If c is r.m.s speed of molecules in a gas and `upsilon` is the speed of sound waves in the gas, show that `c//upsilon` is contant and independent of temperature for all diatomic gases.

Explanation

From kinetic theory of gases, `p=(1)/(3)rhoc^(2)`, where c is rms speed of molecules of gas
`c=sqrt((3P)/(rho))` …(i)
and speed of sound in the gas is `upsilon=sqrt((gammaP)/(rho))` …(ii)
`(c)/(upsilon)=sqrt((3P)/(rho)xx(rho)/(gammaP))=sqrt((3)/(gamma))` ...(iii)
As `gamma` is constant and independent of temp. `:. (c) /(upsilon)=` constant and independent of temp.
For diatomic gases,`gamma=1.4`
`:. (c)/(upsilon)=sqrt((3)/(1.4))=1.46=a` constant.