A sample of an ideal gas is taken through the cyclic process $abca$ as shown in the figure. The change in the internal energy of the gas along the path $ca$ is $-180\, J$. The gas absorbs $250\, J$ of heat along the path $ab$ and $60\, J$ along the path $bc$. The work done by the gas along the path $abc$ is ….. $J$

Carnot cycle (reversible) of a gas represented by a Pressure-Volume curve is shown in the diagramConsider the following statements

$I.$ Area $ABCD =$ Work done on the gas

$II.$ Area $ABCD =$ Net heat absorbed

$III.$ Change in the internal energy in cycle $= 0$

Which of these are correct

$1 \,\,kg$ of a gas does $20\,\, kJ$ of work and receives $16 \,\,kJ$ of heat when it is expanded between two states. $A$ second kind of expansion can be found between the initial and final state which requires a heat input of $9\,\, kJ$. The work done by the gas in the second expansion is  ……. $kJ$

A thermodynamic system is taken through cyclic process. The total work done in the process is $………\,J$

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 $ABCDA$