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Question

An ideal gas of volume V and pressure P expands isothermally to volume 16V and is then compressed adiabatically to volume V. The final pressure of the gas is :-
[Take γ=1.5]

A
P
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B
3P
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C
4P
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D
6P
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Solution

The correct option is C 4P
Initially, ideal gas undergoes isothermal expansion.
For an isothermal process, temperature remains constant
i.e P1V1=P2V2
From the data given in the question,
PV=16V×P
P=P16 ......(1)
Later, gas undergoes adibatic compression to come back to initial volume V.
Let the final pressure be P′′.
The equation of state in terms of P and V is given by
P2Vγ2=P′′Vγ1
From the data given in the question, we get
P×(16V)1.5=P′′×(V)1.5 (P2=P and V2=16V)
P16×(16V)1.5=P′′×(V)1.5
P′′=4P
Thus, option (c) is the correct answer.

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