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

• A

  $3 V$
• B

  $\frac{8}{3} v$
• Correct answer
  C

  $\frac{10}{3} v$
• D

  $\frac{13}{3} V$

Solution

For adiabatic expression in part A and B, we have,
Solving for $V_A$ with $r=1 \cdot 5$, we get $$ V_A=\frac{10}{3} \mathrm{~V} $$

Hence, the correct answer is option: 'C'.