A mass of ideal gas at pressure P is expanded isothermally to four times the original volume and then slowly compressed adiabatically to its original volume. Assuming γ to be 1.5, the new pressure of gas is
A
2P
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B
P
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C
4P
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D
P2
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Solution
The correct option is A2P Let P and V be the initial pressure and volume of ideal gas. After isothermal expansion, pressure is P/4. So volume is 4V. Let P1 be the pressure after adiabatic compression then P1Vγ=(P/4)(4V)γ P1=(P4)(4)3/2=2P