Question

If one mole of a monoatomic gas $(\gamma =5/3)$ is mixed with one mole of a diatomic gas $(\gamma =7/5)$, the value of $\gamma$ for the mixture is A
If A is written as (x + 0.5), then x is

Answer 1

As we know,

$C_v=\frac{3}{2}RT;C_p=\frac{5}{2}RT$ for monoatomic gas;

$C_v=\frac{5}{2}RT;C_p=\frac{7}{2}RT$ for diatomic gas

Thus, for mixture of 1 mole each,

$C_v=\frac{\frac{3}{2}RT+\frac{5}{2}RT}{2}=2RT$ and $C_p=\frac{\frac{5}{2}RT+\frac{7}{2}RT}{2}=3RT$

Therefore, $C_p/C_v=\frac{3RT}{2RT}=1.5$