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

The Clapeyron equation can be simplified for liquid–vapor and solid–vapor

phase changes by utilizing some approximations. At low pressures vg vf,

and thus vfg
vg. By treating the vapor as an ideal gas, we have vgRT/P.

Substituting these approximations into Eq. 12–22, we find

or

For small temperature intervals hfgcan be treated as a constant at some aver-

age value. Then integrating this equation between two saturation states yields

(12–24)

This equation is called the Clapeyron–Clausius equation,and it can be

used to determine the variation of saturation pressure with temperature. It

can also be used in the solid–vapor region by replacing hfg by hig (the

enthalpy of sublimation) of the substance.

lna

P 2

P 1

b

sat

hfg

R

a

1

T 1



1

T 2

b

sat

a

dP

P

b

sat



hfg

R

a

dT

T^2

b

sat

a

dP

dT

b

sat



Phfg

RT^2

660 | Thermodynamics

where, from Table A–11,

since 
T(°C) 
T(K). Substituting, we get

The tabulated value of hfgat 20°C is 182.27 kJ/kg. The small difference

between the two values is due to the approximation used in determining the

slope of the saturation curve at 20°C.

182.40 kJ/kg

hfg 1 293.15 K 21 0.035153 m^3 >kg 21 17.70 kPa>K2a

1 kJ

1 kPa#m^3

b



646.18504.58 kPa

8°C

17.70 kPa>K

a

dP

d T

b

sat,20°C

a

¢P

¢T

b

sat,20°C



Psat @ 24°CPsat @ 16°C

24°C16°C

vfg 1 vgvf (^2) @ 20°C0.0359690.00081610.035153 m^3 >kg
EXAMPLE 12–6 Extrapolating Tabular Data
with the Clapeyron Equation
Estimate the saturation pressure of refrigerant-134a at 50°F, using the
data available in the refrigerant tables.
Solution The saturation pressure of refrigerant-134a is to be determined
using other tabulated data.
Analysis Table A–11E lists saturation data at temperatures 40°F and
above. Therefore, we should either resort to other sources or use extrapolation