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AP Physics 2
9.4 The First Law of Thermodynamics
AdvancedMCQMathematicalConceptual15.2k
A PV diagram with pressure P on the vertical axis and volume V on the horizontal axis. The origin represents zero volume and pressure. On the horizontal axis, two volume values are labeled: V_0 and 2V_0. On the vertical axis, one pressure value is labeled: P_0. An initial state point labeled i is located at coordinates (V_0, P_0). Three paths originate from state point i and extend to a final volume of 2V_0. Path 1 is a horizontal line segment from (V_0, P_0) to (2V_0, P_0) with an arrow pointing right, labeled Path 1. Path 2 is a smooth curve bending downward from (V_0, P_0) to a point at volume 2V_0 with pressure equal to 0.5 P_0, with an arrow pointing down and right, labeled Path 2. Path 3 is a steeper curve bending downward below Path 2 from (V_0, P_0) to a point at volume 2V_0 with pressure less than 0.5 P_0, with an arrow pointing down and right, labeled Path 3. No other labels, lines, text, or axes appear.
PV diagram showing three expansion paths from initial state i.
A sample of an ideal gas is initially in state \(i\) with pressure \(P_0\) and volume \(V_0\). The gas expands to a final volume of \(2V_0\) along three different thermodynamic paths shown in the \(PV\) diagram: Path 1 is an isobaric expansion, Path 2 is an isothermal expansion, and Path 3 is an adiabatic expansion. Which of the following statements correctly compares the work done by the gas along these paths and provides the correct physical justification?

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