Law of Equipartition of Energy
The principle stating that, for a system in thermal equilibrium, the total energy is equally distributed among all degrees of freedom, with each contributing 1/2kT per molecule.
What is Law of Equipartition of Energy?
The number of independent ways in which a molecule can store energy. These include translational, rotational, and vibrational modes.
Key formula / rule: Average Energy per Molecule
Key points
- Understand the principle of energy distribution in thermal equilibrium.
- Relate average molecular energy to degrees of freedom.
- Calculate the average energy of a molecule based on its degrees of freedom.
- Apply the law to determine specific heats of gases.
Common exam trap
Forgetting to account for all degrees of freedom (e.g., missing rotational or vibrational modes).
Definitions
- Term
Degrees of Freedom (f)
- Meaning
The number of independent ways in which a molecule can store energy. These include translational, rotational, and vibrational modes.
- Term
Thermal Equilibrium
- Meaning
A state where there is no net flow of heat between any two systems in thermal contact, and their macroscopic properties remain constant over time.
- Term
Boltzmann Constant (k)
- Meaning
A physical constant that relates the average kinetic energy of particles in a gas with the thermodynamic temperature of the gas. k ≈ 1.38 × 10-23 J/K.
Learning objectives
Understand the principle of energy distribution in thermal equilibrium.
Relate average molecular energy to degrees of freedom.
Calculate the average energy of a molecule based on its degrees of freedom.
Apply the law to determine specific heats of gases.
Formulae
- Name
Average Energy per Molecule
- Note
f is the number of degrees of freedom, k is the Boltzmann constant, T is the absolute temperature.
- Expression
Eavg = (f/2)kT
- Name
Molar Specific Heat at Constant Volume
- Note
R is the universal gas constant. Derived from equipartition principle.
- Expression
Cv = (f/2)R
- Name
Molar Specific Heat at Constant Pressure
- Note
Relationship between Cp and Cv.
- Expression
Cp = Cv + R
- Name
Adiabatic Index
- Note
Ratio of specific heats, dependent on degrees of freedom.
- Expression
γ = Cp / Cv = 1 + 2/f
Prerequisites
Concept of Thermal Equilibrium
Degrees of Freedom (Translational, Rotational, Vibrational)
Boltzmann Constant
Kinetic Theory of Gases
Common mistakes
Forgetting to account for all degrees of freedom (e.g., missing rotational or vibrational modes).
Confusing average energy per molecule with total energy.
Assuming vibrational modes are always active.
Incorrectly applying the law to non-equilibrium systems.
Keywords
Equipartition of Energy
Degrees of Freedom
Thermal Equilibrium
Boltzmann Constant
Specific Heat
Internal Energy
Kinetic Theory of Gases
Practice preview
The law of equipartition of energy is applicable to systems that are:…
easy
What is the average energy per molecule for a diatomic gas at high temperatures where rotational and vibrational modes are active?…
medium
Which of the following statements is INCORRECT regarding the law of equipartition of energy?…
hard