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221.


Problem 24.9 (RHK)


We have to estimate the frequency for which the wavelength of sound will be of the order of the mean free path in nitrogen at 1.02 atm pressure and temperature. We can take the diameter of the nitrogen molecule to be 315 pm.


Solution:           Click For PDF Version

Data of the problem are

and

Number density is given by


Mean free path will be

Velocity of sound is given in terms of thermodynamic quantities as

For nitrogen gas made up of molecules, the molar mass is

and as the nitrogen gas is diatomic

.

Therefore, the velocity of sound in the nitrogen gas at 291.16 K will be

Therefore, the frequency of sound for which the wavelength will be of the order of the mean free path will be