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TOPIC 10- Thermodynamic (First Law )

Exercise 10 a

1. Fill in the boxes with suitable formula

Process w q ∆U= w + q ∆H= ∆U + ∆(PV) Etc.

Isobaric

Isochoric

Isothermal

reversible

Irreversible

(T not

constant, but

Tinitial =Tfinal )

Adiabatic

reversible

γ

γ

γ

1

1

21

1

1

2

1

2

−

−

=

=

P

P

V

V

T

T

v

p

C

C=γ , Cp,m-Cv,m =R

Adiabatic

irreversible

2. Classify each of the following properties as (a) intensive or extensive , and (b) state function or non state

function ?

(a) Properties Intensive or extensive (b) Properties State function or non

state function

• Mass

• V

• Cp

• Cp,m

• P

• T

• Molar mass

• Density

• w

• q

• Cv

• Cp

• U

• H

• n

• P

3. Find w, q, ∆U and ∆H if 4 mol of monatomic gas undergoes a constant-pressure expansion from 2 L to 5

L at 0.90 bar.

Process w q ∆U= w + q ∆H= ∆U + ∆(PV)

Isobaric

w = -P(V2-V1)

= -0.90bar(5-2)L

= -2.7(bar L)barL

J

0821.0

314.8× = -273.4 J.

Find T1 & T2

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4. Find w, q, ∆U and ∆H if 2 mol of He(g) with Cv,m=1.5R undergoes a reversible heating with P going

from 600 torr to 800 torr while V remains fixed at 30 dm3?

Process w q ∆U= w + q ∆H= ∆U + ∆(PV)

V remains

fixed

(Isochoric)

0

nR

VPT 11

1 = =144.24K. =2T 192.32K

J

KmolJKmol

TTRdTCnq

T

T

mv

2.1199

)08.48)(314.8)(5.1(2

))(5.1(2

11

2

1

12,

=

=

−==

−−

∫

5. Calculate w, q, ∆U and ∆H if 1.2 mol of a certain perfect gas, undergoes a reversible isothermal

compression at 25 oC from 40.0 L to 28.0 L.

Process w q ∆U ∆H

Isothermal

reversible 1

2lnV

VnRT−

= -(1.2 mol)(8.314 JK-1

mol-1

)(298K) ln

40

28

= +1060 J

? 0 0

6. An ideal monatomic gas at 298.15 K and 1 bar is expanded in a reversible adiabatic process to final

pressure of 0.5 bar. Calculate w, q, ∆U and ∆H (each per mole).

Process w q ∆U ∆H

Adiabatic

reversible

?

0

KKT

P

P

T

T

R

R

C

C

mv

mp

96.225)15.298(1

5.0

,667.12/3

2/5

4.0

2

1

1

2

1

2

,

,

=

=

====

−

γ

γ

γ

1

11

2

1

,

3.900

)19.72)(314.8)(5.1(

−

−−

−=

−==∆ ∫

molJ

KmolJKndTCnU

T

T

mv

?

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7. A tank contains 20 L of compressed nitrogen at 10 bar and 25 oC. Calculate w, q, ∆U and ∆H when the

gas is allowed to expand reversibly to 1 bar pressure adiabatically. (Cv,m= 20.811 JK-1

mol-1

)(Ans:-24.1

kJ,0,-24.1 kJ,-33.7 kJ)

8. One mole of an ideal gas expands from 5 to 1 kPa at 298 K. Calculate w and q for a reversible expansion

at constant temperature. (Ans.: -3988 J, +3988 J).

9. Two moles of gas at 100 Pa and 300 K are compressed by use of a constant pressure of 500 Pa. How

much work is done on the gas? (Ans.: +19.95 kJ)

10. A sample consisting of 2 mol of perfect-gas atoms (for which CV,m = 3/2R) is taken through the

cycle shown bellow. (a) Determine the temperature at the points 1, 2, and 3. (b) Calculate q, w, ∆U, and

∆H for each step and for the overall cycle.

Answer: P/atm V/L T/K Step w/kJ q/kJ ∆U/kJ ∆H/kJ

1

2

3

2.00

2.00

0.50

22.44

44.8

44.8

273.5

546.9

273.5

1→2

2→3

3→1

?

0

?

?

?

-w

w+q

qv

0

qp

?

0

Cycle (1→2→3→1) -ve +ve 0 0

11. The molar heat capacity of oxygen at constant pressure for temperatures in the range 300 to 400 K and for

low or moderate pressures can be approximated as Cp,m = a + bT, where a= 25.73 J mol-1

K-1

and b= 0.01297

J mol-1

K-2

. Calculate w, q, ∆U and ∆H when 2.00 mol of O2 is reversibly heated from 27 oC to 127

oC with

P held fixed at 1.00 atm. Assume perfect-gas behavior.(Ans.:-1.66 kJ, +6.05 kJ, +4.39 kJ, +6.05 kJ)

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Exercise 10 b (Objective questions)

1. Which of the following statements is FALSE?

A. w is positive when work is done on the system of interest.

B. w is negative when the system done work on the surroundings.

C. For a thermodynamic process of expansion, wrev < wirrev .

D. For a thermodynamic process of expansion, wrev > wirrev .

E. For a thermodynamic process of compression, wrev < wirrev .

2. Choose the INNCORRECT statement about heat, q.

A. It is a state function.

B. It is an extensive property.

C. The value of q is dependent of the process.

D. For every adiabatic process, q = 0.

E. q is an energy transfer between system and surroundings due to a temperature difference.

Choose the following answers for questions 3-4:

I. A closed system II. An open system

III. An isolated system IV. A system enclosed in adiabatic walls.

3. For which of these systems is/are the system’s matter can exchange with its

surroundings in every process:

A. I B. II C. III D. I & II E. None of the above

4. For which of these systems is/are the system’s energy conserved in every process:

A. I B. II C. III D. I & II E. None of the above

5. An ideal gas is heated slowly and expands reversibly at a constant pressure of P from

a volume of V1 to V2. What are the signs of w and q of the process?

A. +w, + q B. +w, - q C. -w, +q D. -w, - q E. The signs cannot determine.