Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300K. 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 30K, then rise in temperature of the gas in B is
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For cylinder A (free piston, constant pressure process): ΔQ = nCpΔTA. For cylinder B (fixed piston, constant volume process): ΔQ = nCvΔTB. Since the same heat ΔQ is added, nCpΔTA = nCvΔTB. For a diatomic gas, Cp = 7R/2 and Cv = 5R/2. Substituting: (7R/2)(30) = (5R/2)ΔTB. Solving gives ΔTB = 42K.
Final Answer: 42K