Free · Ideal gas models
Ideal Gas Equipartition Energy and RMS Speed
Relate ideal-gas temperature, quadratic degrees of freedom, amount, molar mass and three-dimensional translational RMS speed with exact SI constants.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
For one mole at 300 K with 28 g/mol molar mass and 3 active degrees of freedom, total equipartition energy is 3741.50817816895800 J; molecular translational RMS speed is approximately 516.962846 m/s.
E molecule=f kB T/2; U=n NA E; v rms=sqrt(3 kB NA T/Mkg)
Worked example
Enter these known values and leave the other values blank.
- Molar mass
- 28 g/mol
- Temperature
- 300 K
- Amount of gas
- 1 mol
- Equipartition energy per molecule
- 38.78 meV
- Translational root-mean-square speed
- 517 m/s
- Total equipartition energy
- 3741.5 J
Assumptions and limitations
- Three-dimensional classical ideal gas in equilibrium. Quantum suppression of rotational/vibrational modes and intermolecular potential/binding energies are not calculated.
- The default 3 degrees describe translation. Custom f models additional quadratic energy contributions; adding internal degrees increases equipartition energy but does not increase translational RMS speed at unchanged temperature.
- The energy-per-molecule control is equipartition energy across the specified modes, not purely translational kinetic energy when f exceeds3. RMS is the square root of mean squared speed, not arithmetic mean speed.
- Enter molar mass in g/mol and amount in mol. All endpoints must be positive and f must be a whole count of at least 3; the absolute-zero/empty-gas endpoints are excluded from the invertible classical model.
- The show/hide choice controls visibility and preserves an entered mode count. Reset restores the initial three-mode count.
Common questions
Does increasing degrees of freedom increase RMS speed?
At fixed temperature and molar mass, translational RMS speed remains fixed. Additional active quadratic modes increase total equipartition energy.
What does total energy mean here?
It is the classical quadratic-mode equipartition contribution for the specified amount of ideal gas. It excludes chemical binding energies and does not determine quantum activation of individual modes.
References
- Exact SI constants and classical ideal-gas relationships
- Exact SI constants and classical ideal-gas relationships
- Exact SI constants and classical ideal-gas relationships
- Exact SI constants and classical ideal-gas relationships
- Calculation definition and unit reference
Use exact SI Boltzmann and Avogadro constants. Equipartition energy includes the declared f modes, while three-dimensional translational RMS speed depends on 3 rather than f; update all three captured RMS inverse branches with the corresponding 3/f relation. The classical three-dimensional ideal-gas model requires positive absolute temperature, molar mass, amount and corresponding energies/speed, and a whole quadratic-mode count including at least three translational degrees of freedom. Zero endpoints are excluded because captured inverse relationships divide by these quantities.