Two cylinders A and B fitted with pistons contain equal amount of an ideal 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 of heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder B is 63 K then the rise in temperature of the gas in A is

Step-by-step solution

For cylinder A, the piston is free to move, so the process is isobaric. The heat supplied is Q_A = n C_P T_A . For cylinder B, the piston is fixed, so the process is isochoric. The heat supplied is Q_B = n C_V T_B . Given that the same amount of heat is supplied to both cylinders, Q_A = Q_B . n C_P T_A = n C_V T_B T_A = C_V C_P T_B For an ideal diatomic gas, the molar heat capacity at constant volume is C_V = 5 2 R and at constant pressure is C_P = 7 2 R . C_V C_P = 5 7 Substituting T_B = 63 K: T_A = 5 7 63 = 45 K