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_("final") ((V)/(8))^(5//3) [gamma = (C_(P))/(C_(V)) =(5R)/(2)l(3R)/(2) =(5)/(3)]`
`P_("final") = 32 P_(0)`.
Since process is adiabatic therefore
`T_(1)V_(1)^(gamma-1) = T_(2)V_(2)^(gamma-1) rArr T_(0) V_(0)^(2//3) =T_("final") ((V_(0))/(8))^(2//3)`
`rArr T = 4T_(0)`