4-54
4-102 Methane is heated in a rigid container. The final pressure of the methane is to be determined using
the ideal gas equation and the Benedict-Webb-Rubin equation of state.
Analysis (a) From the ideal gas equation of state,
P2
P1
T2
T1
(100 kPa)
673 K
293 K
Methane
100 kPa
229.7 kPa
20qC
The specific molar volume of the methane is
v1 v 2
Ru T1
P1
(8.314 kPa ˜ m 3 /kmol ˜ K)(293 K)
100 kPa
Q
24.36 m 3 /kmol
(b) The specific molar volume of the methane is
v1 v 2
Ru T1
P1
(8.314 kPa ˜ m 3 /kmol ˜ K)(293 K)
100 kPa
24.36 m 3 /kmol
Using the coefficients of Table 4-4 for methane and the given data, the Benedict-Webb-Rubin equation of
state for state 2 gives
RuT2
P2
v2
§
J ·
C · 1 bR T a aD
c §
¨¨ B0 RuT2 A0 02 ¸¸ 2 u 23
6 3 2 ¨1 2 ¸ exp(J / v 2 )
v
v
v
v
v
T
T
©
¹
2 ¹
2
©
(8.314)(673) §¨
2.286 u106 ·¸ 1
0.003380u 8.314 u 673 5.00
0.04260 u 8.314 u 673 187.91 2
2
¨
¸
24.36
673
24.363
©
¹ 24.36
5.00 u 1.244 u104
2.578 u105 § 0.0060 ·
2
¨1 ¸ exp(0.0060 / 24.36 )
24.366
24.363 (673)2 © 24.362 ¹
229.8 kPa
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