Statistical Mechanics · Problem 1.15

Elements of Ensemble Theory — R. K. Pathria

Physics — Statistical Mechanics · adiabatic-exponent-ideal-gas-mixture

Problem

We have shown that the

P

V

relationship during a reversible adiabatic process in an ideal gas is governed by the exponent

\gamma

, such that

PV^\gamma = \text{const.}

Consider a mixture of two ideal gases, with mole fractions

f_1

and

f_2

and respective exponents

\gamma_1

and

\gamma_2

. Show that the effective exponent

\gamma

for the mixture is given by

\frac{1}{\gamma - 1} = \frac{f_1}{\gamma_1 - 1} + \frac{f_2}{\gamma_2 - 1}.