Question

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

Answer 1

Hey mate,

# Answer- f=5

# Given-

NTP

v(sound) = 330m/s

d = 1.3kg/m^3

# Solution-

At NTP, P=10^5 Pa

RMS velocity is given by,

v(rms) = √(3P/d)

v(rms) = √(3×10^5/1.3)

v(rms) = 480 m/s

To calculate degrees of freedom,

v(rms)/v(sound) = √[3f/(f+2)]

(480/330)^2 = 3f/(f+2)

f = 5

Hence, Degrees of freedom are 5.

Hope that helped...