Calculator Inputs
Plotly Graph
The chart compares per-particle energy and per-mole energy against temperature in kelvin.
Formula Used
Average kinetic energy per particle = (3/2) × kB × T
Average kinetic energy per mole = (3/2) × R × T
Here, kB is the Boltzmann constant, R is the gas constant, and T must be in kelvin.
For custom totals, multiply the per-particle value by particle count, or multiply the per-mole value by the chosen number of moles.
How to Use This Calculator
- Enter the temperature value.
- Choose kelvin, Celsius, or Fahrenheit.
- Select whether you need per-particle, per-mole, or total energy.
- Enter particle count or moles when required.
- Choose the output unit and decimal precision.
- Set a chart range for temperature analysis.
- Press Calculate to view results above the form.
- Use the export buttons to save CSV or PDF output.
Example Data Table
| Temperature (K) | Per Particle Energy (J) | Per Particle Energy (eV) | Per Mole Energy (kJ/mol) |
|---|---|---|---|
| 100 | 2.070974e-21 | 0.012926 | 1.247169 |
| 200 | 4.141947e-21 | 0.025852 | 2.494339 |
| 300 | 6.212921e-21 | 0.038778 | 3.741508 |
| 500 | 1.035487e-20 | 0.064630 | 6.235847 |
| 1000 | 2.070974e-20 | 0.129260 | 12.471694 |
Frequently Asked Questions
1. What equation does this calculator apply?
It uses the translational ideal-gas relation: average kinetic energy per particle equals (3/2)kBT. For per-mole values, it uses (3/2)RT.
2. Why is kelvin important in this calculation?
Kelvin starts at absolute zero, which matches the physics formula directly. Celsius and Fahrenheit are converted first, then the energy is calculated.
3. Does particle mass change the average kinetic energy?
No. At the same temperature, average translational kinetic energy depends on temperature, not directly on particle mass. Mass affects speed, not this average energy expression.
4. Can I enter Celsius or Fahrenheit values?
Yes. The calculator accepts kelvin, Celsius, and Fahrenheit. It automatically converts the chosen unit into kelvin before applying the energy formula.
5. What is the difference between per-particle and per-mole results?
Per-particle energy describes one atom or molecule. Per-mole energy describes Avogadro’s number of particles together. Both come from the same temperature-based relationship.
6. Is this exact for real gases?
It is most accurate for ideal translational behavior. Real gases can deviate because of interactions, quantum effects, or additional molecular energy modes.
7. Why does the electronvolt result look very small?
Electronvolts are microscopic energy units. Individual particles carry tiny energies, so eV values often appear small yet remain physically meaningful.
8. Can I export the output for reports?
Yes. After calculation, use the CSV button for spreadsheet-friendly data, or the PDF button for a compact report you can store or share.