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Mean kinetic energy of a gas atom calculator

A-level Thermal physics and gases

The average translational kinetic energy of an atom in an ideal gas depends only on the temperature.

E = (3 / 2) kB T

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

6.21 × 10−21 J
J/K

Working

  1. Write the equation
    E = (3 / 2) kB T
  2. Constants used
    kB = 1.38 × 10−23 J/K
  3. Substitute the values
    E = (3 ÷ 2) × (1.38 × 10−23) × 300
  4. Calculate
    E = 6.21 × 10−21 J
  5. Give the answer to 3 significant figures
    E = 6.21 × 10−21 J

Worked example

Find E, the mean kinetic energy of an atom. Given: temperature T = 300 K; Boltzmann constant kB = 1.38 × 10⁻²³ J/K.

  1. Write the equation
    E = (3 / 2) kB T
  2. Constants used
    kB = 1.38 × 10−23 J/K
  3. Substitute the values
    E = (3 ÷ 2) × (1.38 × 10−23) × 300
  4. Calculate
    E = 6.21 × 10−21 J
  5. Give the answer to 3 significant figures
    E = 6.21 × 10−21 J

Symbols and units

SymbolQuantitySI unit
EMean kinetic energy of an atomJ
kBBoltzmann constant (constant)J/K
TTemperatureK

Mean kinetic energy of a gas atom: rearranged

  • To find mean kinetic energy of an atom: E = (3 / 2) kB T
  • To find temperature: T = 2E / (3kB)

Exam tip

Temperature in kelvin. The result is the energy of a single atom, so it is very small.

Common questions

What is the formula for mean kinetic energy of a gas atom?

The equation is E = (3 / 2) kB T, where E is the mean kinetic energy of an atom (J); T is the temperature (K); kB is the Boltzmann constant (J/K).

What units should I use for mean kinetic energy of a gas atom?

In SI units: mean kinetic energy of an atom in J, Boltzmann constant in J/K, temperature in K. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange E = (3 / 2) kB T?

Rearranging gives these forms: to find mean kinetic energy of an atom: E = (3 / 2) kB T. to find temperature: T = 2E / (3kB).

Practise mean kinetic energy of a gas atom questions

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Related

More thermal physics and gases equations: Specific heat capacity, Specific latent heat, Ideal gas equation, Boyle’s law, Gas equation with molecules, Stefan–Boltzmann law, Wien’s law. See the full list on the a-level physics equation calculator page.