Question

The velocity of sound in Chlorine gas is 220 m/s. Find the velocity of sound in oxygen , if the molecular weight of chlorine and oxygen are 72 and 32 respectively.

Answer 1

Speed of sound in an ideal gas :

$v=\sqrt{\frac{\gamma\ R\ T}{M}}=\sqrt{\frac{\gamma\ P}{\rho}}=\sqrt{\frac{\gamma\ k_B\ T}{m}}$

        γ = ratio of specific heats = 1.4 for diatomic gases. = same for both gases.
         T = absolute temperature = constant for this case.
         R universal gas constant.
         M = molar mass of the gas.
         k_B = Boltzmann's constant
         m = mass of a molecule of gas.

$\frac{v_{oxygen}}{v_{chlorine}}=\sqrt{\frac{M_{chlorine}}{M_{oxygen}}}\\\\=\sqrt{\frac{72}{32}}=\frac{3}{2}\\\\v_{oxygen}=220\ m/s * \frac{3}{2}=330\ m/s$