Two cylinders A and B fitted with pistons contain equal amount of an ideal rigid diatomic gas at 303 K . The piston of cylinder A is free to move and that of cylinder B is held fixed. The same amount heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder B is 49 K , then the rise in temperature of the gas in A is

Step-by-step solution

Given a rigid diatomic ideal gas with initial temperature T = 303 K and molar specific heats C_v = 5 2 R and C_p = 7 2 R . For cylinder B under constant volume, W_B = 0 , so by the first law Q = U_B = nC_v T_B = n 5 2 R 49 . For cylinder A under constant pressure, Q_A = nC_p T_A = n 7 2 R T_A . Equating the heat supplied to both cylinders gives n 5 2 R 49 = n 7 2 R T_A . Simplifying, 5 49 = 7 T_A , so T_A = 5 49 7 = 35 . The temperature rise in cylinder A is 35 K .