Two cylinders A and B fitted with piston contain equal amount of an ideal diatomic gas at temperature T K. The piston of cylinder A is free to move while that of cylinder B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise of temperature of the gas in A is dT _ A , then the rise in temperature of the gas in B is ( = C _ p C _ v )

Step-by-step solution

Given: Two identical cylinders containing ideal diatomic gas at temperature T , one with free piston (constant pressure), the other with fixed piston (constant volume). Both receive equal heat dQ . The temperature rise in cylinder A (isobaric process) satisfies dQ = n C_p dT_A . For cylinder B (isochoric process), dQ = n C_v dT_B . Equating and simplifying: n C_p dT_A = n C_v dT_B yields dT_B = C_p C_v dT_A = dT_A . Result: The temperature rise in cylinder B is times that in cylinder A.