Temperature is a measure of the average kinetic energy of molecules. Each degree of freedom carries ½k_BT of energy: 3 for single atoms, 5 for diatomic molecules like N₂ and O₂ at room temperature.
How to use the Thermal Energy Calculator
- Temperature T
- Amount n (mol)
- Molar mass M (g/mol)
- Molecule type (degrees of freedom)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the temperature, amount of gas, molar mass and choose the molecule type.
Tips
- Use absolute temperature (K) in gas laws and efficiency formulas.
- Temperature differences are the same in K and °C.
- Heat = mass × specific heat × temperature change when no phase change occurs.
- Phase changes need latent heat at a constant temperature.
Common mistakes to avoid
- Using °C in pV = nRT.
- Forgetting latent heat during melting or boiling.
- Confusing heat capacity (J/K) with specific heat (J/(kg·K)).
Inputs explained
| Field | What to enter |
|---|---|
| Temperature T | Units: K, °C, °F |
| Amount n (mol) | A number |
| Molar mass M (g/mol) | A number |
| Molecule type (degrees of freedom) | Choose one: Monatomic (f = 3), Diatomic (f = 5), Polyatomic (f = 6) |
What each result means
- Average energy per molecule = [Molecule type (degrees of freedom)]÷2×1.380649[Average energy per molecule]-23×[Temperature T]
- Average translational KE = 1.5×1.380649[Average energy per molecule]-23×[Temperature T]÷1.602176634[Average energy per molecule]-19×1000
- Total thermal energy = [Molecule type (degrees of freedom)]÷2×[Amount n (mol)]×8.314462618×[Temperature T]
- RMS speed = sqrt(3×8.314462618×[Temperature T]÷([Molar mass M (g÷mol)]÷1000))
Example values
How the main result changes when Temperature T changes and everything else stays at the example values above:
| Temperature T (K) | Total thermal energy (J) |
|---|---|
| 150 | 3,117.9235 |
| 225 | 4,676.8852 |
| 300 | 6,235.847 |
| 375 | 7,794.8087 |
| 450 | 9,353.7704 |
| 600 | 12,471.6939 |
Formula
ε̄ = (f/2)·k_B·T, U = (f/2)·n·R·T, v_rms = √(3RT/M)Worked example
Inputs — Temperature T: 300 K; Amount n (mol): 1; Molar mass M (g/mol): 28.965; Molecule type (degrees of freedom): Diatomic (f = 5).
Results — Average energy per molecule = 1.0355e-20 J; Average translational KE = 38.778 meV; Total thermal energy = 6,235.84696 J; RMS speed = 508.27831 m/s.
Key terms
- Equipartition
- Equal sharing of energy among degrees of freedom.
Frequently asked questions
What is the equipartition theorem?
Each quadratic degree of freedom has ½k_BT of energy on average.
Why do diatomic molecules have 5 degrees of freedom?
3 translational + 2 rotational (vibrations are frozen at room temperature).
Is thermal energy the same as heat?
No – heat is energy transferred; thermal energy is stored.
How much thermal energy is in 1 mol of air?
About 6.2 kJ at 300 K.
What formula does the Thermal Energy Calculator use?
ε̄ = (f/2)·k_B·T, U = (f/2)·n·R·T, v_rms = √(3RT/M).