Page 192 - Advanced Thermodynamics for Engineers, Second Edition

9.2 STATE EQUATION FOR IDEAL GASES 179

Table 9.2 Values of the Universal Gas
Constant, <, in Various Units
8314 J/kmol K
1.985 kcal/kmol K
1.985 Btu/lb-mol K
1.985 CHU/lb-mol R
2782 ft lb f /lb-mol K
1545 ft lb f /lb-mol R

Hence, any other gas, b, at the same pressure and temperature will occupy the same volume as gas
a, i.e.
pv m
¼ m w a a ¼ m w b b ¼ .m w i i ¼ . ¼<: (9.5)
R
R
R
T
If a system contains an amount of substance n a of gas, a, then Eqn (9.5) may be written
pV m ¼ n a m wa R a T ¼ n a <T: (9.6)
R
It can be seen that for ideal gases the product m w i i is the same for all gases: it is called the
universal gas constant, <. The values of the universal gas constant, <, together with its various units
are shown in Table 9.2.

9.2.1 IDEAL GAS EQUATION
The evaluation of the properties of an ideal gas will now be considered. It has been shown that
the internal energy and enthalpy of an ideal gas are not functions of the volume or pressure,
and hence these properties are simply functions of temperature alone. This means that the
specific heats at constant volume and constant pressure are not partial derivatives of temper-
ature, but can be written

vu du
c v ¼ ¼
vT dT
v
(9.7)

vh dh
c p ¼ ¼ :
vT dT
p
Also, if c v and c p in molar quantities are denoted by c v,m and c p,m then, for ideal and perfect gases
c p;m c v;m ¼<: (9.8)
It is possible to evaluate the properties of substances in terms of unit mass (specific
properties) or unit amount of substance (molar properties). The former will be denoted by lower
case letters (e.g. v, u, h, g, etc.), and the latter will be denoted by lower case letters and a suffix m