PV Diagrams
A PV diagram is the single most important graph in MCAT thermodynamics. Pressure on the y-axis, volume on the x-axis. Every thermodynamic process traces some path across this diagram, and the shape of that path tells you everything: what’s constant, what’s changing, how much work was done, and how much heat flowed.
Master the four standard processes (each with a distinctive shape) and you can answer almost any first-law or work question the exam throws at you, often without doing arithmetic — just by reading the graph.
The Four Key Processes
Every MCAT-relevant thermodynamic process holds one variable constant (or, in the case of adiabatic, holds heat transfer at zero). Here is the complete set:
Isothermal - Constant Temperature
“Iso” = same, “thermal” = temperature. The temperature doesn’t change, so for an ideal gas, ΔU = 0. By the first law, Q = W - all heat absorbed becomes work (or vice versa).
On a PV diagram, an isothermal process follows a hyperbola (since PV = nRT = constant). The curve bows away from the origin.
Isobaric - Constant Pressure
Pressure stays the same throughout the process. On a PV diagram, this is a horizontal line. Heating a gas in a cylinder with a freely moving, weightless piston is approximately isobaric.
Work is easy to calculate: W = PΔV (the rectangle under the horizontal line).
Isovolumetric (Isochoric) - Constant Volume
Volume doesn’t change, so the process appears as a vertical line on the PV diagram. Since the gas neither expands nor compresses, W = 0. By the first law, ΔU = Q - all heat goes directly into changing the internal energy.
Heating gas in a rigid, sealed container is isovolumetric.
Adiabatic - No Heat Transfer
“Adiabatic” means Q = 0. The system is perfectly insulated. By the first law, ΔU = -W. Any work done by the gas comes at the expense of its internal energy (temperature drops), and any work done on the gas raises its internal energy (temperature rises).
On a PV diagram, an adiabatic curve looks like an isothermal curve but is steeper. It crosses isotherms because the temperature is changing.
Summary Table
| Process | Constant | PV Shape | Work | ΔU | Special |
|---------|----------|----------|------|-----|---------|
| Isothermal | T | Hyperbola | Q = W | 0 | ΔU = 0 (ideal gas) |
| Isobaric | P | Horizontal | PΔV | Q - PΔV | Most common in lab |
| Isovolumetric | V | Vertical | 0 | Q | All heat → ΔU |
| Adiabatic | Q = 0 | Steep curve | -ΔU | -W | Steeper than isothermal |
A gas expands from 2 L to 5 L twice: once at constant pressure, once isothermally, starting from the same state each time. Which expansion does more work on the surroundings?
Now check your prediction directly. Pick a process and a direction, press Run, and watch the state point sweep along its curve while the area under the path fills in. That shaded area is the work, and the readouts track W, ΔU, and Q live as the piston moves.
Reading a PV Diagram
To extract information from a PV diagram:
- Identify the process type from the shape (horizontal, vertical, curve, steep curve)
- Check the direction - rightward expansion means positive work by the gas; leftward compression means negative work (work done on the gas)
- Compare areas to compare work done in different processes
- Check if it is a cycle - if the path returns to the starting point, ΔU = 0 for the whole cycle
Distinguishing Isothermal from Adiabatic
Both look like downward-curving paths on a PV diagram during expansion. The key differences:
- Isothermal stays on one isotherm (constant T). It is gentler because heat flows in to compensate for the work done.
- Adiabatic crosses isotherms toward lower temperatures. It is steeper because no heat enters - the gas uses its own internal energy to do work, so it cools.
For a given expansion from to , the isothermal process always does more work (more area under the curve) than the adiabatic process.
An isovolumetric (constant volume) process. Work = 0. Since the volume doesn’t change, there is no area under the curve and the gas does no work. By the first law, ΔU = Q, so all heat directly changes the internal energy and temperature.
Isothermal does more work. The isothermal curve stays at higher pressure throughout the expansion (because heat flows in to maintain temperature), so the area under the curve is larger. The adiabatic curve drops to lower pressures as the gas cools, resulting in less area and less work.