Number of degrees of freedom of a gas A are higher compared to that of gas B at the same temperature. It means

Difficult

A

It is relatively more difficult to compress the gas B adiabatically
B

At a given temperature, RMS velocity of gas A is more
C

If gases are mixed, then number of degrees of freedom of mixture is equal to sum of number of degrees of freedom of the two gases
D

Dalton’s law of partial pressure may only be applicable for gas A

Solution

In adiabatic process, $P V^{γ} = c o n s \tan t$
But $γ = 1 + \frac{2}{f}$ .
As f is high, $γ$ is low.
Adiabatic Bulk modulus (which gives measure of elasticity of gas in adiabatic process) = $B_{A D I A} = γ P$ .
If $γ$ is low, $B_{A D I A}$ also low. It is easier to compress the gas A. Option (A) is correct.
RMS velocity only depends on temperature and molar mass. Option (B) is wrong.
$f_{M I X T U R E} = \frac{f_{1} n_{1} + f_{2} n_{2}}{n_{1} + n_{2}}$ . Option (C) is wrong.
Dalton’s law is true for all gases. Option (D) is wrong.

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