Degrees of Freedom and Equipartition of Energy
Each quadratic ° of freedom carries an average energy kT/2, which fixes Cv, Cp and γ for a gas.
What is Degrees of Freedom and Equipartition of Energy?
Each quadratic ° of freedom carries an average energy kT/2, which fixes Cv, Cp and γ for a gas.
Key formula / rule: Energy per ° of freedom = kT/2.
Key points
- Compute Cv, Cp and γ from the degrees of freedom.
- Apply the equipartition theorem to mixtures.
Common exam trap
Counting vibrational modes at ordinary temperature.
Definitions
- Term
Degrees of Freedom and Equipartition of Energy
- Meaning
Each quadratic ° of freedom carries an average energy kT/2, which fixes Cv, Cp and γ for a gas.
- Term
Degrees of Freedom and Equipartition of Energy — explanation
- Meaning
Monatomic gases have three translational degrees of freedom giving γ = 5/3, diatomic gases add two rotational ones giving 7/5. Vibrational modes activate only at high temperature.
Learning objectives
Compute Cv, Cp and γ from the degrees of freedom.
Apply the equipartition theorem to mixtures.
Formulae
- Key point
Energy per ° of freedom = kT/2.
- Key point
Cp - Cv = R; γ = Cp/Cv.
- Key point
Monatomic γ = 1.67, diatomic γ = 1.40.
Prerequisites
PHY-U3-KTG-T1-S1-C2
PHY-U3-THR-T2-S1-C1
Common mistakes
Counting vibrational modes at ordinary temperature.
Confusing molar and specific heat capacities.
Keywords
Degrees
Freedom
Equipartition
Energy
Practice preview
What is the definition of degrees of freedom for a thermodynamic system?…
easy
According to the law of equipartition of energy, what is the average energy associated with each degree of freedom of a molecule at temperature T?…
easy
How many degrees of freedom does a monatomic gas molecule possess?…
easy