Question

An ideal gas of volume $V$ and pressure $P$ expands isothermally to volume $16\, V$ and then compressed adiabatically to volume $V$. The final pressure of gas is $[\gamma=1.5]$

• A. P
• B. 3P
• C. 4P
• D. 6P

Answer 1

Answer: (C)

Isothermal expansion
$P_{1} V_{1}=P_{2} V_{2} $
$P V=16 V \times P' $
$\frac{P}{16}=P' $
$P_{1} V_{1}^{\gamma}=P_{2} V_{2}^{\gamma} $
[adiabatic compression]
$P(16 V)^{1.5}=P''(V)^{1.5} $
$\frac{P}{16} \times 16^{1.5}=P''=4 P$