One mole of an ideal diatomic gas undergoes a transition from $A$ to $B$ along a path $AB$ as shown in the figure. The change in internal energy of the gas during the transition is ............ $kJ$.

The density $\rho$ versus volume $V$ graph is shown in the figure. Find the corresponding pressure $P$ versus temperature $T$ graph.

The $P-V$ diagram of $2\,g$ of helium gas for a certain process $A \to B$ is shown in the figure. What is the heat given to the gas during the process $A \to B$ (in $,P_0V_0$)?

Three moles of an ideal monatomic gas perform a cyclic process as shown in the figure. The temperatures in different states are $T_1 = 400\,K, T_2 = 800\,K, T_3 = 2400\,K$ and $T_4 = 1200\,K$. Determine the work done by the gas during the cycle in $kJ$. (Given $R = 8.31\, J\, mol^{-1} K^{-1}$)

$A$ system goes from $A$ to $B$ via two processes $I$ and $II$ as shown in the figure. If $\Delta U_I$ and $\Delta U_{II}$ are the changes in internal energies in the processes $I$ and $II$ respectively,then:

Two moles of an ideal monoatomic gas undergo a cyclic process as shown in the figure. The temperatures in different states are given as $6 T_1 = 3 T_2 = 2 T_4 = T_3 = 2400 \text{ K}$. The work done by the gas during the complete cycle is $(R = \text{Universal gas constant})$ (in $R$)