A reversible cyclic process for an ideal gas is shown below. Here, $P, V$, and $T$ are pressure, volume and temperature, respectively. The thermodynamic parameters $q, w, H$ and $U$ are heat, work, enthalpy and internal energy, respectively.

(image)

The correct option ($s$) is (are)

$(A)$ $q_{A C}=\Delta U_{B C}$ and $W_{A B}=P_2\left(V_2-V_1\right)$

$(B)$ $\mathrm{W}_{\mathrm{BC}}=\mathrm{P}_2\left(\mathrm{~V}_2-\mathrm{V}_1\right)$ and $\mathrm{q}_{\mathrm{BC}}=\mathrm{H}_{\mathrm{AC}}$

$(C)$ $\Delta \mathrm{H}_{\mathrm{CA}}<\Delta \mathrm{U}_{\mathrm{CA}}$ and $\mathrm{q}_{\mathrm{AC}}=\Delta \mathrm{U}_{\mathrm{BC}}$

$(D)$ $\mathrm{q}_{\mathrm{BC}}=\Delta \mathrm{H}_{\mathrm{AC}}$ and $\Delta \mathrm{H}_{\mathrm{CA}}>\Delta \mathrm{U}_{\mathrm{CA}}$

Work done for the process shown in the figure is ………… $J$

A student records $\Delta Q, \Delta U \& \Delta W$ for a thermodynamic cycle $A$ $\rightarrow$ $B \rightarrow C \rightarrow A$. Certain entries are missing. Find correct entry in following options.

A constant amount of an ideal gas undergoes the cyclic process $A B C A$ in the $p-V$ graph shown below. The path $B C$ is an isothermal. The work done by the gas during one complete cycle, beginning and ending at $A$ is nearly ………. $\,kJ$

A gas taken through cyclic process $ABCA$ is shown in figure. If $2.4\,cal.$ of heat is given in the process, what is value of $J$ …… $J/cal$ (mechanical equivalent of heat)?