Thermodynamics
Average Kinetic Energy (Gas)
Average translational KE of gas molecule.
Variables
KEavgJ
Average KE per molecule
Mean kinetic energy
In SI units: kg·m²/s²
Allowed values: greater than 0
kBJ/K
Boltzmann constant
1.38×10⁻²³
In SI units: kg·m²/(s²·K)
Allowed values: greater than 0
TK
Temperature
Absolute temperature
Allowed values: greater than 0
Derivation
From equipartition: ½kT per DoF × 3 translational DoF.
Your notes
0/5000
Constants in this formula
Check value
Round inputs run through this page's calculator, with each constant at its tabulated value. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.
- kB = 1.380 649 × 10⁻²³ J/K (Boltzmann constant)
- T = 2 K (Temperature)
Result: KEavg = 4.141947 × 10⁻²³ J
Other thermodynamics formulas with the same quantities
- Ideal Gas Law (Molecular) (Kinetic Theory) shares Boltzmann constant, Temperature
- Mean Free Path (Kinetic Theory) shares Boltzmann constant, Temperature
- Most Probable Speed (Kinetic Theory) shares Boltzmann constant, Temperature
- Mean Speed (Kinetic Theory) shares Boltzmann constant, Temperature
- Stefan-Boltzmann Law (Heat & Temperature) shares Temperature
- Work (Isothermal Process) (First Law) shares Temperature
Where this formula is listed
- Thermodynamics formulas, under Kinetic Theory, alongside Pressure (Kinetic Theory).
- In the thermodynamics list it comes after Ideal Gas Law (Molecular) and before Root Mean Square Speed.
- Thermodynamics formula sheet, one of 34 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Average Kinetic Energy (Gas) formula?
Average Kinetic Energy (Gas) is written KE_avg = (3/2)k_B T. Average translational KE of gas molecule. It belongs to Thermodynamics, under Kinetic Theory.
What are the units in KE_avg = (3/2)k_B T?
In SI units, KE_a vg is average ke per molecule, measured in kg·m²/s²; k_B is boltzmann constant, measured in kg·m²/(s²·K); T is temperature, measured in K.
How is the Average Kinetic Energy (Gas) formula derived?
From equipartition: ½kT per DoF × 3 translational DoF. The result is KE_avg = (3/2)k_B T.