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:

detailed solution

Correct option is C

in first case heat is supplied at constant pressure ∴QA=nCpΔT1And in second case heat is supplied at constant volume∴QB=nCvΔT2here n = number of moles of gasCP = specific heat of gas at constant pressure Cv=specific heat of gas at constant volume ∆T=change in temperatureQB=QA    as amount of heat given is samenCvΔT2=nCpΔT1For ΔT2=CρCv.ΔT1substitute specific heat ratio for diatomic gas =7/5ΔT2=75.30=42 K=rise in temperature of gas in B