Determine the work done on the gas on the right hand side,

Question

A cylinder closed at both ends is thermally insulated from the surroundings. It contains a movable, thermally insulated, frictionless and leak proof piston. Initially the pressure, volume and temperature on each side of the piston are P₀, V­₀, and T₀. The number of moles of gas on each side is n.  Heat is now slowly supplied to the gas on the left side of the piston by an electric heating coil. As a result the gas on the left-hand side expands and displaces the piston, compressing the gas on the right-hand side until its pressure reaches (27/8) P₀. If the ratio of specific heats is 1.5 and the molecular weight of the gas is M, determine, in terms of n, C_v, M and T₀

(i) the work done on the gas on the right hand side,

(ii) the final temperature of the gas on the right hand side,

(iii) the final temperature of the gas on the left hand side

(iv) the heat supplied to the gas on the left hand side.

         All assumptions made must be clearly stated.