An open vessel at $27\,^{\circ}C$ is heated until two-fifths of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant,the temperature to which the vessel has been heated is:

An ideal gas undergoes a cyclic transformation starting from the point $A$ and coming back to the same point by tracing the path $A$ $\rightarrow B$ $\rightarrow C$ $\rightarrow A$ as shown in the diagram. The total work done in the process is . . . . . . $J$.

For an ideal gas,the compressibility factor $(Z)$ is

The graph of pressure $(P)$ versus density $(d)$ is shown for an ideal gas at two temperatures $T_1$ and $T_2$. Which of the following is correct?

Match the laws given in List-$I$ with their mathematical forms given in List-$II$.

List-$I$	List-$II$
$(1)$ Boyle's Law	$(A)$ $p \propto T$
$(2)$ Charles's Law	$(B)$ $V \propto n$
$(3)$ Gay-Lussac's Law	$(C)$ $p \propto \frac{1}{V}$
$(4)$ Avogadro's Law	$(D)$ $pV = nRT$
$(5)$ Ideal Gas Equation	$(E)$ $V = k_2T$

At temperature $t \, ^oC$,the pressure exerted by $12 \, g$ of an ideal gas in a container of volume $V \, L$ is $1 \, atm$. When the temperature is increased by $10 \, ^oC$ without changing the volume,the pressure increases by $10 \%$. Find the temperature $t$ and volume $V$ in $L$. (Molar mass of the gas = $120 \, g/mol$)