Heat (thermal energy): definition, transfer, measurement, and uses

The physical technical term of heat differs significantly from the colloquial use of the word "heat". In everyday language, it usually refers to the property of a body that makes it "warm" and thus describes a certain state. This is best expressed physically by the term thermal energy. For historical reasons, the word "heat" is also used in this sense in numerous technical terms (e.g. heat capacity, heat content, etc.).

The quantity referred to as "heat" in physics is not a state quantity. Rather, it is used to describe processes in which the state of the system changes. Consequently, it is a process variable. According to the first law of thermodynamics, the change in the internal energy of any system is equal to the sum of the heat supplied and the work done on the system. Conversely, this means that the heat supplied exactly equal to the increase in internal energy Δ minus the work done : . How much energy is transferred in total depends only on the initial and final state; however, the division into work and heat can be different - depending on the definition of the limits of the physical system and the course of the process.

Since energy is a conservation variable, heat and work cannot arise in the system itself, but describe the transport of energy across the system boundaries. If only two systems are involved in the process, then one system gives off exactly as much work and exactly as much heat as the other takes in. Therefore, the quantities heat, work, and change in internal energy have the same values for both systems, only with opposite signs. A process in which no heat is transferred is called adiabatic. A process in which only heat is transferred is sometimes called work-tight, an example being the isochoric change of state of a gas.

When two systems exchange heat, it always flows from the high to the low temperature. Often the lower temperature increases and the higher temperature decreases, but there are also exceptions, e.g. when ice at 0 °C is converted into water at 0 °C by adding heat.

A machine that continuously or periodically absorbs heat and performs work is called a heat engine. For reasons of principle, the energy absorbed by heat cannot be completely released again as work, but must be partially dissipated again as waste heat (for more details, see the 2nd law of thermodynamics).

In the basic explanation of thermodynamic phenomena by statistical mechanics, every system consists of a multitude of individual particles in more or less ordered motion. Heat is exclusively linked to the proportion of disordered motion. If a radiation field belongs to the system under consideration, heat refers to the energy that is distributed in a disordered manner among the various possible waveforms (see thermal radiation). In the energy level picture, the particles are distributed among all the different levels and alternate between them in a statistically fluctuating manner, but in the equilibrium state the average occupation number of each level remains the same and is fixed in the form of a statistical distribution. Addition of heat shifts this distribution curve to higher energy, while work done on the system raises the energies of the individual energy levels.

As far as the technical-scientific field is concerned, "heat" is and was colloquially used, on the one hand, as an expression of an elevated temperature, and on the other hand, for the associated energies and energy flows, which were initially referred to as heat quantity. The distinction between the two aspects was already prepared by the nominalists in the 14th century, i.e. before the beginning of the modern natural sciences. With regard to temperature, reliable thermometers were developed in the 17th and 18th centuries. The amount of heat, however, was only considered more closely after the equilibrium temperatures after mixing substances of different initial temperatures were investigated with the help of calorimeters from 1750 onwards. The quantity of heat later acquired its own physical dimension with the unit calorie, defined in the form (but modified several times): "1 calorie is the supply of heat that raises the temperature of 1 g of water by 1 °C." This resulted in a law of conservation ("heat given off = heat taken in"), which is still valid today, provided no work is done.

Until about 1850, there were two opposing doctrines on the interpretation of what heat was: One explanation was based on a hypothetical "heat substance", to which Antoine de Lavoisier gave the name calorique (caloricum). The heat substance is immortal, uncreatable, imponderable, permeates every piece of matter and determines its "heat content" through its quantity and its temperature through its concentration. The expressions "heat quantity", "heat energy" and "specific heat" originate from the environment of this heat substance theory. On the other hand, a mechanical theory of heat was proposed as early as the 13th century by Roger Bacon and, from the 17th century, by Johannes Kepler, Francis Bacon, Robert Boyle, Daniel Bernoulli and others: heat was a movement of small particles of matter hidden from the eyes. In fact, in 1798, Benjamin Thompson (later Lord Rumford) observed, while drilling cannon barrels, that drilling produced heat in any quantity by mechanical work alone. Thompson could even have estimated the approximate value of the mechanical heat equivalent from this. However, a precise measurement was only achieved by James Prescott Joule around 1850.

The fact that heat, conversely, can also be a source of mechanical work had been known since the beginning of the 18th century through the first steam engines. The attempts at explanation within the framework of the theory of heat culminated in 1824 in the realization by Sadi Carnot that the work to be gained from the supply of heat is limited for reasons of principle, because the heat absorbed at a high temperature must be released again at a low temperature. In this case, the ideal efficiency that can be achieved does not depend on the design of the machine, but solely on the two temperatures, and is always less than 100%. Carnot argued entirely on the basis of the theory of thermal materials, but also gave a value for the mechanical heat equivalent, but his writings were initially forgotten.

Decisive for the refutation of the heat theory was the insight published by Rudolf Clausius in 1850 that the relationship between heat and work involves mutual transformation, i.e. heat is consumed when work is gained and vice versa. In the transformation of work into heat, Clausius relied on the aforementioned observation of Thompson and other findings on frictional heat. In the transformation of heat into work, he relied on the increased heat requirement when a gas is heated, if it can also expand in the process, and on a key experiment carried out by Joule in 1844: Compressed air performs mechanical work when it expands, precisely when it extracts heat from its surroundings, i.e. cools them down. This enabled the mechanical theory of heat to finally prevail.

The realization that heat is energy paved the way for the law of conservation of energy, which Hermann von Helmholtz formulated in general terms for the first time in 1847. In the further development of the concept of heat, the concept of energy moved to the centre.

Despite the refutation of the heat-matter theory, Carnot's discovery that the extraction of work from heat is limited by the temperature difference remained valid. Rudolf Clausius succeeded in deriving from this the concept of another quantity-like quantity which must always flow when heat is transferred. In 1865 he called this quantity entropy. In many ways, entropy corresponds to the caloricum postulated in the theory of heat. However, the law of conservation assumed at the time for the caloricum does not apply to entropy: entropy cannot be destroyed, but it can be created. For example, this happens in heat conduction from high to low temperature.

Heat does not correspond to a special form of energy, but to the property of transporting entropy. Today's definition of heat, which also corresponds to the definition given in the introduction above, no longer refers to temperature changes or substance transformations, but is based entirely on the concept of energy. It was formulated by Max Born in 1921, after Constantin Carathéodory had put thermodynamics into an axiomatic form in 1909. According to this, the actual definition of heat lies in the 1st law of thermodynamics (see below) and reads: If work is performed on a macroscopic system in a process, and its internal energy changes in the process by Δ then the difference is the heat that was transferred into the system.

The two quantities of heat and work are not as independent of each other as they might appear at first glance: If, for example, heat is added to the air in a balloon, this does not manifest itself exclusively in an increase in temperature and entropy. The balloon inflates, its volume increases. Thus the gas also performs work (against the ambient pressure and against the elasticity of the rubber envelope) as a result of the heat input. Conversely, external work can also have an indirect influence on the internal parameters of the system. For example, when you knead a dough, you are obviously doing work. Due to internal friction, this causes the temperature of the dough to increase and also its entropy. The work was dissipated in this process. It did lead to an increase in the internal energy of the dough, but it has the same effect as added heat. Therefore, it can no longer be extracted from the dough in the form of work. This process is therefore irreversible.

In the international system of units, the special heat unit calorie was abolished in 1948 and replaced by the general unit joule for energy.