13-49
13-72 Heat is transferred to a gas mixture contained in a piston cylinder device. The initial state and the final temperature
are given. The heat transfer is to be determined for the ideal gas and non-ideal gas cases.
Properties The molar masses of H2 and N2 are 2.0, and 28.0 kg/kmol. (Table A-1).
Analysis From the energy balance relation,
E in  E out  E
Qin  Wb,out  U

Qin  H  H H 2  H N 2  N H 2 h2  h1
H
2

 N N 2 h2  h1
N
2
since Wb and U combine into H for quasi-equilibrium constant pressure processes
NH2 
NN2 
mH 2
MH 2
mN 2
MN 2

6 kg
 3 kmol
2 kg / kmol

21 kg
 0.75 kmol
28 kg / kmol
6 kg H2
21 kg N2
5 MPa
160 K
Q
(a) Assuming ideal gas behavior, the inlet and exit enthalpies of H2 and N2 are determined from the ideal gas tables to be
Thus,
H2 :
h1  [email protected] K  4,535.4 kJ / kmol,
N2 :
h1  [email protected] K  4,648 kJ / kmol,
h2  [email protected] 200 K  5,669.2 kJ / kmol
h2  [email protected] 200 K  5,810 kJ / kmol
Qideal  3  5,669.2  4,535.4   0.75  5,810  4,648  4273 kJ
(b) Using Amagat's law and the generalized enthalpy departure chart, the enthalpy change of each gas is determined to be
T R1 ,H 2 
H 2:
Tm,1
Tcr,H 2
PR1 ,H 2  PR2 ,H 2
T R2 ,H 2 
Tm , 2
Tcr,H 2



 Z h1  0
Pm
5



 3.846 
Pcr,H 2 1.30
Zh  0
 2
200


 6.006

33.3


160
 4.805
33.3
(Fig. A-29)
Thus H2 can be treated as an ideal gas during this process.
T R1 , N 2 
N 2:
Tm,1
Tcr, N 2
PR1 , N 2  PR2 , N 2
T R2 , N 2 
Tm , 2
Tcr, N 2



 Z h1  1.3
Pm
5



 1.47 
Pcr, N 2 3.39
 Z h  0.7
 2
200


 1.58

126.2


160
 1.27
126.2
(Fig. A-29)
Therefore,
h2  h1 H  h2  h1 H ,ideal  5,669.2  4,535.4  1,133.8kJ/kmol
2
h2  h1 N
2
2

 
 Ru Tcr Z h1  Z h2  h2  h1
ideal
 (8.314kPa  m 3 /kmol  K)(126.2K)(1.3  0.7)  (5,810  4,648)kJ/kmol  1,791.5kJ/kmol
Substituting,
Qin  3 kmol1,133.8 kJ/kmol  0.75 kmol1,791.5 kJ/kmol  4745 kJ
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are given. The heat transfer is to be determined for... and N are 2.0, and 28.0 kg/kmol. (Table A-1).