In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than thermodynamic work or transfer of matter. Heat refers to a quantity transferred between systems, not to a property of any one system, or 'contained' within it. On the other hand, internal energy is a property of a single system. Heat and work depend on the way in which an energy transfer occurred, whereas internal energy is a property of the state of a system and can thus be understood without knowing how the energy got there. In a statistical mechanical account of an ideal gas, in which the molecules move independently between instantaneous collisions, the internal energy is the sum total of the gas's independent particles' kinetic energies, and it is this kinetic motion that is the source and the effect of the transfer of heat across a system's boundary. For a gas that does not have particle interactions except for instantaneous collisions, the term 'thermal energy' is effectively synonymous with 'internal energy'. In many statistical physics texts, "thermal energy" refers to kT |, the product of Boltzmann's constant and the absolute temperature, also written as. In a material, especially in condensed matter, such as a liquid or a solid, in which the constituent particles, such as molecules or ions, interact strongly with one another, the energies of such interactions contribute strongly to the internal energy of the body, but are not simply apparent in the temperature. The term 'thermal energy' is also applied to the energy carried by a heat flow, although this can also simply be called heat or quantity of heat.
Historical context
In an 1847 lecture titled "On Matter, Living Force, and Heat", James Prescott Joule characterised various terms that are closely related to thermal energy and heat. He identified the terms latent heat and sensible heat as forms of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively. He described latent energy as the energy of interaction in a given configuration of particles, i.e. a form of potential energy, and the sensible heat as an energy affecting temperature measured by the thermometer due to the thermal energy, which he called the living force.
Useless thermal energy
If the minimum temperature of a system's environment is and the system's entropy is, then a part of the system's internal energy amounting to cannot be converted into useful work. This is the difference between the internal energy and the Helmholtz free energy.
