Question

The initial pressure of a gas is $P$. It is kept in an insulated container and suddenly its volume is reduced to one-third. Its final pressure will be

• A. $3^{\gamma }P$
• B. $\frac{P}{3^{\gamma }}$
• C. $\frac{P}{3}$
• D. $3P$

Answer 1

Answer: (A)

$3^{\gamma }P$

As the container is insulated which implies that no heat exchange will take place through the wall of the container. Thus the given process is an adiabatic process.

Thus, we get
$P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$
or
$P_1{V}_1^{\gamma }=P_2(\frac{V_1}{3}{)}^{\gamma }$

Thus, we get the final pressure as
$P_2=P_1\times 3^{\gamma }$

Option A is correct.