In ideal gas is enclosed in an adiabatic container having cross section `A = 27 cm^(2)` for a part of it and `(A)/(2)` for remaining part. Pistons `P_(1)` and `P_(2)` can move freely without friction along the inner wall. In the position shown in the figure the spring attached to the piston `P_(1)` is relaxed. Sprig constant the spring is `K = 3700 N//m`. Piston `P_(2)` is pushed up gradually through a distance `(H)/(2)` and its was observed that the piston `P_(1)` goes up by `(3H)/(32)` . Take `gamma = 1.5`, mass of piston `P_(1) = 13.5 kg` and atmospheric pressure `P_(0) = 1 xx 10^(5) N//m^(2)`
(a) Find H.
(b) Find final temperature of the gas if its initial temperature is 300 K.

Answer

`(a) 16/15 m" " 400 K`