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Question

# Consider two containers A and B containing gases at the same pressure, volume and temperature. The gas in container A is compressed to half of its original volume isothermally while the gas in container B is compressed to half of its original volume adiabatically. The ratio of final pressure of gas in B to that of gas in A is

A
2γ1
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B
(12)γ1
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C
(11γ)2
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D
1γ1
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Solution

## The correct option is A 2γ−1Given data: PA1=PB1;VB1=VA1;TA1=TB2 Let the final pressure of gas in A be PA2 and gas in B be PB2. For isothermal compression of gas in A, PA1VA1=PA2VA2 PA2=PA1VA1VA2=PA1VA1VA1/2=2PA1 For adiabatic compression of gas in B, PB2VγB1=PB2VγB2 PB2=PB1(VB1VB2)γ=PB12γ So, PB2PA2=PB12γ2PA1=2γ−1

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