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 $\gamma =5/3 )$

• A. 64P
• B. 32P
• C. $\frac{P}{64}$
• D. 16P

Answer 1

Answer: (C)

$\frac{P}{64}$

Answer 2

First, isothermal expansion
$PV=P'(2V)$
(For isothermal process, PV=constant)
$P'= \frac {P}{2}$
Then, adiabatic expansion
$P'(2V)^? =P_f(16V)^?$
(For adiabatic process, $PV^? =$ constant)
$\frac {P}{2}(2V)^{5/3}=P_f(16V)^{5/3}$
$P_f=\frac {P}{2}\bigg (\frac {2V}{16 V}\bigg )^{\frac{5}{3}}=\frac {P}{2}\bigg (\frac {1}{8}\bigg )^{\frac{5}{3}}=\frac {P}{2}$
$\bigg (\frac {1}{2^3}\bigg )^{\frac{5}{3}}$
$h\,space\,\,5mm =\frac {P}{2} \bigg (\frac {1}{2^5}\bigg ) = \frac {P}{64}$