$A$ cyclic process $ABCA$ is shown in the $T-V$ diagram. An ideal gas of $2 \text{ mole}$ undergoes this process. $A$ total of $1200 \text{ J}$ of heat is rejected by the gas in the complete cycle. Find the work done by the gas during the process $BC$. (in $\text{ J}$)

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,

$A$ system goes from $P$ to $Q$ by two different paths in the $P-V$ diagram as shown in the figure. Heat given to the system in path $1$ is $1000 \, J$. The work done by the system along path $1$ is more than path $2$ by $100 \, J$. What is the heat exchanged by the system in path $2$?

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 $\,J$)?

$A$ thermodynamic system is taken through a cyclic process as shown in the $P-V$ diagram. The total work done in the process is $.........\,J$.

In the following figures,in which case is heat absorbed by the gas?