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(C) $1$. In an isothermal expansion from $V_1$ to $V_2$,the work done by the gas is positive $(W_{iso} > 0)$.$2$. In an adiabatic compression from $V_

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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 $(W_{iso} > 0)$.$2$. In an adiabatic compression from $V_2$ back 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 adiabatic compression returns to $V_1$ from a lower pressure point at $V_2$,the final pressure $P_3$ must be greater than the initial pressure $P_1$ $(P_3 > P_1)$.$4$. The net work done $W = W_{iso} + W_{adia}$ corresponds to the area enclosed by the cycle. Since the cycle is traversed in a counter-clockwise direction,the net work done 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 $P_3$. If the total work done is $W$,then:

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