A gas consisting of rigid diatomic molecules (degrees of freedom r = 5) under standard conditions `(P_(0) = 10^(5)` Pa and `T_(0) = 273 K`) was compressed adiabatically `eta = 5` times. Find the mean kinetic energy of a rotating molecule in the final state.

Explanation

In an adiabatic expansion,
`TV^(gamma-1)=` constant
`T_(0)V^(gamma-1)=T((V)/(5))^(gamma-1) gamma=1+(2)/(5)`
`therefore T=(273).(5)^(2//5)`
`lt(KE)_("rotational")gt` `= kT`
`=1.38xx10^(-23)xx273xx(5)^(2//5)`
`=7xx10^(-21)J` (approx).