Answer:

We know that the equation for molecules is:

$ c=\sqrt{\frac{3RT}{M}} $

Where, M represents the molar mass of the gas

$ v=\sqrt{\frac{\gamma P}{\rho }}=\sqrt{\frac{\gamma RT}{M}} $

We know that, $ PV=nRT $

$ n=1 $

$ \gamma =\frac{{{C}_{p}}}{{{C}_{v}}} $

$ \frac{c}{v}=\frac{\sqrt{\frac{3RT}{M}}}{\sqrt{\frac{\gamma RT}{M}}} $

$ \frac{c}{v}=\sqrt{\frac{3}{7/5}}=\sqrt{\frac{15}{7}} $

which is a constant.