IDEAL AND REAL GASES 379dharm
\M-therm\Th8-1.pm5The magnitude of this constant depends upon the particular gas and it is denoted by R,
where R is called the specific gas constant. Then
pv
T = R
The equation of the state for a perfect gas is thus given by the equation
pv = RT ...(8.6)
or for m kg, occupying V m^3 ,
pV = mRT ...(8.7)
If the mass is chosen to be numerically equal to the molecular weight of the gas then 1 mole
of the gas has been considered, i.e., 1 kg mole of oxygen is 32 kg oxygen, or 1 kg mole of hydrogen
is 2 kg hydrogen.
The equation may be written as
pV 0 = MRT ...(8.8)
where V 0 = Molar volume, and
M = Molecular weight of the gas.
Avogadro discovered that V 0 is the same for all gases at the same pressure and temperature
and therefore it may be seen that MR = a constant ; R 0 and thus
pV 0 = R 0 T ...(8.9)
R 0 is called the molar or universal gas constant and its value is 8.3143 kJ/kg mol K.
If there are n moles present then the ideal gas equation may be written as
pV = nR 0 T ...(8.10)
where V is the volume occupied by n moles at pressure p and temperature T.
8.3. p-V-T Surface of an Ideal Gas
The equation of state of an ideal gas is a relationship
between the variables pressure (p), volume (V) and tempera-
ture (T). On plotting these variables along three mutually
perpendiculars axes, we get a surface which represents the
equation of state (pv = RT). Such a surface is called p-v-T
surface. These surfaces represent the fundamental proper-
ties of a substance and provide a tool to study the thermo-
dynamic properties and processes of that substance. Fig. 8.4
shows a portion of a p-v-T surface for an ideal gas. Each
point on this surface represents an equilibrium state and a
line on the surface represents a process. The Fig. 8.4 also
shows the constant pressure, constant volume and constant
temperature lines.
8.4. Internal Energy and Enthalpy of a Perfect Gas
Joule’s Law. Joule’s law states that the specific internal energy of a gas depends only on
the temperature of the gas and is independent of both pressure and volume.
i.e., u = f(T)
Fig. 8.4