Thermal Physics · Physics

Heating at constant pressure is not the same as heating at constant volume.

Learn what Cp and Cv mean, why they differ, and how they simplify energy calculations for ideal gases.

This topic

Heat Capacities (Cp and Cv)

Focus on physical meaning first: what energy goes into “raising T” versus “doing expansion work.”

Definition

Heat capacity at constant volume

At constant volume, the system does no P–V work, so added heat primarily changes internal energy.

Definition

Heat capacity at constant pressure

At constant pressure, heating typically causes expansion, so some energy goes into P–V work.

Relationship

Relationship between Cp and Cv

For an ideal gas, Cp and Cv are connected by a simple difference involving the gas constant (per mole).

Applications

Applications to ideal gases

Cp and Cv let you compute Q and ΔU quickly for common ideal-gas processes under simple constraints.

Practice

Practice & Exercises

Practice choosing Cp vs Cv, computing energy transfers, and explaining physically why Cp > Cv.