Internal energy

In a nutshell

The internal energy of a system is defined as the sum of the kinetic and potential energies of all its particles. The temperature of a substance does not change while its phase is changing.

Equations

description	equation
Internal energy	$U=E_k+E_p$

Variable definitions

quantity name	symbol	derived units	si base units
$internal\ energy$	$U$	$J$	$kg\ m^2\ s^{-2}$
$kinetic\ energy$	$E_k$	$J$	$kg\ m^2\ s^{-2}$
$potential\ energy$	$E_p$	$J$	$kg\ m^2\ s^{-2}$

Internal energy

Internal energy is defined as the sum of the random distribution of the kinetic and potential energies associated with the molecules of a system. It can be expressed as an equation:

$U=E_k+E_p$

The higher the temperature, the higher the internal energy of a system, as kinetic energy increases. As temperature decreases, the particles move less and they become completely immobile at absolute zero.

Absolute zero or $0\ K$ is the lowest possible temperature and it is the point at which the internal energy is at a minimum. Kinetic energy is zero but potential energy is still stored between the particles.

Changing phases

When adding energy to a substance its kinetic energy increases, however when a phase change occurs the potential energy increases instead.

When reaching its melting or boiling point, the temperature of a substance does not increase as all the energy is transferred to the electrostatic potential energy which causes changes in the electrostatic forces holding the particles together.

This is better shown through state change graphs:

Physics; Thermal physics; KS5 Year 12; Internal energy

A	Temperature
B	Time
1.	Boiling point
2.	Melting point
3.	Gas
4.	Vaporisation
5.	Liquid
6.	Fusion
7.	Solid

As the substance reaches its melting or boiling point, the temperature stops increasing until the phase change is completed.

Electrostatic potential energy in different phases

Particles have different electrostatic potential energies depending on their phase:

Solids- the electrostatic potential energy between molecules has a large negative value, due to large electrostatic forces.
Liquids- the electrostatic potential energy between molecules has a moderate negative value, as energy is still required to break bonds.
Gases- the electrostatic potential energy is zero due to the large distances between molecules.

Therefore, the electrostatic forces decrease when going from solids $\rightarrow$ liquid $\rightarrow$ gases, but the electrostatic potential energy increases.