An adiabatic cylinder has length 2 L and cross sectional area A. A freely moving non conducting piston of negligible thickness divides the cylinder into two equal parts. The piston is connected to the right face of the cylinder with an ideal spring of force constant k. The right chamber contains 28 g nitrogen in which one third of the molecules are dissociated into atoms. The left chamber container 4 g helium. With piston in equilibrium and spring relaxed the pressure in both chamber is `P_(0)`. The helium chamber is slowly given heat using an electric heater (H), till the piston moves to right by a distance `(3L)/(4)`. Neglect the volume occupied by the spring and the heating coil. Also neglect heat capacity of the spring. (a) Find the ratio of `C_(P)` and `C_(V)` for nitrogen gas in right chamber. (b) Calculate change in temperature of helium. (c) Calculate heat supplied by the heater.