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Question

Two cylinders A and B fitted with pistons contain an equal number of moles of an ideal monoatomic gas at 400K. The piston of A is free to move while that of B is held fixed. The same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in A is 42K, the rise in temperature of the gas in B is

A
21K
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B
35K
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C
42K
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D
70K
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Solution

The correct option is C 42K
From first law of thermodynamics
Q=ΔU+W
For cylinder A pressure remains constant
Work done by a system
W=μRγ1T1T2
For monatomic gases
μ=1
γ=53
W=1×R5442400=32R×42
or W=63R
But Δ=0, for cylider A
Q=0+63R
Q=63R
For cylinder B Volume is constant,
W=0
and Q=μCvΔT
For mono atomic gas
CV=32R
Q=1×32RΔT
As heat given to both cylinder is game
63R=32RΔT
Δ=42K

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