A cylindrical container is divided into three parts by two tight fitting pistons. The pistons are connected by a spring. The region between the pistons is vacuum and the other two parts have same number of moles of an ideal gas. Initially, both the gas chambers are at temperature `T_(0)` and the spring is compressed by 1 m. Length of both gas chambers is 1 m in this position. Now the temperature of the left and right chambers are raised to `(4T_(0))/(3)` and `(5T_(0))/(3)` respectively. Find the final compression in the spring in equilibrium. Assume that the pistons slide without friction

Answer

`(sqrt(13)-1)/(2)m`