Question

One mole of ideal monoatomic gas $(v=5/3)$ is mixed with one mole of diatomic gas $(\gamma =7/5)$. What is $\gamma$ for the mixture? ($\gamma$ denotes the ratio of specific heat at constant pressure, to that at constant volume.)

• A. $3/2$
• B. $23/15$
• C. $35/23$
• D. $4/3$

Answer 1

The correct option is A $3/2$

For a monoatomic gas:

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

For a diatomic gas:

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

Thereofore $C_{v_{avg}}=\frac{\frac{3R}{2}+\frac{5R}{2}}{2}=2R$

Also $C_p=C_v+R$

$⟹C_{p_{avg}}=3R$
$⟹\gamma =\frac{C_{p_{avg}}}{C_{v_{avg}}}=\frac{3}{2}$