In the reported figure,the heat energy absorbed by a system in going through a cyclic process is $......\,\pi \text{ J}$.

The figure given below shows the variation in the internal energy $U$ with volume $V$ of $2.0 \text{ mole}$ of an ideal gas in a cyclic process $abcda$. The temperatures of the gas during the processes $ab$ and $cd$ are $500 \text{ K}$ and $300 \text{ K}$ respectively. The heat absorbed by the gas during the complete process is .... $J$. (Take $R = 8.3 \text{ J/mol-K}$ and $\ln 2 = 0.69$)

$A$ thermodynamic system is taken through the cycle $ABCD$ as shown in the figure. Heat rejected by the gas during the cycle is:

The pressure versus temperature $(P-T)$ graph of an ideal gas is shown in the figure.

One mole of an ideal gas is taken from $a$ to $b$ along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is $w_s$ and that along the dotted line path is $w_d$,then the integer closest to the ratio $w_d / w_s$ is

$A$ system goes from $A$ to $B$ via two processes $I$ and $II$ as shown in the figure. If $\Delta U_1$ and $\Delta U_2$ are the changes in internal energies in the processes $I$ and $II$ respectively,then