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)

A
64 P
B
32 P
C
P / 64
D
16 P

Solution:

$First, isothermal expansion$

$P V = P^{'} (2 V)$

(For isothermal process, PV = constant)

$P^{'} = \frac{P}{2}$

Then, adiabatic expansion

$P^{'} (2 V)^{γ} = P_{f} (16 V)^{γ}$

$(For adiabatic process, P V^{γ} = constant)$

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

$P_{f} = \frac{P}{2} {(\frac{2 V}{16 V})}^{5 / 3} = \frac{P}{2} {(\frac{1}{8})}^{5 / 3} = \frac{P}{2} {(\frac{1}{2^{3}})}^{5 / 3} = \frac{P}{2} (\frac{1}{2^{5}}) = \frac{P}{64}$

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)

Solution:

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