Question

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $\frac{\alpha^2}{4}$ RJ/mol k; then the value of α will be _______.
(Assume that the given diatomic gas has no vibrational mode).

Answer 1

$C_V = \frac{f}{2}R$
Total degree of freedoms
$= 1 × 3 + 3 × 5 = 18$
$\frac{\alpha^2}{4} = \frac{18}{2n} = \frac{18}{2 \times 4}$
$⇒ α^2 = 9$
$α = 3$
So, the answer is 3.