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

Answer 1

Answer: (D)

The correct option is C $\frac{P}{64}$
Isothermally $PV=P_{1}2V$
$P_1=\frac{P}{2}$
Adiabatically, $\frac{P}{2}(2V{)}^{\gamma }=P_1(16V{)}^{\gamma }$
$P_f=\frac{P}{2}{\left(\frac{1}{2^3}\right)}^{\frac{5}{3}}$
$P_t=\frac{P}{2}{\left(\frac{1}{2^3}\right)}^{\frac{5}{3}}=\frac{P}{\left(2\right)(2{)}^5}$
$P_f=\frac{P}{6}$