A cylindrical vessel of uniform cross-section consisting of a gas of $\gamma=1.5$ is divided into two parts…
A cylindrical vessel of uniform cross-section consisting of a gas of $\gamma=1.5$ is divided into two parts $A$ and $B$ using a piston. Initially the piston is kept fixed such that part $A$ has pressure $p$ and volume $5 \mathrm{~V}$ and the part $B$ has pressure $8 p$ and volume $V$. If the piston is let free and the gas is allowed to undergo adiabatic process, then the final volume of the gas in part $A$ is
$3 V$
$\frac{8}{3} v$
$\frac{10}{3} v$
$\frac{13}{3} V$
Solution
For adiabatic expression in part A and B, we have,
Solving for $V_A$ with $r=1 \cdot 5$, we get
$
V_A=\frac{10}{3} \mathrm{~V}
$
