# Thermal energy

Thermal energy (also heat energy , but not to be confused with heat ) is a collective name for macroscopic and microscopic forms of energy, which refer to the disordered movement of particles (including photons) in macroscopic matter or in other many-particle systems. The macroscopic forms of energy include internal energy , heat and enthalpy . The microscopic forms of energy include the mean energy of a particle per degree of freedom (i.e. for translation in one direction, etc., where the absolute temperature and the Boltzmann constant is), or the size of the typical random energy exchange between the particles , which also occurs in the Boltzmann distribution sets the energy standard. ${\ displaystyle {\ tfrac {1} {2}} k _ {\ mathrm {B}} T}$${\ displaystyle T}$${\ displaystyle k _ {\ mathrm {B}}}$${\ displaystyle k _ {\ mathrm {B}} T}$

## Relationship with temperature

Colloquially, the thermal energy is somewhat imprecisely referred to as " heat " or "thermal energy" or is confused with the temperature.

In fact, in an ideal gas, the (macroscopic) thermal energy is equal to the internal energy and is therefore proportional to the absolute temperature .

${\ displaystyle E _ {\ mathrm {th}} = {\ frac {f} {2}} \, N \, k _ {\ mathrm {B}} \, T = {\ frac {f} {2}} \ , n \, R \, T}$

with the number of degrees of freedom , the number of particles and the Boltzmann constant or alternatively with the amount of substance and the gas constant . The specific heat capacity for ideal gases is independent of the temperature. ${\ displaystyle f}$ ${\ displaystyle N}$ ${\ displaystyle k _ {\ mathrm {B}}}$ ${\ displaystyle n}$ ${\ displaystyle R}$ ${\ displaystyle c = {\ frac {f} {2}} R}$

In the general case, however, it is a function of temperature , so that the thermal energy is not simply proportional to the temperature . ${\ displaystyle c = c (T)}$${\ displaystyle \ Rightarrow E _ {\ mathrm {th}} \ propto \! \! \! \! \! \! / \; \; T}$

During a phase transition , the thermal energy of a body can even change without a temperature change occurring. An example that illustrates the relationship between heat and temperature is a melting process . If ice has a temperature of 0 ° C, its thermal energy must be increased in order to melt it. To do this, heat must be supplied. However, the temperature does not rise during the melting process , since all the heat supplied is required for the phase transition from solid to liquid ( heat of fusion ).