# Thermal Energy Calculator

Our thermal energy calculator can find the thermal energy of an ideal gas based on a few parameters from kinetic molecular theory.

We've paired this calculator with a short text covering:

- What is
**thermal energy**; **How to calculate thermal energy**for an ideal gas;- Relationship between
**kinetic energy**and**thermal energy**for an ideal gas; and **More about thermodynamics**.

Keep reading to learn more!

## Kinetic molecular theory postulates

We can derive all the definitions used in this text from the **kinetic molecular theory**, which states:

- Gases consist of a large number of particles (atoms or molecules) in
**constant random motion**; - The size of these particles is
*negligible*compared to the average distance between them; - The collisions between particles themselves or with the walls of the container are
**perfectly elastic**; and - The particles exert
**no force**on one another except during collisions.

Let's now take a look at the thermal energy definition.

## What is thermal energy?

**Thermal energy** is the part of the *internal energy* of a system associated with the **random motion of molecules.**

For an **ideal gas**, its thermal energy is proportional to the *average* *kinetic energy* of its molecules. Therefore, gas at higher temperatures will possess greater internal energy.

## Thermal energy equation

For a **monoatomic gas with three degrees of freedom**, the average kinetic energy of its atoms will be:

where:

- $k_{B}$ is
**Boltzmann's constant**, $k_{B} = 1.38064852 * 10^{-23}\ \text{J/K}$; - $T$ is the temperature;
- $KE$ is the average kinetic energy of its atoms.

🙋 You can change the degrees of freedom number in the `advanced-mode`

of this thermal energy calculator

And we can relate this formula to thermal energy in the **thermal energy equation**:

where:

- $n$ is the number of moles;
- $N_{A}$ is
**Avogadro constant**, $N_{A} = 6.02214076×10^{23}\ \text{mol}^{−1}$; and - $U$ is the thermal energy of the gas.

### Average velocity of particles

Our thermal energy calculator also allows you to input the average velocity of particles derived from this equation:

where $M$ is the molar mass of the gas.