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Question

Two cylinders A and B are fitted with pistons. A and B contain equal moles of an ideal monoatomic gas at 400 K. Piston in A is free to move, while piston in B is held fixed. Same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 42 K, then the increase in the temperature of the gas in B is (γ=53):

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

The correct option is B 70 K
In the first case, energy supplied is equal to the change in enthalpy since pressure is constant, while in the second case, it is equal to the change in internal energy since the volume is constant.

Q1=nCPΔT=nγγ1RΔT1

Q2=nCPΔT=n1γ1RΔT2

Hence, γΔT1=ΔT2

Now, ΔT1=42 K, so ΔT2=70 K

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