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Q.

monoatomic gas at a pressure P having a volume V expands isothermally to a volume 2V and then adiabatically to a volume 16V. Then the final pressure of the gas is $(γ = \frac{5}{3})$

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a

16 P

b

64 P

c

32 P

d

$\frac{P}{64}$

answer is C.

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Detailed Solution

Isothermal $\to P_{1} V_{1} = P_{2} V_{2}$

$P V = P_{2} \times 2 V$

$P_{2} = P / 2$

$P_{1} V_{1}^{r} = P_{2} V_{2}^{2}$

$(\frac{P}{2}) (2 V)^{5 / 3} = P_{2} (16 V)^{5 / 3}$

$P_{2} = \frac{P}{64}$

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monoatomic gas at a pressure P having a volume V expands isothermally to a volume 2V and then adiabatically to a volume 16V. Then the final pressure of the gas is γ=53