An ideal gas is in thermodynamic equilibrium. The number of degrees...

As we know, internal energy of one mole of the gas ${U}_{n} = \dfrac{nRT}{2}$.

Clearly, ${U}_{n} ∝ n$, where $n$ is degree of freedom. Therefore, as $n$ increases, ${U}_{n}$ also increases.

Now, speed of sound in gas

${v}_{n} = \sqrt{\dfrac{\gammaRT}{M}} = \sqrt{\dfrac{\left(1 + \dfrac{2}{n}\right)RT}{M}}$

Clearly, as $n$ increases and ${v}_{n}$ decreases.

Hence,

${U}_{7} > {U}_{5}$ and ${U}_{7} > {U}_{6}$

and ${v}_{5} > {v}_{7}$.