First slide

Different type of processes

Question

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)

Moderate

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
$P^{'} (2 V)^{γ} = P_{f} (16 V)^{γ}$
$(For adiabatic process, P V^{γ} = constant)$
$\frac{P}{2} (2 V)^{5 / 3} = P_{f} (16 V)^{5 / 3}$
$P_{f} = \frac{P}{2} {(\frac{2 V}{16 V})}^{5 / 3} = \frac{P}{2} {(\frac{1}{8})}^{5 / 3} = \frac{P}{2} {(\frac{1}{2^{3}})}^{5 / 3} = \frac{P}{2} (\frac{1}{2^{5}}) = \frac{P}{64}$

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