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Q.

Two identical vessels A and B with frictionless pistons contain the same ideal gas at the same temperature and the same volume V. The masses of gas in A and B are mA and mB respectively. The gases are allowed to expand isothermally to the same final volume 3 V. The change in pressure of the gas in A and B are found to be ∆P and 1.5 ∆P respectively. Then

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a

9mA=4mB

b

3mA=2mB

c

2mA=3mB

d

4mA=9mB

answer is C.

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Detailed Solution

At constant temperature PV = constant dP=−PdVV and dVV= constant ∴dP∝P….. (1)  from PV=mMRT⇒P=mRTMV⇒P∝m …..(2) from (1) and (2)  dP∝m
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Two identical vessels A and B with frictionless pistons contain the same ideal gas at the same temperature and the same volume V. The masses of gas in A and B are mA and mB respectively. The gases are allowed to expand isothermally to the same final volume 3 V. The change in pressure of the gas in A and B are found to be ∆P and 1.5 ∆P respectively. Then