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(C) $1$. In an isothermal expansion from $V_1$ to $V_2$,the work done by the gas is positive $(W_{iso} > 0)$,and the area under the curve represents t

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$P_3 > P_1, W < 0$

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(C) $1$. In an isothermal expansion from $V_1$ to $V_2$,the work done by the gas is positive $(W_{iso} > 0)$,and the area under the curve represents this work.$2$. In an adiabatic compression from $V_2$ to $V_1$,the work done on the gas is negative $(W_{adia} $3$. On a $P-V$ diagram,the adiabatic curve is steeper than the isothermal curve. Since the compression happens from $V_2$ to $V_1$ along the adiabatic path,the final pressure $P_3$ will be higher than the initial pressure $P_1$ $(P_3 > P_1)$.$4$. The total work done $W$ is the sum of the work done in both processes. Since the area under the adiabatic compression curve (which is negative work) is greater than the area under the isothermal expansion curve (which is positive work),the net work done $W$ 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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