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

vZRT/Pand simplifying Eq. 12–56, we can write the enthalpy departure
at any temperature Tand pressure Pas

The above equation can be generalized by expressing it in terms of the reduced
coordinates, using TTcrTRand PPcrPR. After some manipulations, the
enthalpy departure can be expressed in a nondimensionalized form as

(12–57)

where Zhis called the enthalpy departure factor.The integral in the above
equation can be performed graphically or numerically by employing data from
the compressibility charts for various values of PRand TR. The values of Zhare
presented in graphical form as a function of PRand TRin Fig. A–29. This
graph is called the generalized enthalpy departure chart,and it is used to
determine the deviation of the enthalpy of a gas at a given Pand Tfrom the
enthalpy of an ideal gas at the same T.By replacing h* by hidealfor clarity, Eq.
12–53 for the enthalpy change of a gas during a process 1-2 can be rewritten as

(12–58)

or

(12–59)

where the values of Zhare determined from the generalized enthalpy depar-
ture chart and (h

• 2 h
  
  
  • 1 )idealis determined from the ideal-gas tables. Notice
    that the last terms on the right-hand side are zero for an ideal gas.
  
  
  
  

Internal Energy Changes of Real Gases

The internal energy change of a real gas is determined by relating it to the
enthalpy change through the definition h

• u–Pv–u–ZRuT:

(12–60)

Entropy Changes of Real Gases

The entropy change of a real gas is determined by following an approach
similar to that used above for the enthalpy change. There is some difference
in derivation, however, owing to the dependence of the ideal-gas entropy on
pressure as well as the temperature.
The general relation for dswas expressed as (Eq. 12–41)

where P 1 ,T 1 and P 2 ,T 2 are the pressures and temperatures of the gas at the
initial and the final states, respectively. The thought that comes to mind at
this point is to perform the integrations in the previous equation first along a
T 1 constant line to zero pressure, then along the P0 line to T 2 , and

s 2 s 1 

T 2

T 1

cp

T

dT

P 2

P 1

a

0 v

0 T

b

P

dP

u 2 u 1  1 h 2 h 12 Ru 1 Z 2 T 2 Z 1 T 12

h 2 h 1  1 h 2 h 12 idealRTcr 1 Zh 2 Zh 12

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

Zh

1 hh (^2) T
RuTcr
T^2 R
PR
0
a
0 Z
0 TR
b
PR
d 1 ln PR 2
1 hh (^2) TRT^2 
P
0
a
0 Z
0 T
b
P
dP
P
Chapter 12 | 671