces it through the resistors where it is heated. If

the density of air is 1.20 kg/m3 at the inlet and 1.05 kg/m

3 at the exit, determine the percent

increase in the velocity of air as it flows through the dryer.

9. Refrigerant-134a enters a 28-cm diameter pipe steadily at 200 kPa and 20°C with a velocity

of 5 m/s. The refrigerant gains heat as it flows and leaves the pipe at 180 kPa and 40°C.

Determine (a) the volume flow rate of the refrigerant at the inlet, (b) the mass flow rate of the

refrigerant, and (c) the velocity and volume flow rate at the exit.

10. Air flows steadily in a pipe at 300 kPa, 77oC, and 25 m/s at a rate of 18 kg/min. Determine

(a) the diameter of the pipe, (b) the rate of flow energy, (c) the rate of energy transport by

mass, and (d) the error involved in part (c) if the kinetic energy is neglected.

11. A water pump increases the water pressure from 75 kPa to 350 kPa. Determine the flow

work, in kJ/kg, required by the pump.

12. Air at 4.18 kg/m3 enters a nozzle that has an inlet-to exit area ratio of 2:1 with a velocity of

120 m/s and leaves with a velocity of 380 m/s. Determine the density of air at the exit.

Answer: 2.64 kg/m3

13. Steam at 3 MPa and 400°C enters an adiabatic nozzle steadily with a velocity of 40 m/s and

leaves at 2.5 MPa and 300 m/s. Determine (a) the exit temperature and (b) the ratio of the

inlet to exit area A1/A2.

14. Air enters a gas turbine at 1000 kPa and 350°C and leaves at 100 kPa and 40°C. Determine

the inlet and outlet volume flow rates when the mass flow rate through this turbine is 2 kg/s.

15. A heat exchanger is to cool ethylene glycol (cp = 2.56 kJ/kg.oC) flowing at a rate of 2 kg/s

from 80°C to 40°C by water (cp = 4.18 kJ/kg.oC) that enters at 20°C and leaves at 55°C.

Determine (a) the rate of heat transfer and (b) the mass flow rate of water.

Tutorial 5:1


ANSWER 1.

In reality the amount of heat rejected - be lower (lost to the surrounding air) through the pipes and other components.

2.

3.

4.

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 5:2

5.

6.

7.

8.

9.

Tutorial 5:3

10.

11.

12.

(a)

(b)

Tutorial 6:1

Tutorial-6: CARNOT CYCLE, PRINCIPLE & HEAT ENGINE SSP2113: Thermodynamic

1.

2.

3.

4.

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 6:2

5.

the claim is FALSE

6.

7.

8.

Tutorial 6:3

9.

10.

11.

12.

Tutorial 7:1


1. Assumptions

1 This is a steady-flow process since there is no change with time.

2 Kinetic and potentialenergy changes are negligible.

3 Air is an ideal gas.

4 The process involves no internal irreversibilitiessuch as friction, and thus it is an isothermal, internally

reversible process.

2.

entropy - increased, transfer of heat - possible 3.

violates the increase in entropy principle the entropy is decreasing

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 7:2

4.

rate is positive (i.e., the entropy increases as time passes),this transfer of heat is possible

5.

net rate of entropy change is zero as it must be in order to satisfy the second law

6.

heat pump is completely reversible

Tutorial 7:3

7.

8.

entropy increases, a refrigerator with COP = 4 is possible.

refrigerator can no longer be possible.

9.

positive-satisfies the increase in entropy principle

Tutorial 8:1


1.

2.

3.

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 8:2

4.

5.

6.

ΔU + Wb= ΔH

(a)

(b)

Tutorial 8:3

7.

8. (a)

(b)

(c)

9.

Tutorial 8:4

10.

.

11.

12.

Tutorial 8:5

13.

14.

Tutorial 9:1


1.

The minimum number of windmills

2. Potential energy it possesses, Exergy = PE = mgh

3. (a) The reversible power

(b) The irreversibility rate

(c) The second law efficiency is determined from its definition,

4. Air:

The entropy change

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 9:2

The air’s specific volumes at the given state and dead state

The specific closed system exergy of the air is then

The total exergy available, Φ = m = (1.730 kg)(83.06 kJ/kg) = 144 kJ

Helium:

helium system has a greater potential for the production of work

5. Ideal-gas entropy change relation,

Tutorial 9:3

6. (a)

(b)

7. (a)

from Table A-17,

(b)

Tutorial 9:4

Alternative

8.

minimum power input - for compression process.

9. (a)

Tutorial 9:5

(b)

10. (a) The mass flow rate

The power input

the actual power

(b) The given isothermal efficiency

(c) An energy balance

The mass flow rate

11. (a)

Tutorial 9:6

An energy balance

(b) The specific exergy changes

The exergy destruction

(c) The second-law efficiency

,

12.

entropy balance

entropy generation

X destroyed = ToSgen= (278 K)(7.098 kJ/K) = 1973 kJ

Tutorial 10:1

Tutorial – 10 : GAS POWER CYCLES SSP2113: Thermodynamic 1. maximum efficiency

efficiency of 55 percent is possible.

2. (a)

(b)

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 10:2

3. (a)

(b)

(c)

4. (a)

Tutorial 10:3

(b)

5. (a)

(b)

Tutorial 10:4

6.

7. (a)

(b)

(c)

(d)

8.

Tutorial 10:5

9.

10. (a)

(b)

(c)

(d)

11. (a)

Tutorial 10:6

(b)

(c)

(d)

(e)

Tutorial 10:7

12.

13.

14.

Tutorial 11:1


1.

(a)

TH

= 30°C = 303 K

TL

= Tsat @ 160 kPa

= -15.60°C = 257.4 K (Refer Table A-12),

COP -Carnot refrigerator

(b) Refer Table A-11,

(c) The net work input is determined from

2.

(a) Refer Table A-13;TH

= Tsat @ 0.6 MPa

= 21.55°C = 294.6 K and TL

= Tsat @ 0.2 MPa

= -10.09°C = 262.9 K.

(b) Process 4-1 : isentropic

(c) s

3= s

g @ 0.6 MPa= 0.92177 kJ/kg·K,

ANSWER


FAKULTI SAINS

JABATAN FIZIK

Tutorial 11:2

3. Refer the refrigerant tables (Tables A-11, A-12, and A-13),

Mass flow rate

Power requirement

COP of the refrigerator

4. Refer refrigerant tables (Tables A-12 and A-13),

Rate of heat removal

(b) Rate of heat rejection

(c) COP of the refrigerator

Tutorial 11:3

5. (a) The properties of refrigerant-134a are (Tables A-11 through A-13)

The isentropic efficiency

(b) The rate of heat

(c) The power input and the COP

(d) The ideal vapor-compression cycle

Tutorial 11:4

6. From the air table (Table A-17),

Then the rate of refrigeration

(b) The net power input

(c) The COP

7. (a) From the isentropic relations,

(b) The COP

(c) The mass flow rate

Tutorial 11:5

8.

(a) the isentropic relations,

The temperature at state 4

T4 = 281.3 K.

energy balance on the regenerator

effectiveness of the regenerator

(b) The refrigeration load

(c)

(d)

Tutorial 11:6

9.

10.

The mass flow rate

The rate of heat addition to the cycle

The rate of heat rejection

11.

claim is possible, but not probable.

Tutorial 11:7

12. (a)

(b)

(c)

13.

14. (a)

(b)

(c)

Tutorial 11:8

15. (a)

(b)

(c)

sem4 termo tuto tsh

Education