A pressure-volume graph (PV diagram) plots a gas's pressure against its volume during a thermodynamic process. In AP Physics 2, the area under the curve equals the magnitude of work done on or by the gas, making it the main tool for applying the first law of thermodynamics, ΔU = Q + W.
A pressure-volume graph, usually called a PV diagram, puts volume on the horizontal axis and pressure on the vertical axis and traces the path a gas follows as it expands, compresses, heats, or cools. Each point on the graph is one state of the gas, and the line connecting points is the process that takes the gas from one state to another.
The reason this graph matters so much is that it turns work into geometry. The work done on a gas by an external pressure that changes its volume is W = -PΔV, and on a PV diagram that work shows up as the area under the process curve. Compress the gas (volume decreases) and positive work is done on it. Let it expand and the gas does work on its surroundings, so W on the system is negative. The shape of the curve also tells you what kind of process is happening. A horizontal line means constant pressure, a vertical line means constant volume (zero work, since the area under a vertical line is zero), and a smooth downward hyperbola-like curve means constant temperature for an ideal gas.
PV graphs live in Topic 9.4, The First Law of Thermodynamics, and directly support learning objectives 9.4.A (describe the internal energy of a system) and 9.4.B (describe the behavior of a system using thermodynamic processes). Here's the logic chain the exam expects you to run. For an ideal gas, internal energy depends only on temperature (U = 3/2 nRT). The PV graph hands you the work term through the area under the curve. Plug both into ΔU = Q + W and you can solve for the heat transferred, which is the quantity you usually can't see directly. Almost every thermodynamics problem in Unit 9 either gives you a PV diagram or expects you to sketch one, so reading these graphs fluently is the skill that unlocks the whole unit.
Keep studying AP® Physics 2 Unit 9
ΔU = Q + W (Unit 9)
The PV graph is the visual version of the first law. The graph gives you W from the area under the curve, the temperatures at the endpoints give you ΔU, and the first law lets you solve for Q. One equation, one picture, three quantities.
Work done on a system (Unit 9)
W = -PΔV is literally the area under the PV curve with a sign attached. Moving left on the graph (compression) means positive work done on the gas; moving right (expansion) means the gas does work on its surroundings.
Thermodynamic cycle (Unit 9)
When a process curve forms a closed loop on a PV diagram, the gas returns to its starting state, so ΔU for the whole cycle is zero. The area enclosed by the loop equals the net work, which is how heat engines get analyzed.
Constant volume process (Unit 9)
On a PV graph this is a vertical line, and a vertical line has zero area under it. That means W = 0, so the first law collapses to ΔU = Q. Any heat added goes straight into internal energy.
Multiple-choice questions hand you a PV diagram and ask you to identify the process (constant pressure, constant volume, constant temperature), compare work done along different paths, or rank changes in internal energy. Fiveable practice questions hit this exact skill, like recognizing that an isothermal compression appears as a curved path along an isotherm, or that a PV diagram is the right tool to visualize a gas being compressed. On free-response questions, expect to sketch a process on labeled axes, justify the sign of W from the direction of the path, and connect the area under the curve to ΔU = Q + W in a paragraph-length argument. The most common point-loser is the sign convention, so always state whether work is being done on the gas or by the gas before you write a number.
Both are read from the same area under the PV curve, but they have opposite signs, and the AP Physics 2 equation sheet uses W = -PΔV, meaning work done ON the system. Compression (moving left on the graph) gives positive W on the gas. Expansion (moving right) means the gas does positive work on its surroundings, so W on the gas is negative. If your ΔU comes out with the wrong sign, this convention is almost always the culprit.
A pressure-volume graph (PV diagram) plots pressure versus volume, and the area under the process curve equals the magnitude of the work done on or by the gas.
The AP equation W = -PΔV means work done ON the gas, so compression gives positive W and expansion gives negative W on the system.
A vertical line on a PV graph is a constant volume process with zero work, a horizontal line is constant pressure, and a smooth downward curve along an isotherm is constant temperature.
For an ideal gas, internal energy depends only on temperature (U = 3/2 nRT), so endpoints at the same temperature on a PV graph have the same internal energy no matter the path.
Work is path-dependent on a PV graph, so two processes connecting the same two states can do different amounts of work even though ΔU is identical.
A closed loop on a PV diagram is a thermodynamic cycle where ΔU = 0 and the enclosed area equals the net work for the cycle.
It's a graph with volume on the x-axis and pressure on the y-axis that traces a gas through a thermodynamic process. The area under the curve gives the work term in the first law of thermodynamics, ΔU = Q + W, which is why it shows up constantly in Unit 9.
No. The area gives the magnitude of work, but the sign depends on direction. If the gas is compressed (path moves toward smaller volume), work done on the gas is positive. If the gas expands, the gas does work on its surroundings and W on the system is negative under the W = -PΔV convention.
Yes. Pressure-volume graph, pressure-volume diagram, and PV diagram all mean the same plot. The College Board and most textbooks use 'PV diagram,' so treat the terms as interchangeable on the exam.
An isobaric (constant pressure) process is a flat horizontal line. An isothermal (constant temperature) process curves downward like a hyperbola because PV stays constant for an ideal gas at fixed temperature. A vertical line is isochoric, meaning constant volume with zero work done.
No. Internal energy of an ideal gas depends only on temperature (U = 3/2 nRT), so ΔU is fixed by the start and end states. Work and heat, however, are path-dependent, which is why two different curves between the same points can involve different Q and W but the same ΔU.
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