Thermal Energy Calculator
Calculate average kinetic energy, molecular velocity, and total thermal energy of gas particles using kinetic molecular theory
Calculate Thermal Energy
Select a gas from the database or choose 'Custom' to enter manual values
Temperature of the gas system
Molecular weight of the gas
Amount of gas in moles for total thermal energy calculation
Default: 3 (monoatomic gas). Diatomic: 5, Polyatomic: 6
Thermal Energy Results
Formulas used:
• Average kinetic energy: KE = f × k × T / 2
Constants: k = 1.381 × 10⁻²³ J/K, Na = 6.022 × 10²³ mol⁻¹
Gas Analysis
Example Calculation
Nitrogen Gas at Room Temperature
Gas: Nitrogen (N₂)
Temperature: 298.15 K (25°C)
Molar mass: 28.014 g/mol
Degrees of freedom: 5 (diatomic)
Amount: 1.0 mol
Results
KE = 5 × 1.381×10⁻²³ × 298.15 / 2 = 1.03×10⁻²⁰ J
KE = 64.5 meV
v = √(2 × 1.03×10⁻²⁰ × 6.022×10²³ / 0.028014) = 515 m/s
U = 1.0 × 6.022×10²³ × 1.03×10⁻²⁰ = 6.20 kJ
Kinetic Molecular Theory
Particle Motion
Gas particles are in constant random motion
Elastic Collisions
Collisions conserve kinetic energy
Temperature Relation
Average kinetic energy ∝ temperature
Degrees of Freedom
f = translational + rotational + vibrational modes
Physics Tips
Thermal energy is internal kinetic energy
Higher temperature = faster molecular motion
Lighter gases move faster at same temperature
Thermal energy ≠ heat (energy transfer)
Understanding Thermal Energy
What is Thermal Energy?
Thermal energy is the internal kinetic energy that arises from the random motion of molecules and atoms in a substance. It's directly related to temperature and represents the sum of kinetic energies of all particles in a system.
Key Concepts
- •Average kinetic energy depends only on temperature
- •Molecular velocity depends on mass and temperature
- •Total thermal energy depends on amount of substance
- •Degrees of freedom affect energy distribution
Mathematical Framework
KE = f × k × T / 2
v = √(2 × KE × Na / M)
U = n × Na × KE
- KE: Average kinetic energy per molecule
- v: Average molecular velocity
- U: Total thermal energy of the gas
- f: Degrees of freedom
- k: Boltzmann constant
- T: Absolute temperature
- Na: Avogadro's number
- M: Molar mass
- n: Number of moles
Maxwell-Boltzmann Distribution
The Maxwell-Boltzmann distribution describes the distribution of molecular velocities in a gas. While individual molecules have different velocities that change after collisions, the average kinetic energy remains constant at a given temperature. This statistical approach allows us to calculate macroscopic properties from molecular-level behavior.
Most Probable Speed
v_mp = √(2kT/m)
Average Speed
v_avg = √(8kT/πm)
RMS Speed
v_rms = √(3kT/m)