Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

674 | Thermodynamics

and

Then the enthalpy and entropy changes of oxygen during this process are

determined by substituting the values above into Eqs. 12–58 and 12–63,

and

Discussion Note that the ideal-gas assumption would underestimate the

enthalpy change of the oxygen by 2.7 percent and the entropy change by

11.4 percent.

3.70 kJ/kmol # K

3.28 kJ>kmol # K  1 8.314 kJ>kmol # K 21 0.200.25 2

s 2 s 1  1 s 2 s 12 idealRu 1 Zs 2 Zs 12

2396 kJ/kmol

2332 kJ>kmol  1 8.314 kJ>kmol # K 23 154.8 K 1 0.480.53 24

h 2 h 1  1 h 2 h 12 idealRuTcr 1 Zh 2 Zh 12

TR 2 

T 2

Tcr



300 K

154.8 K

1.94

PR 2 

P 2

Pcr



10 MPa

5.08 MPa

1.97

∂Zh 2 0.48, Zs 2 0.20

Some thermodynamic properties can be measured directly, but
many others cannot. Therefore, it is necessary to develop
some relations between these two groups so that the properties
that cannot be measured directly can be evaluated. The deriva-
tions are based on the fact that properties are point functions,
and the state of a simple, compressible system is completely
specified by any two independent, intensive properties.
The equations that relate the partial derivatives of proper-
ties P,v,T, and sof a simple compressible substance to each
other are called the Maxwell relations. They are obtained
from the four Gibbs equations,expressed as

dgs dTv dP

das dTP dv

dhT dsv dP

duT dsP dv

SUMMARY

The Maxwell relationsare

The Clapeyron equationenables us to determine the enthalpy

change associated with a phase change from a knowledge of

P,v, and Tdata alone. It is expressed as

a

dP

dT

b

sat



hfg

T vfg

a

0 s

0 P

b

T

a

0 v

0 T

b

P

a

0 s

0 v

b

T

a

0 P

0 T

b

v

a

0 T

0 P

b

s

a

0 v

0 s

b

P

a

0 T

0 v

b

s

a

0 P

0 s

b

v