Question

At ntp the density of gas is 1.3kg/m3 and velocity of sound propagation in the gas is 330

Answer 1

your question is incomplete . A complete question is ​-----> How many degrees of freedom do the molecules of a gas have if the density at ntp is 1.3 kg/m³ and velocity of sound is 330 m/s ?


solution : use the formula, $\nu=\sqrt{\frac{(i+2)P}{i\rho}}$

where v is velocity of sound , i is degree of freedom, P is atmospheric pressure and $\rho$ is density of gas.

now, $v^2=\frac{(i+2)P}{i\rho}$

or, $v^2i\rho=iP+2P$

or, $i(v^2\rho-P)=2P$

or, $i=\frac{2P}{v^2\rho-P}$

hence, i = (2 × 10^5)/(330 × 330 × 1.3 - 10^5) ≈ 5

hence, degree of freedom is 5