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Question

Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300K. Piston of A is free to move and piston of B is fixed. Same amount of heat is given to the gases in two cylinders. Temperature of the gas in cylinder A increases by 30K. Then, increase in temperature of the gas in the cylinder B is:
(γ=1.4 for diatomic gas)

A
36 K
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B
54 K
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C
42 K
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D
24 K
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Solution

The correct option is B 42 K
Since the piston of A is free to move, the pressure inside the cylinder A remains the same. Thus, for given heat H to the system,
H=nCPΔT1
The piston in cylinder B is fixed. Thus volume remains constant.
H=nCVΔT2
ΔT2ΔT1=CPCV
=1.4
ΔT2=42 K


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