# Heat

In physics, heat, symbolized by Q, is defined as energy in transit. Generally, heat is a form of energy transfer associated with the different motions of atoms, molecules and other particles that comprise matter when it is hot and when it is cold. High temperature bodies, which often result in high heat transfer, can be created by chemical reactions (such as burning), nuclear reactions (such as fusion taking place inside the Sun), electromagnetic dissipation (as in electric stoves), or mechanical dissipation (such as friction). Heat can be transferred between objects by radiation, conduction and convection. Temperature, defined as the measure of an object to spontaneously give up energy, is used as a measure of the internal energy or enthalpy, that is the level of elementary motion giving rise to heat transfer. Heat can only be transferred between objects, or areas within an object, with different temperatures (as given by the zeroth law of thermodynamics), and then, in the absence of work, only in the direction of the colder body (as per the second law of thermodynamics).

## History

The first to have put forward a semblance of a theory on heat was the Greek philosopher Heraclitus who lived around 500 BC in the city of Ephesus in Ionia, Asia Minor. He became famous as the "flux and fire" philosopher for his proverbial utterance: "All things are flowing." Heraclitus argued that the three principle elements in nature were fire, earth, and water. Of these three, however, fire is assigned as the central element controlling and modifying the other two. The universe was postulated to be in a continuous state of flux or permanent condition of change as a result of transformations of fire. Heraclitus summarized his philosophy as: "All things are an exchange for fire."

As early as 460 BC Hippocrates, the father of medicine, postulated that:

 Heat, a quantity which functions to animate, derives from an internal fire located in the left ventricle.

The hypothesis that heat is a form of motion was proposed initially in the 12th century. Around 1600, the English philosopher and scientist Francis Bacon surmised that:

 Heat itself, its essence and quiddity is motion and nothing else.

This echoed the mid-17th century view of English scientist Robert Hooke, who stated:

 heat being nothing else but a brisk and vehement agitation of the parts of a body.

In 1761, Scottish chemist Joseph Black discovered that ice absorbs heat without changing temperature when melting. From this he concluded that the heat must have combined with the ice particles and become latent. Between 1759 and 1763 he evolved that theory of " latent heat" on which his scientific fame chiefly rests, and also showed that different substances have different specific heats. James Watt, who later invented the Watt engine, was Black's pupil and assistant.

In this direction, the ability to be able to use heat transfer to generate work allowed the invention and development of the steam engine by people such as Thomas Newcomen and James Watt. In addition, in 1797 a cannon manufacturer Sir Benjamin Thompson, Count Rumford, demonstrated through the use of friction it was possible to convert work to heat. To do this, he designed a specially shaped cannon barrel, thoroughly insulated against heat loss, then replaced the sharp boring tool with a dull drill bit, and immersed the front part of the gun in a tank full of water. Using this setup, to the amazement of his onlookers, he made cold water boil in two-and-half-hours time, without the use of fire.

Several theories on the nature of heat were developed. In the 17th century, Johann Becher proposed that heat was associated with an undetectable material called phlogiston that was driven out of a substance when it was burnt. This was finally refuted by Lavosier demonstrating the importance of oxygen in burning in 1783. He proposed instead the caloric theory which saw heat as a type of weightless, invisible fluid that moved when out of equilibrium. It was this theory used in 1824 by the French engineer Sadi Carnot when he published Reflections on the Motive Power of Fire. He set forth the importance of heat transfer: "production of motive power is due not to an actual consumption of caloric, but to its transportation form a warm body to a cold body, i.e. to its re-establishment of equilibrium." According to Carnot, this principle applies to any machine set in motion by heat.

Another theory was the kinetic theory of gases, the basis of which was laid out in 1738 by the Swiss physician and mathematician Daniel Bernoulli in his Hydrodynamica. In this work, Bernoulli first proposed that gases consist of great numbers of molecules moving in all directions, that their impact on a surface causes the gas pressure that we feel. The internal energy of a substance is then the sum of the kinetic energy associated with each molecule, and heat transfer occurs from regions with energetic molecules, and so high internal energy, to those with less energetic molecules, and so lower internal energy.

The work of Joule and Mayer demonstrated that heat and work were interchangeable, and led to the statement of the principle of the conservation of energy by Hermann von Helmholtz in 1847. Clausius demonstrated in 1850 that caloric theory could be reconciled with kinetic theory provided that the conservation of energy was employed rather than the movement of a substance, and stated the First Law of Thermodynamics.

## Overview

Under the First Law of Thermodynamics, heat (and work) are processes that change the internal energy of a substance or object. Heat is the transfer of energy over the boundary of a system owing to a temperature gradient. The SI unit for heat is the joule (as it is a form of energy), though the British Thermal Unit is still occasionally used in the United States.

Heat emanating from a red-hot iron rod.

Heat is a process quantity, as opposed to being a state quantity, and is to thermal energy as work is to mechanical energy. Heat flows between regions that are not in thermal equilibrium with each other; it spontaneously flows from areas of high temperature to areas of low temperature. All objects (matter) have a certain amount of internal energy, a state quantity that is related to the random motion of their atoms or molecules. When two bodies of different temperature come into thermal contact, they will exchange internal energy until the temperature is equalized; that is, until they reach thermal equilibrium. The amount of energy transferred is the amount of heat exchanged. It is a common misconception to confuse heat with internal energy: heat is related to the change in internal energy and the work performed by the system. The term heat is used to describe the flow of energy, while the term internal energy is used to describe the energy itself.

In common usage the term heat denotes the warmth, or hotness, of surrounding objects and is used to mean that an object has a high temperature. The concept that warm objects "contain heat" is not uncommon, but hot is nearly always used as a relative term (an object is hot compared with its surroundings or those of the person using the term) so that high temperature is directly associated with high heat transfer.

The amount of heat that has to be transferred to or from an object when its temperature varies by one degree is called heat capacity. Heat capacity is specific to each and every object or substance. When referred to a quantity unit (such as mass or moles), the heat exchanged per degree is termed specific heat, and depends primarily on the composition and physical state (phase) of an object. Fuels generate predictable amounts of heat when burned; this heat is known as heating value and is expressed per unit of quantity. Upon changing from one phase to another, pure substances can exchange heat without their temperature suffering any change. The amount of heat exchanged during a phase change is known as latent heat and depends primarily on the substance and the initial and final phase.

## Notation

The total amount of energy transferred through heat transfer is conventionally abbreviated as Q. The conventional sign convention is that when a body releases heat into its surroundings, Q < 0 (-); when a body absorbs heat from its surroundings, Q > 0 (+). Heat transfer rate, or heat flow per unit time, is denoted by:

$\dot{Q} = {dQ\over dt} \,\!$.

It is measured in watts. Heat flux is defined as rate of heat transfer per unit cross-sectional area, and is denoted q, resulting in units of watts per metre squared. Slightly different notation conventions can be used, which may denote heat flux as, for example, $\dot{Q}''$.

## Thermodynamics

Heat is related to the internal energy U of the system and work W done by the system by the first law of thermodynamics:

$\Delta U = Q - W \$

which means that the energy of the system can change either via work or via heat. The transfer of heat to an ideal gas at constant pressure increases the internal energy and performs boundary work (i.e. allows a control volume of gas to become larger or smaller), provided the volume is not constrained. Returning to the first law equation and separating the work term into two types, "boundary work" and "other" (e.g. shaft work performed by a compressor fan), yields the following:

$\Delta U + W_{boundary} = Q - W_{other}\$

This combined quantity ΔU + Wboundary is enthalpy, H, one of the thermodynamic potentials. Both enthalpy, H, and internal energy, U are state functions. State functions return to their initial values upon completion of each cycle in cyclic processes such as that of a heat engine. In contrast, neither Q nor W are properties of a system and need not sum to zero over the steps of a cycle. The infinitesimal expression for heat, δQ, forms an inexact differential for processes involving work. However, for processes involving no change in volume, applied magnetic field, or other external parameters, δQ, forms an exact differential. Likewise, for adiabatic processes (no heat transfer), the expression for work forms an exact differential, but for processes involving transfer of heat it forms an inexact differential .

The changes in enthalpy and internal energy can be related to the heat capacity of a gas at constant pressure and volume respectively. When there is no work, the heat , Q, required to change the temperature of a gas from an initial temperature, T0, to a final temperature, Tf depends on the relationship:

$Q = \int_{T_0}^{T_f}C_p\,dT \,\!$

for constant pressure, whereas at constant volume:

$Q = \int_{T_0}^{T_f}C_v\,dT \,\!$

For incompressible substances, such as solids and liquids, there is no distinction among the two expressions as they are nearly incompressible. Heat capacity is an extensive quantity and as such is dependent on the number of molecules in the system. It can be represented as the product of mass, m , and specific heat capacity, $c_s \,\!$ according to:

$C_p = mc_s \,\!$

or is dependent on the number of moles and the molar heat capacity, $c_n \,\!$ according to:

$C_p = nc_n \,\!$

The molar and specific heat capacities are dependent upon the internal degrees of freedom of the system and not on any external properties such as volume and number of molecules.

The specific heats of monatomic gases (e.g., helium) are nearly constant with temperature. Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more.

In liquids at sufficiently low temperatures, quantum effects become significant. An example is the behaviour of bosons such as helium-4. For such substances, the behaviour of heat capacity with temperature is discontinuous at the Bose-Einstein condensation point.

The quantum behaviour of solids is adequately characterized by the Debye model. At temperatures well below the characteristic Debye temperature of a solid lattice, its specific heat will be proportional to the cube of absolute temperature. A second, smaller term is needed to complete the expresssion for low-temperature metals having conduction electrons, an example of Fermi-Dirac statistics.

## Changes of phase

The boiling point of water, at sea level and normal atmospheric pressure and temperature will always be at nearly 100 °C no matter how much heat is added. The extra heat changes the phase of the water from liquid into water vapor. The heat added to change the phase of a substance in this way is said to be "hidden," and thus it is called latent heat (from the Latin latere meaning "to lie hidden"). Latent heat is the heat per unit mass necessary to change the state of a given substance, or:

$L = \frac{Q}{\Delta m} \,\!$

and

$Q = \int_{M_0}^{M} L\,dm \,\!$

Note that as pressure increases, the L rises slightly. Here, Mo is the amount of mass initially in the new phase, and M is the amount of mass that ends up in the new phase. Also,L generally does not depend on the amount of mass that changes phase, so the equation can normally be written:

$Q = L\Delta m \,\!$

Sometimes L can be time-dependent if pressure and volume are changing with time, so that the integral can be written as:

$Q = \int L\frac{dm}{dt}dt \,\!$

## Heat transfer mechanisms

As mentioned previously, heat tends to move from a high temperature region to a low temperature region. This heat transfer may occur by the mechanisms conduction and radiation. In engineering, the term convective heat transfer is used to describe the combined effects of conduction and fluid flow and is regarded as a third mechanism of heat transfer.

### Conduction

Conduction is the most significant means of heat transfer in a solid. On a microscopic scale, conduction occurs as hot, rapidly moving or vibrating atoms and molecules interact with neighboring atoms and molecules, transferring some of their energy (heat) to these neighboring atoms. In insulators the heat flux is carried almost entirely by phonon vibrations.

The "electron fluid" of a conductive metallic solid conducts nearly all of the heat flux through the solid. Phonon flux is still present, but carries less than 1% of the energy. Electrons also conduct electric current through conductive solids, and the thermal and electrical conductivities of most metals have about the same ratio. A good electrical conductor, such as copper, usually also conducts heat well. The Peltier-Seebeck effect exhibits the propensity of electrons to conduct heat through an electrically conductive solid. Thermoelectricity is caused by the relationship between electrons, heat fluxes and electrical currents.

### Convection

Convection is usually the dominant form of heat transfer in liquids and gases. This is a term used to characterize the combined effects of conduction and fluid flow. In convection, enthalpy transfer occurs by the movement of hot or cold portions of the fluid together with heat transfer by conduction. For example, when water is heated on a stove, hot water from the bottom of the pan rises, heating the water at the top of the pan. Two types of convection are commonly distinguished, free convection, in which gravity and buoyancy forces drive the fluid movement, and forced convection, where a fan, stirrer, or other means is used to move the fluid. Buoyant convection is because of the effects of gravity, and hence does not occur in microgravity environments.

Radiation is the only form of heat transfer that can occur in the absence of any form of medium and as such is the only means of heat transfer through a vacuum. Thermal radiation is a direct result of the movements of atoms and molecules in a material. Since these atoms and molecules are composed of charged particles (protons and electrons), their movements result in the emission of electromagnetic radiation, which carries energy away from the surface. At the same time, the surface is constantly bombarded by radiation from the surroundings, resulting in the transfer of energy to the surface. Since the amount of emitted radiation increases with increasing temperature, a net transfer of energy from higher temperatures to lower temperatures results.

The frequencies of the emitted photons are described by the Planck distribution. A black body at higher temperature will emit photons having a distributional peak at a higher frequency than will a colder object, and their respective spectral peaks will be separated according to Wien's displacement law. The photosphere of the Sun, at a temperature of approximately 6000 K, emits radiation principally in the visible portion of the spectrum. The solar radiation incident upon the earth's atmosphere is largely passed through to the surface. The atmosphere is largely transparent in the visible spectrum. However, in the infrared spectrum that is characteristic of a blackbody at 300K, the temperature of the earth, the atmosphere is largely opaque. The blackbody radiation from earth's surface is absorbed or scattered by the atmosphere. Though some radiation escapes into space, it is the radiation absorbed and subsequently emitted by atmospheric gases. It is this spectral selectivity of the atmosphere that is responsible for the planetary greenhouse effect.

The behaviour of a common household lightbulb has a spectrum overlapping the blackbody spectra of the sun and the earth. A portion of the photons emitted by a tungsten light bulb filament at 3000K lie in the visible spectrum. However, the majority of the photonic energy is associated with longer wavelengths and will transfer heat to the environment, as can be deduced empirically by observing a household incandescent lightbulb. Whenever EM radiation is emitted and then absorbed, heat is transferred. This principle is used in microwave ovens, laser cutting, and RF hair removal.

### Other heat transfer mechanisms

• Latent heat: Transfer of heat through a physical change in the medium such as water-to-ice or water-to-steam involves significant energy and is exploited in many ways: steam engine, refrigerator etc. (see latent heat of fusion)
• Heat pipe: Using latent heat and capillary action to move heat, it can carry many times as much heat as a similar sized copper rod. Originally invented for use in satellites, they are starting to have applications in personal computers.

## Heat dissipation

In cold climates, houses with their heating systems form dissipative systems. In spite of efforts to insulate such houses, to reduce heat losses to their exteriors, considerable heat is lost, or dissipated, from them which can make their interiors uncomfortably cool or cold. Furthermore, the interior of the house must be maintained out of thermal equilibrium with its external surroundings for the comfort of its inhabitants. In effect domestic residences are oases of warmth in a sea of cold and the thermal gradient between the inside and outside is often quite steep. This can lead to problems such as condensation and uncomfortable draughts which, if left unaddressed, can cause structural damage to the property. This is why modern insulation techniques are required to reduce heat loss.

In such a house, a thermostat is a device capable of starting the heating system when the house's interior falls below a set temperature, and of stopping that same system when another (higher) set temperature has been achieved. Thus the thermostat controls the flow of energy into the house, that energy eventually being dissipated to the exterior.