A system goes from $P$ to $Q$ by two different paths in the $P – V$ diagram as shown in 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 is taken through the cycle $A \to B \to C \to A$ , as shown in the figure. If the net heat supplied to the gas in the cycle is $5\ J$, the work done by the gas in the process $C \to A$ is  …. $J$

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 in the given $P-V$ diagram in the cyclic process is

A polyatomic gas with six degrees of freedom does $25\,\,J$ of work when it is expanded at constant pressure. The heat given to the gas is ….. $J$