A cylinder with a movable piston contains 3 moles of hydrogen at constant temperature and pressrue. The walls of a cylinder are made up of a heat insulator and the piston is insulated by having a pile of sand on it By what factor does the pressure of a gas increases if the gas is compressed to half its original volume ?

Explanation

Since the process is adiabatic
`P_(1)V_(1)^(gamma) = P_(2) V_(2)^(gamma) , (P_(2))/(P_(1)) = (V_(1)^(gamma))/(V_(2)^(gamma)) = ((V_(1))/(V_(2)))^(gamma)`
But `(V_(1))/(V_(2)) = (2)/(1) =2`
`gamma = (7)/(5 )` for hydrogen.
`:. ` Factory by which pressure of the gas increases
`(P_(2))/(P_(1)) = ((2)/(1))^((-7)/(5)) -= (2) ^((7)/(5))`