Equipartition and the Heat Capacities of Gases
Each way a molecule can store energy holds an average of half kT, so monatomic, diatomic and polyatomic gases have different heat capacities. Freezing out of modes at low temperature is the first hint that classical physics is incomplete.
What a learner can do afterwards
- Counts the degrees of freedom of a monatomic and a diatomic molecule and predicts the heat capacity
- Explains the difference between heat capacity at constant volume and at constant pressure
- Describes why measured heat capacities fall below the classical prediction at low temperature
1 · Read
Equipartition says each independent way a molecule stores energy holds an average of one half kT per molecule, or one half RT per mole. Count those ways, called degrees of freedom, and the heat capacity at constant volume is that count times R over 2.
A lone atom drifts in three directions, so a monatomic gas has Cv of 3R over 2. A two atom molecule at room temperature also spins about two axes, adding two more ways, so a diatomic gas has Cv of 5R over 2. Nitrogen and oxygen follow this rule.
Heat a gas in a rigid box and every joule stays inside as internal energy. Heat it while it pushes a piston and part of the heat leaves as expansion work. That is why Cp beats Cv by exactly R per mole.
Cool a gas far down and some spins and shivers freeze out, so fewer ways share the energy. Measured heat capacities then fall below the classical count, which was the first hint that classical physics is incomplete.
Count the active ways to store energy, halve R times that count for Cv, and add R for Cp.
2 · Watch
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.