The volume of an ideal gas `(gamma = 1.5 )` is changed adiabatically from 4.00 liters to 3.00 liters . Find the ratio of (a) the final pressure to the initial pressure and (b) the final temperature to the initial temperature.

Explanation

`gamma=1.5`
Since it is an adiabatic process,
So, `PV^(gamma) =constant`.
(a) `P_1V_1^(gamma) = P_2V_2^(gamma)`
Given, `V_1 = 4L`, `V_2 = 3L`, `(P_2)/(P_1)=?`
implies`P_2/P_1=((V_1)/(V_2))^gamma`
`=(4/3)^(15)=1.5396=1.54`
(b) `TV^(gamma-1) =Constant`
`T_1V_1^(gamma-1) = T_2V_2^(gamma-1)`
implies ` T_2/T_1=((V_1)/(V_2))^(gamma-1)=((4)/(3))^(0.5)=1.154`.