An isochoric process is a thermodynamic process in which a gas's volume stays constant, so the gas does no work (W = 0) and, by the first law of thermodynamics, any heat added or removed changes the internal energy directly (ΔU = Q). It appears as a vertical line on a PV diagram.
An isochoric process (also called isovolumetric or constant-volume) is a thermodynamic process where the volume of the gas never changes. Picture a gas sealed in a rigid steel container. You can heat it or cool it all you want, but the walls don't move. Since work done by a gas comes from changing volume (the area under the curve on a PV diagram), no volume change means zero work. W = 0, full stop.
That makes the first law of thermodynamics collapse into its simplest form. Normally ΔU = Q + W (or Q − W, depending on sign convention), but with W = 0 you get ΔU = Q. Every joule of heat that flows in becomes internal energy, which for an ideal gas means the temperature rises. On a PV diagram, an isochoric process is a perfectly vertical line. Pressure changes, volume doesn't. If pressure goes up, heat flowed in and temperature increased; if pressure drops, heat flowed out.
Isochoric processes live in Topic 2.7, Internal Energy and Energy Transfer, where you analyze how heat, work, and internal energy trade off in thermodynamic systems. It's the cleanest test of whether you actually understand the first law, because it strips one variable to zero. If you can't explain why a rigid container heated on a stove gains internal energy without doing work, the first law hasn't clicked yet. Isochoric segments also show up constantly inside thermodynamic cycles on PV diagrams, so recognizing the vertical line and immediately writing W = 0 saves you time and prevents sign errors on multi-step problems.
Keep studying AP Physics 2 Unit 2
PV Diagrams (Unit 2)
An isochoric process is a vertical line on a PV diagram, and since work equals the area under the curve, a vertical line has zero area underneath it. That's the visual proof that W = 0. When a cycle question gives you a rectangle on a PV diagram, the two vertical sides are the isochoric legs where you only track heat and internal energy.
Conservation of Energy / First Law (Unit 2)
The first law (ΔU = Q + W) is just conservation of energy for thermodynamics. The isochoric case is its simplest special case, since W drops out and ΔU = Q. Master this one first and the messier processes feel like the same equation with one more moving part.
Isobaric Process (Unit 2)
Isobaric is the mirror-image special case. It holds pressure constant instead of volume, so the gas DOES do work (W = −PΔV) as it expands or compresses. Comparing the two side by side is the fastest way to see why heat added at constant volume raises temperature more than the same heat added at constant pressure, where some energy leaks out as work.
Adiabatic Process (Unit 2)
Adiabatic and isochoric each zero out a different term of the first law. Adiabatic kills Q (no heat exchange), so ΔU = W. Isochoric kills W, so ΔU = Q. Knowing which term dies in which process is the core skill for ranking ΔU, Q, and W across processes on the exam.
Isochoric processes show up most often in PV diagram questions. A typical multiple-choice stem shows a gas moving along a vertical segment and asks for the work done (answer: zero), the sign of Q, or the change in internal energy. You're expected to connect three facts instantly: constant volume means W = 0, ΔU = Q, and pressure change tells you the direction of heat flow and temperature change. In free-response questions, isochoric legs appear inside full cycles, where you justify in words why no work is done during that step or fill in a table of Q, W, and ΔU for each leg. No released FRQ hinges on the word 'isochoric' alone, but the constant-volume reasoning it represents is standard first-law territory, so be ready to argue from the area under the curve rather than just memorizing the label.
The prefixes do the work here. Iso-CHORIC means constant volume (a vertical line on a PV diagram, zero work). Iso-BARIC means constant pressure (a horizontal line, with work W = −PΔV because the volume changes). Students swap them constantly under time pressure. A quick check: 'baric' relates to pressure (like a barometer), so isobaric locks pressure, and isochoric locks the other one, volume.
An isochoric process keeps volume constant, which means the gas does zero work, no matter how much heat flows in or out.
With W = 0, the first law of thermodynamics simplifies to ΔU = Q, so all heat added goes directly into internal energy and temperature.
On a PV diagram, an isochoric process is a vertical line, and the zero area under that line is the geometric reason work is zero.
If pressure rises during an isochoric process, heat entered the gas and temperature increased; if pressure falls, heat left and temperature dropped.
Isochoric (constant volume) and isobaric (constant pressure) are different processes, and only the isobaric one involves work done by or on the gas.
It's a thermodynamic process where the gas's volume stays constant, like heating gas in a sealed rigid container. Because volume doesn't change, the gas does zero work, and any heat transferred changes internal energy directly (ΔU = Q).
No. Work in thermodynamics requires a volume change (it's the area under the curve on a PV diagram), and an isochoric process is a vertical line with zero area under it. So W = 0 always, even if pressure and temperature change a lot.
Isochoric means constant volume (vertical line on a PV diagram, zero work), while isobaric means constant pressure (horizontal line, work equals −PΔV). Memory trick: 'baric' comes from the same root as barometer, so isobaric locks pressure.
Yes, and it usually does. Since ΔU = Q at constant volume, adding heat raises internal energy and therefore temperature, which you'll see as rising pressure on the PV diagram. Constant volume does not mean constant temperature (that's isothermal).
A perfectly vertical line. Pressure moves up or down while volume stays fixed, and the zero area under the line confirms zero work. Spot the vertical segment in a cycle and you can immediately write W = 0 for that leg.