thermodynamics tutorial example

8/12/2019 Thermodynamics Tutorial Example

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EG-210 Tutor ial Sheet No. 1 (2014)

Ideal and Non-Ideal Process Systems

Please complete and hand-in Question 4 by 3pm Monday 24thFebruary 2014.

1) I have some ethylene gas at a pressure 10 MPa and a temperature of 47C. Calculate;

a) The specific volume, (V/m), in m3/kg, using the ideal gas model:PV = mRT.[4 marks]

b) The specific volume via the non-ideal gas function:PV = ZmRT.[5 marks]

c) Using the non-ideal gas function, what pressure is required in order that the ethylenehave a specific volume of 0.0062 m3/kg at a temperature of 47C.

[8 marks]

d) Using the non-ideal gas function, what will be the temperature of ethylene when it hasa specific volume of 0.01 m3/kg and a pressure of 10 MPa[8 marks]

Supplied Data: R= 0.29637 kJ / kg K for ethylene

T(K) = T(C) + 273

Data Sheet No. 2.1 Table of Critical Constants of Gases.

Data Sheet No. 2.2 Generalized Compressibility Factor Plot.

2) Calculate the molar volume, = V/n, (m3/kmol) of a mixture of gases containing 59.39

mol% CO2and 40.61 mol% methane (CH4) at 310.94 K and 86.19 bar ab pressure using:

a) The ideal gas law equation:PV= nRT[3 marks]

b) Van der Waals equation:2

a

b

RTP m

m

where 2jjiim ayaya , jjiim bybyb and

i

i

C

C

iP

TRa

64

2722

,i

i

C

C

i

P

RTb

8

[10 marks]

c) Psuedo-crictical constants (Kays Rule) and the compressibility factor chart.[10 marks]

d) The measured specific volume is 0.2205 m3/kmol. What is the percentage deviation ofeach model from the real value?

[2 marks]

Supplied Data: Data Sheet No. 2.1 Table of Critical Constants of Gases.

Data Sheet No. 2.2 Generalized Compressibility Factor Plot.

Universal Gas Constant:R= 8.314 kJ kmol-1K-1

1 bar = 1 105Pa


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3) In the soft drinks industry, there is considerable demand for food grade carbon dioxide for

product carbonation. The carbon dioxide is supplied as a gas at low pressure, and the first

step in the production process of the food grade carbon dioxide is to pressurize the carbon

dioxide gas.

Accordingly, estimate the work (Win kJ per kmol) required to compress 1.0 kmol CO2fromP1= 14.7 psia to P2= 4042.5 psia in a compressor unit operating reversibly with inter-stage

cooling so that the gas temperature is constant at T = 61.6 C, using the following

mathematical models:

a) An ideal gas, such that:

1

2ln

P

PnRTW

[4 marks]

b) A non-ideal gas, such that the compressibility factor, Z, has to be used to

evaluate the actual CO2volumes of V1and V2for:

2

1ln

V

VnRTW

[10 marks]

Existing compressors indicate that the actual compressibility factor for the carbon dioxide

over this range of system pressures isZ= 0.72.

c) Hence, comment on how the predicted Zvalues obtained in part (b) relate to

this actualZvalue.

[4 marks]

d) When the carbon dioxide gas flow to the suction inlet of the compressor is

1020 m3h-1 (at T= 61.6 C and P1= 14.7 psia) and the compressor has an

operational efficiency of 35%, specify the total power rating (in kW) of the

compressor motor.

[7 marks]

Supplied Data: Data Sheet No. 2.1 Table of Critical Constants of Gases.

Data Sheet No. 2.2 Generalized Compressibility Factor Plot

Universal Gas Constant:R= 8.314 kJ kmol-1K-1

1 bar = 1 105Pa = 14.5 psi

T(K) = T(C) + 273


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4) Hydrogen is under consideration as an alternative fuel to petrol in vehicles. High pressure

hydrogen tanks make it possible for the hybrid vehicle to travel further distances on a single

tank of fuel. A typical tank will contain 4.5 kg of hydrogen stored at a pressure of 35 MPa. If

the average temperature for storage is 20 C calculate the volume of the tank required (in

litres) using the following mathematical models, namely:

(a) The Ideal Gas Law:

nRTPV

[3 marks]

(b) The Van der Waals Equation, namely:

TRbvva

P w2w -

where

C

2

C

2

wP64

TR27a

andC

CwP8

TRb

with TCbeing the critical temperature of hydrogen, PC the critical pressure of

hydrogen and n/Vv , the molar volume of hydrogen (Vis the volume and n

the number of kmols).

[6 marks]

(c) The Non-ideal Gas function, namely:

ZnRTPV

whereZis the generalised compressibility factor.

[9 marks]

(d) The Department of Energy are aiming for the storage tank size to be 62 litres

by 2015. Using the non-ideal gas function calculate the temperature at which

the hydrogen needs to be stored assuming the pressure remains the same. What

implication does this have for hydrogen powered vehicles?

[7 marks]

Data Supplied:

1 Pa = 1 N m-2= 1 10-5bar

R= 8.314 kJ / kmol K

T(K) = T(C) + 273

Data Sheet No. 2.1 Table of Critical Constants of Gases.

Data Sheet No. 3 Generalized Compressibility Factor Plot for the high pressure range.


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Data Sheet No. 2.1: Table of Critical Constants of Gases.

Substance Formula Molar Mass

kg/kmol

TC

K

PC

MPa

Air - 28.97 132.5 3.77

Ammonia NH3 17.03 405.5 11.28Argon Ar 39.948 151 4.86

Benzene C6H6 78.115 562 4.92

Bromine Br2 159.808 584 10.34

n-Butane C4H10 58.124 425.2 3.80

Carbon dioxide CO2 44.01 304.2 7.39

Carbon monoxide CO 28.011 133 3.50

Carbon tetrachloride CCl4 153.82 556.4 4.56

Chlorine Cl2 70.906 417 7.71

Chloroform CHCl3 119.38 536.6 5.47

Dichlorodifluoromethane (R-12) CCl2F2 120.91 384.7 4.01

Dichlorofluoromethane (R-21) CHCl2F 102.92 451.7 5.17

Ethane C2H6 30.070 305.5 4.48

Ethyl alcohol C2H5OH 46.07 516 6.38

Ethylene C2H4 28.054 282.4 5.12

Helium He 4.003 5.3 0.23

n-Hexane C6H14 86.179 507.9 3.03

Hydrogen (normal) H2 2.016 33.3 1.30

Krypton Kr 83.80 209.4 5.50

Methane CH4 16.043 191.1 4.64

Methyl alcohol CH3OH 32.042 513.2 7.95

Methyl chloride CH3Cl 50.488 416.3 6.68Neon Ne 20.183 44.5 2.73

Nitrogen N2 28.013 126.2 3.39

Nitrous oxide N2O 44.013 309.7 7.27

Oxygen O2 31.999 154.8 5.08

Propane C3H8 44.097 370 4.26

Propylene C3H6 42.081 365 4.62

Sulfur dioxide SO2 64.063 430.7 7.88

Tetrafluoroethane (R-34a) CF3CH2F 102.03 374.2 4.059

Trichlorofluoromethane (R-11) CCl3F 137.37 471.2 4.38

Water H2O 18.015 647.1 22.06

Xenon Xe 131.30 289.8 5.88


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Data Sheet No. 2.2 a: Dimensionless Plot of the Generalized Compressibility Factor (Z)

versus Reduced Pressure (Pr) and Reduced Temperature (Tr).


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Data Sheet No. 2.2 b: Dimensionless Plot of the Generalized Compressibility Factor (Z)

versus Reduced Pressure (Pr) and Reduced Temperature (Tr).


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Data Sheet No. 3: Generalized Compressibility Factor (Z) versus Reduced Pressure (P r)

and Reduced Temperature (Tr) for the high pressure range.

thermodynamics tutorial example

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