A pressure-volume (PV) diagram is a graph with pressure on the vertical axis and volume on the horizontal axis, where each point represents a state of a gas and each curve represents a thermodynamic process; the area under a process curve gives the magnitude of work done as the gas's volume changes.
A pressure-volume diagram (PV diagram) is the standard way AP Physics 2 visualizes what a gas is doing. Every single point on the graph is a complete state of the gas, with one pressure and one volume (and through the ideal gas law, one temperature). A line or curve connecting two points is a process, meaning the gas changed from one state to another. So a PV diagram is basically a map of the gas's journey, where location tells you the state and the path tells you how it got there.
The payoff is work. The area under a process curve equals the magnitude of the work associated with the volume change, which connects directly to the equation W = -PΔV (work done on the gas by an external pressure). If the gas expands, the surroundings do negative work on it (the gas does positive work on the surroundings). If the gas is compressed, work done on the gas is positive. When a gas runs through a complete cycle, a closed loop on the diagram, the area enclosed by the loop equals the net work for the whole cycle. A clockwise loop means the gas does net positive work on its surroundings.
PV diagrams live in Topic 9.4, The First Law of Thermodynamics, in Unit 9. They directly support learning objective 9.4.B (describe the behavior of a system using thermodynamic processes) and feed into 9.4.A, since the position of a point on the diagram tells you the gas's temperature and therefore its internal energy through U = 3/2 nRT. The first law, ΔU = Q + W, only becomes usable on the exam once you can read W off a PV diagram. Almost every Unit 9 problem about isothermal, isobaric, isochoric, or adiabatic processes either gives you a PV diagram or expects you to sketch one. It is the single most-tested graph in AP Physics 2 thermodynamics.
Keep studying AP® Physics 2 Unit 9
ΔU = Q + W (Unit 9)
The PV diagram hands you W as an area, and the point's location hands you T (so ΔU through U = 3/2 nRT). That means the first law lets you solve for Q, the one quantity the diagram never shows directly.
Thermodynamic cycle (Unit 9)
A cycle is a closed loop on a PV diagram. The gas returns to its starting state, so ΔU = 0 for the full loop, and the enclosed area equals the net work. Clockwise loops do net work on the surroundings.
Work done by a gas (Unit 9)
Work done by the gas and work done on the gas are the same area under the curve with opposite signs. Expansion means the gas does positive work; compression means positive work is done on the gas (W = -PΔV).
Constant volume process (Unit 9)
A vertical line on a PV diagram has zero area under it, so W = 0 for an isochoric process. The first law then collapses to ΔU = Q, the cleanest special case the exam loves to test.
PV diagrams show up in multiple-choice questions that ask you to match a process to its shape (an isothermal compression is a hyperbolic curve moving toward smaller volume, since PV = nRT stays constant), to interpret a closed loop (the area inside a clockwise loop is the net work done by the gas over the cycle), or to scale areas (a rectangular cycle stretched to width 2V and height 2P encloses four times the area, so net work becomes 4W_net). In free-response questions, expect to sketch a process on given axes, rank processes by work using area comparisons, or combine the diagram with ΔU = Q + W to determine whether heat enters or leaves the gas. The skill being tested is always translation: turn the picture into signed values of W, ΔU, and Q.
The area under a PV curve gives the magnitude of work, but the AP equation sheet defines W as work done ON the gas. When a gas expands, the area under the curve is the work the gas does on its surroundings, so W in ΔU = Q + W is negative. When the gas is compressed, W is positive. Students lose points by reading area off the diagram and forgetting to attach the sign based on whether volume increased or decreased.
Every point on a PV diagram is one state of the gas, and the ideal gas law assigns that point a specific temperature and internal energy.
The area under a process curve equals the magnitude of the work; expansion means the gas does positive work on its surroundings, and compression means positive work is done on the gas.
In the AP sign convention W = -PΔV, W is the work done ON the gas, so W is negative for expansion and positive for compression.
For a closed loop (a thermodynamic cycle), ΔU = 0 over the full cycle and the area enclosed by the loop equals the net work, with clockwise loops doing net positive work on the surroundings.
An isothermal process appears as a hyperbolic curve because PV = nRT stays constant, while a constant volume process is a vertical line with zero work.
Doubling both the width and height of a rectangular cycle quadruples the enclosed area, so the net work scales with area, not with either side alone.
It's a graph with pressure on the vertical axis and volume on the horizontal axis, used in Unit 9 to represent states of a gas (points) and thermodynamic processes (curves). The area under a process curve gives the magnitude of the work associated with the volume change.
No. The area inside a closed loop equals the net work over the cycle. Since ΔU = 0 for a complete cycle, the net heat transferred happens to match the net work in magnitude, but the area itself is defined as work, not heat.
W = -PΔV only works directly when pressure is constant (a horizontal line on the diagram). The PV diagram generalizes this, since the area under any curve, constant pressure or not, gives the magnitude of the work. You still apply the same sign rule based on whether volume increased or decreased.
A hyperbolic curve, because PV = nRT means pressure and volume are inversely proportional when temperature is constant. An isothermal compression moves up and to the left along that curve.
Yes. A clockwise cycle means the gas does net positive work on its surroundings, equal to the area enclosed by the loop. A counterclockwise loop means net work is done on the gas instead.
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