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Q.

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

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a

30 K

b

18 K

c

50 K

d

42 K

answer is D.

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Detailed Solution

In both cylinders A and B, the gases are diatomic (γ=1.4).Piston A is free to move i.e. it is isobaric process. Piston B is fixed i.e. it is isochoric process. If same amount of heat OQ is given to both, then Qisobaric =Qisochoric ⇒μCP(ΔT)A=μCν(ΔT)B⇒ (ΔT)B=CpCv(ΔT)A=γ(ΔT)A=1.4×30=42K

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