Question

A mass of ideal gas at pressure $P$ is expanded isothermally to four times the original volume and then slowly compressed adiabatically to its original volume. Assuming $\gamma$ to be $1.5$, the new pressure of gas is

• A. $2P$
• B. $P$
• C. $4P$
• D. $\frac{P}{2}$

Answer 1

The correct option is A $2P$

Let $P$ and $V$ be the initial pressure and volume of ideal gas. After isothermal expansion, pressure is $P/4$. So volume is $4V$.
Let $P_1$ be the pressure after adiabatic compression then
$P_1{V}^{\gamma }=\left(P/4\right)(4V{)}^{\gamma }$
$P_1=\left(\frac{P}{4}\right)(4{)}^{3/2}=2P$