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
Therefore,
`T_(0) V^(gamma -1) = T ((V)/(eta))^(gamma -1) implies T = T_(0) eta^(gamma -1) = T_(0) eta^(2//r) ( :' gamma = 1 + (2)/(r ))`
`ltlt epsilon gtgt_(rot) = kT = kT_(0) eta^(2//r)`
`=1.38 xx 10^(-23) xx 273 xx 5^(2//5)`
`7 xx 10^(-21) J`