Page 209 - Advanced thermodynamics for engineers

9.4 MIXTURES OF IDEAL GASES 195

_
Mean specific heat, c

_
c ( )
_ T
c ( )
T
Enthalpy
Enthalpy at T at T

T = 0 T Temperature, T

FIGURE 9.1
Mean specific heat at constant pressure.

If the change of internal energy, u 2 u 1 , is known then the change of enthalpy, h 2 h 1 ,may be
calculated in a similar way. The use of mean specific heat values enables more accurate evaluation of
temperature changes because the mean specific heats enable the energy equation to be solved with
an allowance for the variation of specific heats. The mean specific heats approach is depicted in Fig. 9.1.

9.4 MIXTURES OF IDEAL GASES
Many problems encountered in engineering involve mixtures of gases – air itself is a mixture of many
gases although it can be considered to be oxygen and atmospheric nitrogen (which can be assumed to
contain the nitrogen in the air and the other ‘inert’ gases such as argon and carbon dioxide). If the gases
in a mixture are at a temperature well above their critical temperature and a pressure below the critical
pressure they act as ideal gases. Expressions relating the properties of mixtures of ideal gases will now
be formulated. These expressions are a direct consequence of the Gibbs–Dalton laws.

9.4.1 DALTON PRINCIPLE
Dalton stated that
any gas is as a vacuum to any gas mixed with it.

This statement was expanded and clarified by Gibbs to give the Gibbs–Dalton laws.
9.4.2 GIBBS–DALTON LAW

1. A gas mixture as a whole obeys the equation of state (Eqn (9.2))

pV ¼ n<T
where n is the total amount of substance in mixture.