Library / Foundations: Physics / FPH-50
Foundations: Physics
Mean translational kinetic energy per molecule
Average energy of translation of one molecule of an ideal gas, which depends only on the absolute temperature.
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- FPH-50
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- Foundations: Physics
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- Ē [J]
For an ideal gas each molecule has, on average, 3/2 kBT of translational kinetic energy, with kB = 1.381 × 10−23 J/K the Boltzmann constant and T the absolute temperature. It depends only on temperature, not on the mass of the molecule. It is the translational energy only, not the total internal energy of a gas whose molecules can also rotate and vibrate.
Average energy of translation of one molecule of an ideal gas, which depends only on the absolute temperature. It is not the total internal energy of a gas whose molecules can rotate or vibrate.
Calculator
- Energy in electronvolts, E/e0.03878 eV
- Energy per mole, 3/2 RT3.742 kJ/mol
- Thermal voltage kBT/e25.85 mV
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At 300 K each molecule carries on average 6.213×10−21 J (0.0388 eV) of translational energy, a tiny amount but enough to give nitrogen molecules 517 m/s.
- Doubling the absolute temperature doubles the energy (to 1.243×10−20 J). A chemical bond takes roughly 1 to 10 eV, tens to hundreds of times this amount, which is why most molecules survive collisions at room temperature.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (J) | Local step | Change in result |
|---|---|---|---|---|---|---|
| T Absolute temperature | 10 to 10,000 K | 2.071e-22 | 2.071e-19 | 2.069e-19 | +10% | +10 % |
Sweep of Absolute temperature
| Absolute temperature (K) | Mean translational energy (J) |
|---|---|
| 10 | 2.071e-22 |
| 23.71 | 4.911e-22 |
| 56.23 | 1.165e-21 |
| 133.4 | 2.762e-21 |
| 316.2 | 6.549e-21 |
| 749.9 | 1.553e-20 |
| 1,778 | 3.683e-20 |
| 4,217 | 8.733e-20 |
| 10,000 | 2.071e-19 |
Sweep one variable
Variables and how each one contributes
Mean translational energy
What the equation gives you. Everything else feeds it.
Absolute temperature
The absolute temperature of the gas, in kelvin. Raises the energy in direct proportion to T. Raising it by 25 K (to 325 K) moves the result by +8.33 %, from 6.213×10−21 to 6.731×10−21 J.
Worked example with the values above
- Boltzmann constant: kB = 1.381 × 10−23 J/K.
- Multiply: 3/2 × 1.381 × 10−23 × 300 K.
- E = 6.213×10−21 J.
Assumptions and limits
- An ideal gas in thermal equilibrium at a single absolute temperature.
- Translational energy only; rotation and vibration are extra for molecules.
Common mistakes
- Using degrees Celsius for T.
- Quoting it as the total internal energy of a diatomic gas.
Statistics and uncertainty
This is the average over a huge number of molecules; individual molecules have energies spread over a wide range (the Maxwell–Boltzmann distribution), and a few have many times the mean.
Where it is used
- Linking temperature to molecular energy.
- Comparing thermal energy with the energy needed for chemical and nuclear processes.
Maths you need
- Ideal gas: molecules with negligible size and no attraction
- Absolute temperature: kelvin scale, starting at absolute zero