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 16V. The final pressure of the gas is :(take $γ$ = 5/3)

Moderate

A

64 P
B

32 P
C

$\frac{P}{64}$
D

16 P

Solution

For isothermal process $P_{1} V_{1} = P_{2} V_{2}$
$\Rightarrow PV = P_{2} (2 V) \Rightarrow P_{2} = \frac{P}{2}$
For a adiabatic process $P_{2} V_{2}^{γ} = P_{3} V_{3}^{γ}$
$\Rightarrow (\frac{P}{2}) {(2 V)}^{γ} = P_{3} {(16 V)}^{γ} \Rightarrow P_{3} = \frac{3}{2} {(\frac{1}{8})}^{\frac{5}{3}} = \frac{P}{64}$

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