A monoatomic gas is enclosed in a nonconducting cylinder having a piston which can move freely. Suddenly gas is compressed to `1//8` of its initial volume. Find the final pressure and temperature if initial pressure and temperature are `P_(0)` and `T_(0)` respectively.

Explanation

Since process is adiabatic therefore
`P _(0) V ^(5/3) =P _("total") ((V)/(8))^(5//3)`
`T_(f)` (hence `gamma = (C _(P))/(C _(V))= (5R)/(2) //(3R)/(2)= 5/3`
Since process is adiabatic therefore.
`T _(1) V_(1) ^(gamma -1) =T_(2) V ^(2) ^(gamma -1)`
`implies T_(0) V _(0) ^(2//3) = T _("final")((V_(0))/(8)) ^(2//3) impliesT =4T_(0)`