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

EXAMPLE 12–4 Verification of the Maxwell Relations

Verify the validity of the last Maxwell relation (Eq. 12–19) for steam at

250°C and 300 kPa.

Solution The validity of the last Maxwell relation is to be verified for steam

at a specified state.

Analysis The last Maxwell relation states that for a simple compressible

substance, the change in entropy with pressure at constant temperature is

equal to the negative of the change in specific volume with temperature at

constant pressure.

If we had explicit analytical relations for the entropy and specific volume

of steam in terms of other properties, we could easily verify this by perform-

ing the indicated derivations. However, all we have for steam are tables of

properties listed at certain intervals. Therefore, the only course we can take

to solve this problem is to replace the differential quantities in Eq. 12–19

with corresponding finite quantities, using property values from the tables

(Table A–6 in this case) at or about the specified state.

T

?



T250°C

?


 P300 kPa

T250°C

?


 P300 kPa

?




0.00165 m^3 /kg K 
0.00159 m^3 /kg K

since kJ kPa · m^3 and K °C for temperature differences. The two values

are within 4 percent of each other. This difference is due to replacing the

differential quantities by relatively large finite quantities. Based on the close

agreement between the two values, the steam seems to satisfy Eq. 12–19 at

the specified state.

Discussion This example shows that the entropy change of a simple com-

pressible system during an isothermal process can be determined from a

knowledge of the easily measurable properties P, v, and Talone.

(0.875350.71643) m^3 kg

(300200)°C

(7.38047.7100) kJkg#K

(400200) kPa

c

v300°Cv200°C

 (300200)°Cd

s400 kPas200 kPa

(400200) kPa

a

0 v

0 T


s b


P

a

0 v

0 T

b

 P

s

P

12–3 ■ THE CLAPEYRON EQUATION

The Maxwell relations have far-reaching implications in thermodynamics

and are frequently used to derive useful thermodynamic relations. The

Clapeyron equation is one such relation, and it enables us to determine the

enthalpy change associated with a phase change (such as the enthalpy of

vaporization hfg) from a knowledge of P,v, and Tdata alone.

Consider the third Maxwell relation, Eq. 12–18:

During a phase-change process, the pressure is the saturation pressure,

which depends on the temperature only and is independent of the specific

a

0 P

0 T

b

v

a

0 s

0 v

b

T

658 | Thermodynamics