Q112 / 180 · NEET 2014 · Physics

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

A
$64 P$
B
$32 P$
Correct answer
C
$P / 64$
D
$16 P$

Solution

Isothermally

P V = P_{1} 2 V

P_{1} = \frac{P}{2}

Adiabatically

\frac{P}{2} {(2 V)}^{γ} = P_{f} {(16 V)}^{γ}

P_{f} = \frac{P}{2} {(\frac{1}{2^{3}})}^{\frac{5}{3}}

P_{f} = \frac{P}{2} {(\frac{1}{2^{3}})}^{\frac{5}{3}} = \frac{P}{(2) {(2)}^{5}}

P_{f} = \frac{p}{64}

Hence, the correct answer is option: 'C'.

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