Question

At standard temperature and pressure the density of a gas is 1.3 gm/ m³ and the speed of the sound in gas is 330 m/sec. Then the degree of freedom of the gas will be

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (C)

5

Answer 2

Given velocity of sound $v_{s} = 330\frac{m}{\sec}$,

Density of gas $\rho = 1.3\frac{kg}{m^{3}}$,

Atomic pressure $P = 1.01 \times 10^{5}\frac{N}{m^{2}}$

Substituting these value in $v_{\text{sound}} = \sqrt{\frac{\gamma P}{\rho}}$ we get

$\gamma = 1.41$

Now from $\gamma = 1 + \frac{2}{f}$ we get $f = \frac{2}{\gamma - 1} = \frac{2}{1.4 - 1} = 5.$