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(C) $1$. In the $P-V$ diagram,the isothermal expansion from $V_1$ to $V_2$ follows a curve with a smaller slope compared to the adiabatic compression

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$P_3 > P_1$,$W < 0$

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(C) $1$. In the $P-V$ diagram,the isothermal expansion from $V_1$ to $V_2$ follows a curve with a smaller slope compared to the adiabatic compression from $V_2$ to $V_1$.$2$. Since the adiabatic curve is steeper than the isothermal curve,the final pressure $P_3$ at volume $V_1$ must be greater than the initial pressure $P_1$ $(P_3 > P_1)$.$3$. The work done in a cyclic process is represented by the area enclosed by the $P-V$ loop. Since the process is counter-clockwise (expansion at lower pressure,compression at higher pressure),the net work done on the gas is positive,meaning the work done by the gas $(W)$ is negative $(W < 0)$.

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and is then compressed to the original volume $V_1$ adiabatically. The initial pressure is $P_1$ and the final pressure is $P_3$. The total work done is $W$. Then:

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