Question

N moles of a polyatomic gas (f = 6) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N is :

(1) 6

(2) 3

(3) 4

(4) 2

Answer 1

The correct option is (3) 4.

\(\gamma _{mix} = \frac{n_1f_1+n_2f_2}{n_1+n_2} = \frac{6N+2\times 3}{N+2}\)

Degree of freedom of diatomic is 5.

So, \(5 = \frac{6N + 6}{N + 2}\)

\(\Rightarrow 5N + 10 = 6N + 6\)

\(\Rightarrow N = 4\)