One mole of ideal gas undergoes a linear process as shown in the figure below. Its temperature expressed as a function of volume $V$ is
KVPY 2015, Diffcult
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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 $\Delta \mathrm{H}_{\mathrm{CA}}>\Delta \mathrm{U}_{\mathrm{CA}}$
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