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The heat capacity of one mole an ideal is found to be $C_V=3 R(1+a R T) / 2$, where $a$ is a constant. The equation obeyed by this gas during a reversible adiabatic expansion is
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
The adjoining figure shows the $P-V$ diagram for a fixed mass of an ideal gas undergoing cyclic process. $AB$ represents isothermal process and $CA$ represents isochoric process.Which of the graph shown in the following figures represents the $P-T$ diagram of the cyclic process ?