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(C) $1$. In the $P-V$ diagram,the process $AB$ represents an isothermal expansion from $V_1$ to $V_2$,and the process $BC$ represents an adiabatic com

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$P_3 > P_1, W < 0$

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(C) $1$. In the $P-V$ diagram,the process $AB$ represents an isothermal expansion from $V_1$ to $V_2$,and the process $BC$ represents an adiabatic compression from $V_2$ back to $V_1$.$2$. From the graph,it is clear that the final pressure $P_3$ at point $C$ is greater than the initial pressure $P_1$ at point $A$ $(P_3 > P_1)$.$3$. The work done in an isothermal expansion $(W_{iso})$ is the area under the curve $AB$,which is positive. The work done in an adiabatic compression $(W_{adia})$ is the negative of the area under the curve $BC$,which is negative.$4$. Since the adiabatic curve $BC$ is steeper than the isothermal curve $AB$,the magnitude of work done during adiabatic compression is greater than the work done during isothermal expansion $(|W_{adia}| > |W_{iso}|)$.$5$. Therefore,the net work done $W = W_{iso} + W_{adia}$ is negative $(W < 0)$.

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and then is 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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