Q.

A monoatomic gas at a pressure P, having a volume V expands isothermally to a volume 2V and then adiabatically to a volume 16 V. The final pressure of the gas is (Take γ = 5/3)

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a

64 P

b

32 P

c

P / 64

d

16 P

answer is C.

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Detailed Solution

First, isothermal expansion PV=P′(2V)(For isothermal process, PV = constant)P′=P2Then, adiabatic expansionP′(2V)γ=Pf(16V)γ (For adiabatic process, PVγ= constant )P2(2V)5/3=Pf(16V)5/3Pf=P22V16V5/3=P2185/3=P21235/3=P2125=P64
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A monoatomic gas at a pressure P, having a volume V expands isothermally to a volume 2V and then adiabatically to a volume 16 V. The final pressure of the gas is (Take γ = 5/3)