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Question

# A mass of diatomic gas (γ=1.4) at a pressure of 2 atm is compressed adiabatically so that its temperature rise from 27oC to 927oC. The pressure of the gas is final state is

A
28 atm
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B
68.7 atm
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C
256 atm
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D
8 atm
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Solution

## The correct option is D 256 atmPVγ= constant T1=273+27=300KP(TP)γ= constant T2=273+927=1200KP1−γTγ= constant⇒P1−γ1Tγ1=P1−γ2Tγ2⇒21−1.4(300)1.4=P1−1.42⋅(1200)1.4⇒(P2P1)1−γ=(T1T2)γ⇒P2P1=(T1T2)γ1−γ(P1P2)1−γ=(T2T1)γ(P1P2)1−1.4=(1200300)1.4(P1P2)−0.4=(4)1.4(P2P1)0.4=41.4P2=P14(1.4/0.4)=P14(7/2)=P1(27)=2×128=256

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