# Thermal Energy Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Adena Benn
Last updated: Jun 05, 2023

Our thermal energy calculator is a handy tool that can characterize ideal gas parameters, such as the average kinetic energy of molecules, the average velocity of molecules, or the total thermal energy of gas. The kinetic molecular theory explains the behavior of gases, which describes a gas as a large number of atoms or molecules in constant motion. Those particles can collide with each other and with the walls of the container.

Read on if you want to know more about the kinetic molecular theory definition and find out what the relationship is between temperature and kinetic energy. In the text below, we have explained:

• What is thermal energy (the thermal energy definition); and
• The thermal energy equation.

## Kinetic molecular theory definition

The kinetic molecular theory states that gas pressure is caused by the impacts of molecules on the walls of a container. These molecules collide with each other, thus changing their velocities. The kinetic molecular theory definition is formulated under certain assumptions:

• A gas consists of particles of the same mass and negligible size compared to the average distance between particles.
• Particles are in constant, chaotic motion. Interactions among molecules are negligible, except during collisions between particles which are perfectly elastic. Check our conservation of momentum calculator to learn about different types of collisions.
• The average kinetic energy of the gas particles depends only on the temperature of the gas. The time of collision is very short compared to the time between collisions.

These assumptions are approximately met for gases at not-too-high pressures and not-too-low temperatures.

## Thermal energy definition

Thermal energy is the internal kinetic energy that arises due to the random motion of molecules. Each molecule has a different velocity (that changes after collisions) which can be described by the Maxwell-Boltzmann distribution. We have written more about it in our particle velocity calculator, where you can also compute the average velocity of the particles at a specific temperature. The total thermal energy of a gas is given by the sum of the kinetic energies of all the particles.

It would be best if you remembered that it is a mistake to equate thermal energy with heat. Heat, like work, is a way to transfer energy. And if we want to answer the question of what thermal energy is, we can say that it is an internal property of a system.

## Thermal energy equation

What is the relationship between temperature and kinetic energy in ideal gas? You can find an answer to that question with our thermal energy calculator, which can compute the average kinetic energy of particles, the average velocity of particles, and the total thermal energy of a gas. It uses the following formulas:

KE = f × k × T / 2

v = √(2 × KE × Na / M)

U = n × Na × KE

where

• KE is the average kinetic energy of molecules,
• v is the average velocity of molecules,
• U is the total thermal energy of a gas,
• f is the number of degrees of freedom,
• T is the temperature,
• M is the molar mass of the gas,
• n is the number of moles),
• k is the Boltzmann constant k = 1.38064852 × 10^(-23) J/K,
• Na is the Avogadro constant Na = 6.022140857 × 10^23 1/mol.

The number of degrees of freedom is a physical parameter that is necessary to characterize the state of a physical system. In our thermal energy calculator, we assumed it equals 3, which is true for a monoatomic gas. If you want to change it, go to the advanced mode.

Do you want to estimate other parameters of an ideal gas? Check our ideal gas law calculator to find out what the relation is between temperature, pressure, and volume of gas.

Dominik Czernia, PhD
Molar mass
g/mol
Temperature
K
Moles of gas
mol
Average kinetic energy
meV
Average speed
ft/s
Total thermal energy
J
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