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Heat capacities C_p and C_v
Intermediate
Cp exceeds Cv by R for ideal gases.
C_p − C_v = RFor an ideal gas C_p − C_v = R, since at constant pressure extra heat goes into work. Cv depends on degrees of freedom.
Air: Cv = 20.8, Cp = 29.1 J/mol·K.
Cp is always greater than Cv.
In more detail
At constant volume, C_v describes energy needed per kelvin, and at constant pressure, C_p is larger because the gas also does work as it expands. For an ideal gas, C_p − C_v = R.
Real-world uses
- Engineers use C_p and C_v when analysing gas compression and expansion.
- Acoustic and aerodynamic calculations depend on the ratio of heat capacities.
- Chemists use the difference between the two heat capacities to find the work done when a gas is heated at constant pressure.
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Frequently asked questions
Why is C_p larger?
Because heating at constant pressure allows the gas to expand and do work.
What is the relation for ideal gases?
C_p minus C_v equals the gas constant R.
Why does C_p exceed C_v?
At constant pressure, the gas also does work by expanding, so more heat is needed for the same temperature rise.
Related topics in Heat & Thermodynamics
Isobaric process · Isochoric process · Cyclic process · Ratio of specific heats · P–V diagrams · Second law of thermodynamics