Question

1 mole of a gas with $\gamma =7/5$ is mixed with 1 mole of a gas with $\gamma =5/3$ then the value of $\gamma$ for resulting mixture is

• A. $7/5$
• B. $2/5$
• C. $24/16$
• D. $12/7$

Answer 1

Answer: (C)

$24/16$

The specific heats are given by:

$C_p=\frac{\gamma R}{\gamma -1}$

$C_v=\frac{R}{\gamma -1}$

For gas A:

$C_p=\frac{7}{2}R$

$C_v=\frac{5}{2}R$

For gas B:

$C_p=\frac{5}{2}R$

$C_v=\frac{3}{2}R$

Now upon mixing equal volume of two gases:

Effective $C_p=\frac{C_{p1}+C_{p2}}{2}=\frac{12}{2}R$

Effective $C_v=\frac{C_{v1}+C_{v2}}{2}=\frac{8}{2}R$

New $\gamma =\frac{C_p}{C_v}=\frac{12}{8}=\frac{24}{16}$

Option C is correct.