Heat

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For other uses, see Heat (disambiguation)

In physics, heat, symbolized by Q, is energy transferred from one body or temperature.

Overview

The watt (W = J/s).

Heat transfer is a path function (thermal equilibrium. The adjective hot is used as a relative term to compare the object’s temperature to that of the surroundings (or that of the person using the term). The term heat is used to describe the flow of energy. In the absence of work interactions, the heat that is transferred to an object ends up getting stored in the object in the form of internal energy.

latent heat and depends primarily on the substance and its state.

Thermal energy

See main article: Thermal energy

Thermal energy is a term often confused with that of heat. Loosely speaking, when heat is added to a enthalpy" (heat content), "entropy", "external forces", etc., which can be defined exactly, i.e. without recourse to internal atomic motions and vibrations, tend to be preferred and used more often than the term thermal energy, which is difficult to define.

History

Main article: history of heat.

In the history of science, the history of heat traces its origins from the first hominids to make fire and to speculate on its operation and meaning to modern day particle physicists who study the sub-atomic nature of heat. In short, the phenomenon of heat and its definition evolved from mythological theories of fire, to heat, to terra pinguis, history of thermodynamics.

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 square metre, though slightly different notation conventions can be used.

Entropy

In 1854, German physicist work at the temperature T, has the equivalence-value:"^[3]^[4]

$\frac {Q}{T}$

In 1865, he came to define this ratio as entropy symbolized by S, such that, for a closed, stationary system:

$\Delta S = \frac {Q}{T}$

and thus, by reduction, quantities of heat δQ (an exact differential):

$\delta Q = T dS \,$

In other words, the entropy function S facilitates the quantification and measurement of heat flow through a thermodynamic boundary.

Definitions

In modern terms, heat is concisely defined as energy in transit. Scottish physicist James Clerk Maxwell, in his 1871 classic Theory of Heat, was one of the first to enunciate a modern definition of “heat”. In short, Maxwell outlined four stipulations on the definition of heat. One, it is “something which may be transferred from one body to another”, as per the second law of thermodynamics. Two, it can be spoken of as a “measurable quantity”, and this treated mathematically like other measurable quantities. Third, it “can not be treated as a substance”; for it may be transformed into something which is not a substance, e.g. mechanical work. Lastly, it is “one of the forms of energy”. Similar such modern, succinct definitions of heat are as follows:

In a thermodynamic sense, heat is never regarded as being stored within a body. Like work, it exists only as energy in transit from one body to another; in thermodynamic terminology, between a system and its surroundings. When energy in the form of heat is added to a system, it is stored not as heat but as kinetic and potential energy of the atoms and molecules making up the system.^[2]

The noun heat is defined only during the process of energy transfer by conduction or radiation.^[5]

Heat is defined as any spontaneous flow of energy from one object to another, caused by a difference in temperature between two objects.^[6]

Heat may be defined as energy in transit from a high temperature object to a lower temperature object.^[7]

Heat is an interaction between two closed systems without exchange of work is a pure heat interaction when the two systems, initially isolated and in a stable equilibrium, are placed in contact. The energy exchanged between the two systems is then called heat.^[8]

Heat is a form of energy possessed by a substance by virtue of the vibrational movement, i.e. kinetic energy, of its molecules or atoms.^[9]

Heat is the transfer of energy between substances of different temperatures.

Thermodynamics

Internal energy

Heat is related to 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 flows across the boundary of the Internal energy is the sum of all microscopic forms of energy of a system. It is related to the molecular structure and the degree of molecular activity and may be viewed as the sum of kinetic and potential energies of the molecules; it comprises the following types of energies:^[10]

Type	Composition of Internal Energy (U)
Sensible energy	the portion of the internal energy of a system associated with kinetic energies (molecular translation, rotation, and vibration; electron translation and spin; and nuclear spin) of the molecules.
Latent energy	the internal energy associated with the phase of a system.
Chemical energy	the internal energy associated with the atomic bonds in a molecule.
Nuclear energy	the tremendous amount of energy associated with the strong bonds within the nucleus of the atom itself.
Energy interactions	those types of energies not stored in the system (e.g. system boundary as they cross it, which represent gains or losses by a system during a process.
Thermal energy	the sum of sensible and latent forms of internal energy.

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 $Δ U + W b o u n d a r y$ is inexact differential.

Heat capacity

For a simple compressible system such as an ideal gas inside a piston, the changes in enthalpy and internal energy can be related to the heat capacity at constant pressure and volume respectively. constrained to have constant volume, the heat, $Q$ , required to change its temperature from an initial temperature, T₀, to a final temperature, T_f is given by:

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

Removing the volume constraint and allowing the system to expand or contract at constant pressure:

$Q = \ \Delta U + \int_{V_0}^{V_f}P\,dV = \ \Delta H = \int_{T_0}^{T_f}C_p\,dT \,\!$

For incompressible substances, such as 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 behavior of Bose-Einstein condensation point.

The quantum behavior 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. For low-temperature metals, a second term is needed to account for the behavior of the 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 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, $M o$ 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 Δ 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

Main article: Heat transfer

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 of 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

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 Thermoelectricity is caused by the relationship between electrons, heat fluxes and electrical currents.

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

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 power that a Wien's displacement law, and the fact that the frequency of light is inversely proportional to its wavelength in vacuum, mean that the peak frequency f_maxis proportional to the absolute temperature T of the black body. The photosphere of the Sun, at a temperature of approximately 6000 K, emits radiation principally in the visible portion of the spectrum. The earth's atmosphere is partly transparent to visible light, and the light reaching the earth's surface is absorbed or reflected. The earth's surface emits the absorbed radiation, approximating the behavior of a black body at 300 K with spectral peak at f_max. At these lower frequencies, the atmosphere is largely opaque and radiation from earth's surface is absorbed or scattered by the atmosphere. Though some radiation escapes into space, it has been absorbed and subsequently re-emitted by atmospheric gases. It is this spectral selectivity of the atmosphere that is responsible for the planetary greenhouse effect

The 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 are in the visible spectrum. However, most of the energy is associated with photons of longer wavelengths; these will not help a person see, but will still 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 laser cutting, and RF hair removal.

Other heat transfer mechanisms

latent heat of fusion)
Heat pipes: Using latent heat and capillary action to move heat, heat pipes 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. For the comfort of its inhabitants, the interior of a house must be maintained out of thermal equilibrium with its external surroundings. 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 (drafts) 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.

References

^ Daintith, John (2005). Oxford Dictionary of Physics. Oxford University Press. ISBN 0-19-280628-9.
^ ^a ^b Smith, J.M., Van Ness, H.C., Abbot, M.M. (2005). Introduction to Chemical Engineering Thermodynamics. McGraw-Hill. ISBN 0073104450.
^ Published in Poggendoff’s Annalen, Dec. 1854, vol. xciii. p. 481; translated in the Journal de Mathematiques, vol. xx. Paris, 1855, and in the Philosophical Magazine, August 1856, s. 4. vol. xii, p. 81
^ Clausius, R. (1865). The Mechanical Theory of Heat] – with its Applications to the Steam Engine and to Physical Properties of Bodies. London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.
^ Baierlein, Ralph (2003). Thermal Physics. Cambridge University Press. ISBN 0521658381.
^ Schroeder, Daniel, R. (2000). Thermal Physics. New York: Addison Wesley Longman. ISBN 0201380277.
^ Discourse on Heat and Work - Department of Physics and Astronomy, Georgia State University: Hyperphysics (online)
^ Perrot, Pierre (1998). A to Z of Thermodynamics. Oxford University Press. ISBN 0198565526.
^ Clark, John, O.E. (2004). The Essential Dictionary of Science. Barnes & Noble Books. ISBN 0760746168.
^ Cengel, Yungus, A.; Boles, Michael (2002). Thermodynamics - An Engineering Approach, 4th ed.. McGraw-Hill, 17-18. ISBN 0-07-238332-1.