Question

$1$ mole of a gas with $\gamma = \frac{7}{5}$ is mixed with $1$ mole of gas with $\gamma = \frac{5}{3}$, the value of $\gamma$ of the resulting mixture of

• A. $\frac{7}{5}$
• B. $\frac{2}{5}$
• C. $\frac{3}{2}$
• D. $\frac{12}{7}$

Answer 1

Answer: (C)

$\frac{3}{2}$

Answer 2

$C_{v \, mixture} = \frac{\frac{5}{2} R + \frac{3}{2} R}{2}$ = 2R $C_{p \, mixture} =$ 2R + R = 2R $\gamma_{mixture} = \frac{C_p \, mixture}{C_v \, mixture} = \frac{3}{2}$