Two cylinders fitted with pistons contains 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 gas in B is

Q: Two cylinders fitted with pistons contains 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 gas in B is
(a) 30 K
(b) 18 K
(c) 50 K
(d) 42 K
Solution :(d)
In cylinder A heat is supplied at constant pressure while in cylinder B heat is supplied at constan volume.
(ΔQ)A = nCP (ΔT)A and (ΔQ)B = nCV (ΔT)B
Given that  (ΔQ)A = (ΔQ)B
(ΔT)B = Cp/Cv(ΔT)A
= (1.4) (30)        (Since Cp/Cv = 1.4)
= 42 K

Author: Rajesh Jha

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