Question

At NTP the density of a gas is $1.3kg/m^3$ and the velocity of sound propagation in the gas is $330$m/s. The degree of freedom of the gas molecule is

• A. $3$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is B $5$

Given,

$P={10}^{5}N/m^2$

$\rho =1.3kg/m^3$

$v=330m/s$

Let consider $i=$ degree of freedom

The velocity of sound propagation in the gas is given by

$v=\sqrt{\frac{(i+2)P}{i\rho }}$

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

$330\times 330=\frac{(i+2)\times {10}^5}{1.3i}$

$\frac{(i+2)}{i}=\frac{330\times 330\times 1.3}{{10}^5}=1.4175$

$\frac{2}{i}=1.4-1=0.4175$

$i=\frac{2}{0.4175}$

$i=5$

The correct option is B.