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Question

Two identical cylinders A and B with frictionless pistons contain the same ideal gas at same temperature and the same volume V. The mass of gas A is mA and that of B is mB. The gas in each cylinder is allowed to expand isothermally to the same final volume 2V. The change in the pressure in A and B are found to be ΔP and 1.5ΔP respectively. Then

A
4mA = 9mB
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B
3mA = 3mB
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C
3mA = 2mB
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D
9mA = 4mB
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Solution

The correct option is D 3mA = 2mB
Since the process is isothermal, T will be constant.

From the gas laws we know that,

PV=nRT

P=nRTV

In container A,

dP=P1P2

dP=naRTVnaRT2V

dP=naRT2V

dP=mART2MV ..................... (1)

In container B,

1.5dP=P1P2

1.5dP=nbRTVnbRT2V

1.5dP=nbRT2V

1.5dP=mBRT2MV ..................... (2)

Dividing both the eqn we get,

1.5dPdP=(mBRT2MV)(mART2MV)

mBmA=1.5=32

3mA=2mB

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