When $2 \text{ moles}$ of a monatomic gas expands adiabatically from a temperature of $80^{\circ} C$ to $50^{\circ} C$,the work done is $W$. The work done when $3 \text{ moles}$ of a diatomic gas expands adiabatically from $50^{\circ} C$ to $20^{\circ} C$ is: (in $W$)

The pressure of a motorcar tire at $27^{\circ}C$ is $2$ atmospheres. If the tire suddenly bursts,the final temperature will be ....... $K$ (Take $\gamma = 1.4$).

One mole of an ideal gas expands adiabatically from $200 \,K$ to $250 \,K$. If the specific heat of the gas at constant volume is $0.8 \,kJ \,kg^{-1} \,K^{-1}$, then the work done by the gas 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?

The volume of air increases by $5\%$ in its adiabatic expansion. The percentage decrease in its pressure will be ...... $\%$

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.