Heat is not being exchanged in a body. If its internal energy is increased,then

$A$ cylindrical vessel of uniform cross-section containing a gas with $\gamma = 1.5$ 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 $5V$, and part $B$ has pressure $8p$ and volume $V$. If the piston is released and the gas is allowed to undergo an adiabatic process, then the final volume of the gas in part $A$ is:

If $\gamma = 2.5$ and the final volume is $\frac{1}{8}$ times the initial volume, then the final pressure $P'$ is equal to (Initial pressure $= P$).

In a thermodynamic system,$\Delta U$ represents the increase in its internal energy and $dW$ is the work done by the system. Then,which of the following statements is correct?

$A$ gas at initial temperature $T$ undergoes sudden expansion from volume $V$ to $2 \, V$. Then,

$A$ monoatomic gas $\left( \gamma = \frac{5}{3} \right)$ is suddenly compressed to $\frac{1}{8}$ of its original volume. What will be the final pressure of the gas in terms of its initial pressure?