Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K . The piston of A is free to move, while that of 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 A is 30 K , then the rise in temperature of the gas in B is.

Step-by-step solution

A is free to move; therefore, heat will be supplied at constant pressure. ∆ Q A = n C P A ∆ T A ...(I) B is held fixed, therefore, heat will be supplied at constant volume. ∆ Q B = n C V B ∆ T B ...(ii) But ∆ Q A = ∆ Q B nC P A ∆ T A = nC v B ∆ T B ∆ T B = C P C V ∆ T A = γ ∆ T A ( γ = 1.4   (diatomic) ( Δ T A   =   30   K ) = 1.4 3 0 K ∆ T B = 4 2 K