Chapter 3
Calculation of Changes in Internal Energy,
Enthalpy, and Entropy
In the previous chapter, general expressions for calculating changes in internal energy, enthalpy,
and entropy are developed. These expressions contain partial derivatives involving temperature,
pressure, and molar volume. The purpose of this chapter is to show how to evaluate these
derivatives in a systematic manner.
3.1 EQUATIONS OF STATE
Any mathematical relationship between temperature, pressure, and molar volume is called an
equation of state
,i
.e
.
,
f
(
T,P,
e
V
)=0
(3.1-1)
Equations of state can be expressed either in pressure-explicit form
P
=
P
(
T,
e
V
)
(3.1-2)
or, in volume-explicit form
e
V
=
e
V
(
T,P
)
(3.1-3)
Besides, an equation of state can also be expressed in terms of the dimensionless
compressibility
factor
,
Z
,as
Z
=
P
e
V
RT
(3.1-4)
3.1.1 Ideal Gas Equation of State
Theequat
iono
fstateforanidea
lgasisg
ivenby
P
e
V
=
RT
(3.1-5)
Since
Z
=1
for an ideal gas, the compressibility factor shows the deviation from ideal behavior.
The ideal gas model is dependent on the following assumptions
•
Molecules occupy no volume,
•
Collisions of the molecules are totally elastic, i.e., energy of the molecules before a collision is
equal to the energy of the molecules after a collision. In other words, there are no interactions
between the molecules.
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