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 figure shows the $P-V$ plot of an ideal gas taken through a cycle $ABCDA.$ The part $ABC$ is a semicircle and $CDA$ is half of an ellipse. Then,

Consider the $P-V$ diagram for $1$ mole of an ideal monatomic gas shown in the figure. Which of the following statements is/are true?

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

On a $TP$ diagram,two moles of an ideal gas perform processes $AB$ and $CD$. If the work done by the gas in the process $AB$ is two times the work done in the process $CD$,then what is the value of $T_1/T_2$?

An ideal gas undergoes the cyclic process $abca$ as shown in the given $P-V$ diagram. It rejects $50 \,J$ of heat during $ab$ and absorbs $80 \,J$ of heat during $ca$. During $bc$, there is no transfer of heat and $40 \,J$ of work is done by the gas. What should be the area of the closed curve $abca$ (in $\,J$)?