Problem

A gaseous mixture enclosed in a vessel consists of one gram mole of a gas A with

\gamma = \left(\frac{5}{3}\right)

and some amount of gas B with

\gamma = \frac{7}{5}

at a temperature

T

. The gases A and B do not react with each other and are assumed to be ideal. Find the number of gram moles of the gas B if

\gamma

for the gaseous mixture is

\left(\frac{19}{13}\right)