IF n is the number of degrees of freedom of the molecules of an ideal gas, show that the ratio `C_p/C_v` is `1+2/n`.

Explanation

Average kinetic energy of a gas molecule
`=n.1/2kT`(k=Boltzmann constant )
As the molecules have no potential energy the total interval energy of 1 mol of a gas is
`E=N_0n.1/2kT=n/2N_0kT=n/2RT` [`N_0k=R`, where `N_0`= Avagadro number)
`thereforeC_v=(dE)/(dT)=n/2Rand C_p=C_v+R=(n/2+1)R`, [for ideal gas]
Then, `C_p/C_v=(n/2+1)/(n/2)=1+2/n`