$200 \ cc$ of an ideal gas $(\gamma = 1.5)$ expands adiabatically. If the rms speed of the gas molecules becomes half of the initial value,the final volume of the gas is (in $cc$)

Pressure-temperature relationship for an ideal gas undergoing adiabatic change is $\left( \gamma = C_p/C_v \right)$

$A$ tyre pumped to a pressure of $2 \text{ atm}$ suddenly bursts. If the temperature of air before expansion is $T$, then the air temperature after the tyre bursts is (Assume the expansion is adiabatic and adiabatic constant $\gamma = \frac{3}{2}$).

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

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?

In the provided figure,there is a cyclic process $ABCDA$ on a sample of $1 \, mol$ of a diatomic gas. The temperatures of the gas during the processes $A \rightarrow B$ and $C \rightarrow D$ are $T_{1}$ and $T_{2}$ $(T_{1} > T_{2})$ respectively. Choose the correct option for the work done if processes $BC$ and $DA$ are adiabatic.