A cylinder of cross-section area. A has two pistons of negligible mass separated by distances l loaded with spring of negligible mass. An ideal gas at temperature `T_(1)` is in the cylinder where the springs are relaxed. When the gas is heated by some means its temperature becomes `T_(2)` and the springs get compressed by `(l)/(2)` each . if `P_(0)` is atmospheric pressure and spring constant k=`(2P_(0)A)/(l)`, then find the ratio of `T_(2)` and `T_(1)` .

Answer

4

Explanation

`(P_(1)V_(1))/(T_(1)) = (P_(2)V_(2))/(T_(2)` where `V_(1) = lA` and `V_(2) = 2lA` and `P_(1)=P_(0)` and `P_(2)= (kx)/(A) + P_(0) =2P_(0) implies (T_(2))/(T_(1)) = (P_(2)V_(2)/(P_(1)V_(1)) = 4`