In a thermodynamics process, pressure of a fixed mass of a gas is changed in such a manner that the gas releases $20\,J$ of heat and $8\,J$ of work is done on the gas. If the initial internal energy of the gas was $30\,J$. The final internal energy will be…… $J$

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

$(A)$ the process during the path $\mathrm{A} \rightarrow \mathrm{B}$ is isothermal

$(B)$ heat flows out of the gas during the path $\mathrm{B} \rightarrow \mathrm{C} \rightarrow \mathrm{D}$

$(C)$ work done during the path $\mathrm{A} \rightarrow \mathrm{B} \rightarrow \mathrm{C}$ is zero

$(D)$ positive work is done by the gas in the cycle $ABCDA$

A sample of an ideal gas is taken through the cyclic process $ABCA$ as shown in figure. It absorbs, $40\,J$ of heat during the part $A B$, no heat during $BC$ and rejects $60\,J$ of heat during $CA$. $A$ work $50\,J$ is done on the gas during the part $BC$. The internal energy of the gas at $A$ is $1560\,J$. The work done by the gas during the part $CA$ is………….$J$

One mole of an ideal gas goes from an initial state $A$ to final state $B$ via two processes : It first undergoes isothermal expansion from volume $V$ to $3\, V$ and then its volume is reduced from $3\, V$ to $V$ at constant pressure. The correct $P-V$ diagram representing the two processes is

A cyclic process $ABCD$ is shown in the given $P-V$ diagram. $P-T$ diagram that  represents the same process is