Thermal energy

Thermal energy is a form of energy that manifests itself as an increase of temperature. It is also the sum of sensible heat and latent heat.

Definitions

The thermal energy of a single particle in a thermal bath is:

$U_{thermal}=f\cdot {\tfrac {1}{2}}kT.$

where f refers to the degrees of freedom, T refers to the temperature, and k to Boltzmann's constant. For example, a monatomic particle in an ideal gas has three degrees of freedom, and thus,

$U_{thermal,monatomic}={\tfrac {3}{2}}kT.$

The total thermal energy is the sum of the thermal energies of all particles in the system. Thus, for a system of N particles,

$U_{thermal}=N\cdot f\cdot {\tfrac {1}{2}}kT.$

Note that U_thermal is rarely the total energy of a system; for instance, there can be static energy that doesn't change with temperature, such as potential energy, bond energy or rest energy (E=mc²).

History of the term

The term was first used explicitly by James Joule, who studied the relationship between heat, work, and temperature. He observed that if he did mechanical work on a fluid such as water, by agitating the fluid, its temperature increased. He proposed that the mechanical work he was doing on the system was converted to "thermal energy." Specifically, he found that 4200 joules of energy were needed to raise the temperature of a kilogram of water by one degree Celsius.

Thermal energy in an ideal gas

Thermal energy is most easily defined in the context of an ideal gas. In a monatomic ideal gas, the thermal energy is exactly given by the kinetic energy of the constituent particles.

Other definitions

Thermal energy per particle is also called the average translational kinetic energy possessed by free particles given by equipartition of energy.

Thermal energy is the difference between the internal energy of an object and the amount that it would have at absolute zero. It includes the quantity of kinetic energy due to the motion of the internal particles of an object, and is increased by heating and reduced by cooling.

See also

• Geothermal power
• Enthalpy
• Entropy
• Heat transfer
• Ocean thermal energy conversion
• Radiation
• Thermal efficiency
• Thermal science