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 $\gamma =5/3)$

• A. 64P
• B. 32P
• C. P/64
• D. 16P

Answer 1

Answer: (C)

First, isothermal expansion
$PV=P^{\prime }(2V)$
(For isothermal process, $PV=$ constant)
$P^{\prime }=\frac{P}{2}$
Then, adiabatic expansion
$P^{\prime }(2V{)}^{\gamma }=P_f(16V{)}^{\gamma }$
(For adiabatic process, $P{V}^{\gamma }=$ constant)
$\frac{P}{2}(2V{)}^{5/3}=P_f(16V{)}^{5/3}$
$P_f=\frac{P}{2}{\left(\frac{2V}{16V}\right)}^{5/3}=\frac{P}{2}{\left(\frac{1}{8}\right)}^{5/3}=\frac{P}{2}{\left(\frac{1}{2^3}\right)}^{5/3}$
$=\frac{P}{2}\left(\frac{1}{2^5}\right)=\frac{P}{64}$