Question

If one mole each of a monoatomic and diatomic gases are mixed at low temperature then $C_p/C_v$ ratio for the mixture is :

• A. $1.40$
• B. $1.70$
• C. $1.50$
• D. $1.33$

Answer 1

The correct option is C $1.50$

For monotomic gas,
$C_V=\frac{3}{2}R$
$C_p=\frac{5}{2}R$
For a diatomic gas,
$C_V=\frac{5}{2}R$
$C_p=\frac{7}{2}R$

Thus for mixture of $1$ mole each,
$C_v=\frac{\frac{3}{2}RT+\frac{5}{2}RT}{2}$
and $C_P=\frac{\frac{5}{2}RT+\frac{7}{2}RT}{2}$
Thus, $\frac{C_P}{C_v}=\frac{3RT}{2RT}=1.5$