Thermal Engineering Page 2
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44-88 The specific volume of steam is to be determined using the ideal gas relation, the
compressibility chart, and the steam tables. The errors involved in the first two
approaches are also to be determined.
Properties The gas constant, the critical pressure, and the critical temperature of water
are, from Table A-1,
3
R = 0.4615 kPa·m
/kg·K,
T
= 647.1 K,
P
= 22.06 MPa
cr
cr
Analysis (a) From the ideal gas equation of state,
⋅
⋅
3
(0.4615
kPa
m
/kg
K)(673
K)
RT
=
=
=
v
3
0.03106
m
/kg
(17.6%
error)
P
(10,000
kPa)
(b) From the compressibility chart (Fig. A-15),
⎫
10
MPa
P
=
=
=
P
0.453
⎪
H
O
R
⎪
2
P
22.06
MPa
cr
=
⎬
Z
. 0
84
10 MPa
673
K
T
⎪
=
=
=
T
1.04
⎪
R
⎭
T
647.1
K
400°C
cr
Thus,
=
=
=
v
v
3
3
0.02609
m
/kg
(1.2%
error)
Z
(0.84)(0.0
3106
m
/kg)
ideal
(c) From the superheated steam table (Table A-6),
}
=
P
10
MPa
=
v
3
0.02644
m
/kg
=
°
T
400
C
-97 Methane is heated at constant pressure. The final temperature is to be determined
using ideal gas equation and the compressibility charts.
Properties The gas constant, the critical pressure, and the critical temperature of methane
are, from Table A-1,
3
R = 0.5182 kPa·m
/kg·K,
T
= 191.1 K,
P
= 4.64 MPa
cr
cr
Analysis From the ideal gas equation,
v
=
=
=
2
T
T
(
300
K
)(
. 1
) 5
450
K
2
1
v
1
From the compressibility chart at the initial state (Fig. A-15),
⎫
Methane
T
300
K
=
=
=
1
Q
T
. 1
570
⎪
R
1
⎪
8 MPa
T
191.1
K
cr
=
=
v
⎬
Z
. 0
88
,
. 0
80
1
R
1
300
K
P
8
MPa
⎪
=
=
=
1
P
. 1
724
⎪
R
1
⎭
P
4.64
MPa
cr
At the final state,
=
=
⎫
P
P
. 1
724
=
R
2
R
1
⎬
Z
. 0
975
=
=
=
2
v
v
1
5 .
. 1
( 5
. 0
80
)
1
2 .
⎭
R
2
R
1
Thus,
v
v
T
P
P
8000
kPa
(1.2)(191.
1
K)
=
=
=
=
2
2
2
R
2
cr
T
406
K
2
Z
R
Z
P
0.975
4640
kPa
2
2
cr
Of these two results, the accuracy of the second result is limited by the accuracy with which the charts may
be read. Accepting the error associated with reading charts, the second temperature is the more accurate.
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