$A$ gas is suddenly compressed to $1/4$ th of its original volume at normal temperature. The increase in its temperature is ....... $K$ $(\gamma = 1.5)$

The relation obeyed by a perfect gas during an adiabatic process is $PV^{3/2} = \text{constant}$. The initial temperature of the gas is $T$. When the gas is compressed to half of its initial volume, the final temperature of the gas is:

If $\Delta E_{int}$ represents the increase in internal energy and $W$ represents the work done by the system,which of the following statements is correct for a thermodynamic system?

During an adiabatic process,the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_P}{C_V}$ for the gas is

$A$ diatomic gas undergoes adiabatic change. Its pressure $P$ and temperature $T$ are related as $P \propto T^{x}$ where the value of $x$ is

$A$ 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: