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 the process is adiabatic, therefore
`P_(0) V^((5)/(3)) = P_(fi nal) ((V)/(8))^(5//3) implies gamma = (C_(P))/(C_(V)) = (5R)/(2) // (3R)/(2) = (5)/(3)`
`P_(fi nal) = 32 P_(0)`
Since the process is adiabatic, therefore
`T_(1) V_(1)^(gamma - 1) = T_(2) V_(2)^(gamma - 1) implies T_(0) V_(0)^(2//3) = T_(fi nal) ((V_(0))/(8))^(2//3)`
`implies T = 4 T_(0)`