1.4 Thermodynamic Processes and P-V Diagrams

Reading P-V Diagrams

A P-V diagram plots pressure vs. volume for a gas. The area under the curve equals the work done by or on the gas. Moving right (volume increases) means the gas does positive work on surroundings; moving left means work is done on the gas. A closed loop's enclosed area equals the net work of a full cycle.

Special Thermodynamic Processes

Isothermal (constant T): PV = constant, curved hyperbola, ΔU = 0. Isobaric (constant P): horizontal line, W = PΔV. Isochoric/isovolumetric (constant V): vertical line, W = 0. Adiabatic (Q = 0): steeper curve than isothermal, ΔU = −W. Each relates to the First Law of Thermodynamics: ΔU = Q − W.

First Law Applications

The First Law of Thermodynamics, ΔU = Q − W, connects heat added, work done by the gas, and internal energy change. In a cyclic process, ΔU = 0 over one full loop, so Q_net = W_net. Identifying the process type lets you quickly determine which term in the First Law vanishes or simplifies.

Key terms

P-V diagram area

Represents the work done by or on the gas during a process.

Isothermal process

Constant temperature; ΔU = 0; follows PV = constant (hyperbolic curve).

Isobaric process

Constant pressure; horizontal line on P-V diagram; W = PΔV.

Adiabatic process

No heat transfer (Q = 0); ΔU = −W; steeper curve than isothermal on P-V diagram.

First Law of Thermodynamics

ΔU = Q − W; relates change in internal energy to heat added and work done by the gas.

Try an AP-style question

On a P–V diagram, what does the area under a process curve represent?

1. The heat added
2. The internal energy
3. The change in temperature
4. The magnitude of the work done