An ideal system can be brought from state $A$ to $B$ through four paths as shown in the figure. The energy given to the system is minimum in

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

In the cyclic process shown on the $P-V$ diagram,the magnitude of the work done is

An ideal gas is taken through the path $A \rightarrow B \rightarrow C \rightarrow A$ as shown in the figure. The net work done by the gas is ....... $J$.

The following figure shows a $P-T$ graph for four processes $A, B, C$ and $D$. Select the correct alternative.

In the cyclic process shown in the figure,the work done by the gas in one cycle is (in $,{P_1}{V_1}$)