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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 16V. The final pressure of the gas is: (Take γ=53)


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Solution

Step 1: Given

Pressure is P.

Volume is V.

After isothermal expansion, the volume is 2V.

After adiabatic expansion, volume is 16 V.

Pressure after the isothermal expansion is P' (say).

Pressure after the adiabatic expansion is Pf (say).

Step 2: Formula Used

For isothermal expansion: PV=constant

For adiabatic expansion: PVγ=constant

Step 3: Solution:

Find P' using the formula PV=constant

PV=P'2VP=2P'P'=P2

Find P' using the formula PVγ=constant

P'2Vγ=Pf16VγP22V53=Pf16V53Pf=P2V538V53Pf=P212353Pf=P26=P64

Hence, the final pressure is P64.


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