Difference between revisions of "Heat" - New World Encyclopedia

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In [[physics]] and [[chemistry]], '''heat''' (symbolized by ''Q'') is defined as the ''energy in transit'' from a body at higher temperature to one at lower temperature.<ref>The IUPAC defines "heat" as the "energy transferred from a hotter to a cooler body due to a temperature gradient." [http://www.iupac.org/goldbook/H02752.pdf Heat] IUPAC Compendium of Chemical Terminology, 2nd edition, 1997.</ref> Generally, heat is a form of [[energy]] associated with the motion of [[atom]]s, [[molecule]]s and other particles which comprise [[matter]]. <<Note: The first and second sentences are saying two different things. The first sentence seems to be a more precise definition; the second sentence seems to confuse "heat" with "internal energy". See [http://hyperphysics.phy-astr.gsu.edu/HBASE/thermo/heat.html#c1 Heat].>>
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[[Image:Kochendes wasser02.jpg|thumb|right|250px|When water is boiled, heat is transferred from the flame to the pot of water.]]
  
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Heat can be created by [[chemical reaction]]s (such as [[combustion|burning]]), [[nuclear reaction]]s (such as [[Nuclear fusion|fusion]] taking place inside the [[Sun]]), [[electromagnetic]] [[dissipation]] (as in [[electric stove]]s), or [[mechanics|mechanical]] dissipation (such as [[friction]]). Heat can be transferred between objects by [[thermal radiation|radiation]], [[Heat conduction|conduction]] and [[convection]]. [[Temperature]], defined as the measure of an object to spontaneously give up energy, is used to indicate the level of elementary motion associated with heat. Heat can only be transferred between objects, or areas within an object, with different temperatures, and then only in the direction of the colder body (as per the [[Second Law of Thermodynamics]]).
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In [[thermodynamics]], '''heat''' is [[energy]] transferred from one object to another.<ref>J.M. Smith, H.C. Van Ness, M.M. Abbot, ''Introduction to Chemical Engineering Thermodynamics'' (McGraw-Hill, 2005). ISBN 0073104450</ref> Heat spontaneously flows from an object with a high temperature to an object with a lower temperature. The transfer of heat from an object, to another object with an equal or higher temperature, however, can happen only with the aid of a [[heat pump]].
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{{toc}}
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Heat is transferred between objects by [[thermal radiation|radiation]], [[Heat conduction|conduction]], or [[convection]]. [[Temperature]] 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]]). The temperature and state of a substance subject to heat transfer are determined by [[latent heat]] and [[heat capacity]]. A related term, [[thermal energy]], is loosely defined as the energy in a body that increases with its temperature.  
  
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[[Image:Hot metalwork.jpg|thumb|right|250px|'''Heat''' emanating from a red-hot iron rod.]]
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== Overview ==
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Heat is the transfer of energy caused by temperature difference. The [[first law of thermodynamics]] states that the energy of a [[closed system]] is conserved. Therefore, to change the energy of a system, energy must be transferred to or from the system. Heat and work are the only two mechanisms by which energy can be transferred to or from a control mass. The unit for the amount of energy transferred by heat in [[SI derived unit|International System of Units (SI)]] is the [[Joule]]—though the [[British Thermal Unit]] and [[calorie]] are still occasionally used in the United States—and the unit for the rate of heat transfer is the [[Watt]] (J/s).
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Heat transfer is a [[path function]] ([[process quantity]]), as opposed to a [[point function]] ([[state quantity]]). Heat flows between systems that are not in thermal equilibrium with each other; it spontaneously flows from the areas of high [[temperature]] to areas of low temperature. When two bodies of different temperature come into thermal contact, they will exchange internal energy until their temperatures are equalized ([[thermal equilibrium]]). 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.
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[[Specific heat]] of a substance is the amount of energy that has to be transferred to or from one unit of [[mass]] or [[mole (unit)|mole]] of a substance to change its temperature by one [[degree (temperature)|degree]]. Specific heat is a property, which means that it depends on the substance under consideration and its state as specified by its properties. [[Fuel]]s, when burned, release much of the energy in the chemical bonds of their molecules. Upon changing from one phase to another, a pure substance releases or absorbs heat without its temperature changing. The amount of heat transfer during a phase change is known as [[latent heat]] and depends primarily on the substance and its state.
  
 
== History ==
 
== History ==
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The first to have put forward a semblance of a theory on heat was the Greek philosopher [[Heraclitus]] who lived around 500 B.C.E. 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 [[classical elements|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 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."
 
  
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As early as 460 BCE, [[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."
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The first recorded to have put forward a theory on heat was the [[Greek philosophy|Greek philosopher]] [[Heraclitus]], who lived around 500 B.C.E. 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 [[classical elements|principal elements]] in nature were fire, earth, and water. Of these three, he proposed fire to be the central element that controlled and modified the other two. He postulated the universe to be in a permanent condition of change as a result of transformations of fire; his philosophy could be summarized as: "All things are an exchange for fire." As early as 460 B.C.E., [[Hippocrates]], the father of medicine, postulated that heat was, "a quantity which functions to animate, derives from an internal fire located in the left ventricle."  
  
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In 1738, Swiss physician and mathematician [[Daniel Bernoulli]] published ''Hydrodynamica'' which laid the basis for the [[kinetic theory of gases]].  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, and that what we experience as heat is simply the kinetic energy of their motion.<ref>{{cite book|author=Mahon, Basil |title=The Man Who Changed Everything – the Life of James Clerk Maxwell|location=Hoboken, NJ | publisher=Wiley|year=2003|id=ISBN 0470861711}}</ref>  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."
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The hypothesis that heat is a form of motion was proposed initially in the twelfth 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-seventeenth century view of English scientist [[Robert Hooke]], who stated that heat was, "nothing else but a brisk and vehement agitation of the parts of a body."
  
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The modern history of heat, however, begins in 1797 when cannon manufacturer [[Benjamin Thompson]], otherwise known as Count Rumford, methodically first set out to quantify the well-known phenomenon of ''frictional heat'', i.e. to find out how much heat is produced by metal rubbing against metal. 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.<ref>{{cite book|author=Baeyer, H.C. von |title=Warmth Disperses and Time Passes – the History of Heat|location=New York | publisher=The Modern Library|year=1998|id=ISBN 0375753729}}</ref>
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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 had become [[latent heat|latent]]. Between 1759 and 1763, he developed the theory of "latent heat," on which his scientific fame chiefly rests, and also showed that different substances have different specific heats.
  
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Rumford summarizes this phenomena as follows: “It is hardly necessary to add, that anything which any insulated body … can continue to furnish without limitation, cannot possibly be a material substance; and it appears to me to be extremely difficult, if not quite impossible, to form any distinct idea of anything capable of being excited and communicated in the manner the Heat was excited and communicated in these experiments, except it be Motion.” As far as what of this "heat" is moving, where it is moving, and how it is moving, Rumford was at a relative standstill. As he states: “I am very far from pretending to know how … that particular kind of motion in bodies which has been supposed to constitute heat is excited, continued, and propagated...”
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The ability to use heat transfer to generate work allowed for the invention and development of the [[steam engine]] by such persons as [[Thomas Newcomen]] and [[James Watt]]. In 1797, 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.<ref>H.C von Baeyer, ''Warmth Disperses and Time Passes—the History of Heat'' (New York: The Modern Library, 1998). ISBN 0-375-75372-9</ref>
  
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In 1824, French engineer [[Nicolas Léonard Sadi Carnot|Sadi Carnot]], believing that a functional theory of heat engines would somehow help Napoleon and the French government in their war efforts, published ''Reflections on the Motive Power of Fire''. In this paper, which laid the foundation for the science of [[thermodynamics]], Carnot set forth the [[second law of thermodynamics]]: "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.<ref>{{cite book|author=Mendoza, E. |title=Reflections on the Motive Power of Fire – and other Papers on the Second Law of Thermodynamics by E. Clapeyron and R. Clausius|location=New York | publisher=Dover Publications, Inc.|year=1988|id=ISBN 0486446417}}</ref>
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Several theories on the nature of heat were developed. In the seventeenth century, [[J. J. Becher|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 refuted by [[Antoine Lavoisier|Lavoisier]], who demonstrated the importance of oxygen in burning in 1783. He proposed instead [[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 [[Nicolas Léonard Sadi Carnot|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 from 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.<ref>E. Mendoza, ''Reflections on the Motive Power of Fire—and other Papers on the Second Law of Thermodynamics'' (New York: Dover Publications, 1988). ISBN 0-486-44641-7</ref>
  
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It would not be until 20th century, with confirmation of the theory that all matter is composed of atoms, that more definitive theories on heat could be established. Other important historical postulates of heat include the [[phlogiston]] (1733), [[fire air]] (1775), and the [[caloric]] (1787).
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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 can be felt.<ref>Basil Mahon, ''The Man Who Changed Everything—the Life of James Clerk Maxwell'' (Hoboken, NJ: Wiley, 2003). ISBN 0-470-86171-1</ref> 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 high internal energy, to those with less energetic molecules and lower internal energy.  
  
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== Overview ==
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The work of [[James Prescott Joule|Joule]] and [[Julius Robert von Mayer|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. [[Rudolf Clausius|Clausius]] demonstrated in 1850, that caloric theory could be reconciled with kinetic theory provided that the conservation of energy was considered rather than the movement of a substance, and stated the [[First Law of Thermodynamics]].
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By common knowledge, the term ''heat'' has been used in connection with the [[warm]]th, or [[hot]]ness, of surrounding objects.  The concept that warm objects "contain heat" is not uncommon.  During its 350 year development, the science of [[thermodynamics]] had established a physical quantity named ''temperature'' to quantify the level of "warmth", whereas ''heat'' (also improperly called ''heat change'') was defined as a [[transient]] form of [[energy]] that quantifies the [[spontaneous]] [[transfer]] of [[internal energy]] due to a temperature difference (or [[gradient]].) The [[International System of Units|SI]] unit for heat is the [[joule]];  an alternative unit still in use in the U.S. and other countries is the [[British thermal unit]].
 
  
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The amount of heat exchanged by an object when its temperature varies by one [[degree (temperature)|degree]] is called '''[[heat capacity]]'''.  Heat capacity is specific to each and every object.  When referred to a [[quantity]] unit (such as [[mass]] or [[Mole (unit)|moles]]), the heat exchanged per degree is termed '''[[specific heat]]''', and depends primarily on the [[Composition (natural science)|composition]] and [[physical state]] ([[phase (matter)|phase]]) of objects. [[Fuel]]s generate predictable amounts of heat when burned; this heat is known as '''[[heating value]]''' and is expressed per unit of quantity.  Upon transitioning 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.
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==Thermodynamics==
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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. First, it is “something which may be transferred from one body to another,” as per the [[second law of thermodynamics]]. Second, 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, such as [[mechanical work]]. Lastly, it is “one of the forms of [[energy]].”
  
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Heat is a [[process quantity]]&mdash;as opposed to being a [[state quantity]]&mdash;and is to thermal energy as [[mechanical work|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 [[atom]]s or [[molecule]]s. 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.  Understanding this difference is a necessary part of understanding the [[first law of thermodynamics]].
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The total amount of energy moved through heat transfer is conventionally abbreviated as ''Q''. The conventional sign is that when a body releases heat into its surroundings, ''Q''&nbsp;&lt;&nbsp;0 (-); when a body absorbs heat from its surroundings, ''Q''&nbsp;&gt;&nbsp;0 (+). '''Heat transfer rate,''' or heat flow per unit time, is denoted by:
  
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[[Infrared]] radiation is often linked to heat, since objects at room temperature or above will [[spontaneous emission|emit radiation]] mostly concentrated in the mid-infrared band (see [[black body]]).
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:<math>\dot{Q} = {dQ\over dt} \,\!</math>.
  
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== Notation ==
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This is measured in [[watt]]s. '''Heat flux''' is defined as rate of heat transfer per unit cross-sectional area, and is denoted '''''q,''''' resulting in units of watts per meter squared, though slightly different notation conventions can be used.
  
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'''Total heat''' is traditionally abbreviated as ''Q'', and is measured in British thermal units (BTU or Btu) in the US or joules (J) in [[SI]] units. Total heat, heat transfer rate, and heat flux are often abbreviated with different cases of the letter ''Q''.  They are often switched in different contexts.  Regarding sign convention, when a body releases heat into its surroundings, ''Q''&nbsp;&lt;&nbsp;0 (-). When a body absorbs heat from its surroundings, ''Q''&nbsp;&gt;&nbsp;0 (+). '''Heat transfer rate''', or heat flow per unit time, is labeled:
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Heat is related to the [[internal energy]] <math>U</math> of the system and [[work (thermodynamics)|work]] <math>W</math> done by the system by the [[first law of thermodynamics]]:
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:<math>\Delta U = Q - W \ </math>
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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 (that is, allows a control volume of gas to become larger or smaller), provided the volume is not constrained. Returning to the [[first law of thermodynamics|first law]] equation and separating the work term into two types, "boundary work" and "other" (such as shaft work performed by a compressor fan), yields the following:
  
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:<math>\dot{Q} = {dQ\over dt} \,\!</math>
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:<math>\Delta U + W_{boundary} = Q - W_{other}\ </math>
  
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to indicate a change per unit time. It is measured in [[watt]]s. '''Heat flux''' is defined as amount of heat per unit time per unit cross-sectional area, is abbreviated '''''q''''', and is measured in watts per meter squared. It is also sometimes notated as ''Q''&Prime; or ''q''&Prime; or <math>\dot{Q}''</math>.
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This combined quantity <math>\Delta U + W_{boundary}</math> is [[enthalpy]], <math>H</math>, one of the [[thermodynamic potentials]]. Both enthalpy, <math>H</math>, and internal energy, <math>U</math> are [[state function]]s. 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 <math>Q</math> nor <math>W</math> are properties of a system and need not sum to zero over the steps of a cycle. The infinitesimal expression for heat, <math>\delta Q</math>, forms an [[inexact differential]] for processes involving work. However, for processes involving no change in volume, applied magnetic field, or other external parameters, <math>\delta Q</math>, 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.
  
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==Thermodynamics==
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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, <math>Q</math>, required to change the temperature of a gas from an initial temperature, ''T''<sub>0</sub>, to a final temperature, ''T<sub>f</sub>'' depends on the relationship:
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The amount of heat , <math>Q</math>, required to change the temperature of a material from an initial temperature, ''T''<sub>0</sub>, to a final temperature, ''T<sub>f</sub>'' depends on the [[heat capacity]] of that material according to the relationship:
 
  
 
:<math>Q = \int_{T_0}^{T_f}C_p\,dT \,\!</math>
 
:<math>Q = \int_{T_0}^{T_f}C_p\,dT \,\!</math>
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:<math>Q = \int_{T_0}^{T_f}C_v\,dT \,\!</math>
 
:<math>Q = \int_{T_0}^{T_f}C_v\,dT \,\!</math>
  
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For incompressible substances, such as [[solid]]s and [[liquid]]s, there is no distinction among the two expressions.  
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For incompressible substances, such as [[solid]]s and [[liquid]]s, 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, <math>m</math>, and [[specific heat capacity]], <math>c_s \,\!</math> according to:
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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, <math>m</math> , and [[specific heat capacity]], <math>c_s \,\!</math> according to:
 
  
 
:<math>C_p = mc_s \,\!</math>
 
:<math>C_p = mc_s \,\!</math>
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:<math>C_p = nc_n \,\!</math>
 
:<math>C_p = nc_n \,\!</math>
  
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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.
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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.  
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The specific heats of monatomic gases (e.g., helium) are nearly constant with temperature, whereas that of diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) even more.
 
  
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For liquids at sufficiently low temperatures, quantum effects become significant. An example is the behavior of [[bosons|Bosons]] such as helium-4. For such substances, the behavior of heat capacity with temperature is discontinuos at the [[Bose-Einstein_condensation|Bose-Einstein condensation]] point.
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The specific heats of monatomic gases (for example, [[helium]]) are nearly constant with temperature. Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (forxample, carbon dioxide) still more.
  
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For solids, the Debye model describes the behavior of the lattice at or below the characteristic Debye temperature, in the neighborhood of which the specific heat behaves according to the cube of temperature. In the case of low-temperature metals, to the Debye model is added a second term describing the electrons and their slight contribution to the specific heat, an application of [[Fermi_Dirac_statistics|Fermi-Dirac statistics]].
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In liquids at sufficiently low temperatures, quantum effects become significant. An example is the behavior of [[bosons]] such as helium-4. For such substances, the behavior of heat capacity with temperature is discontinuous at the [[Bose-Einstein condensation]] point.
  
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Heat is related to the [[internal energy]] <math> U </math> of the system and [[work (thermodynamics)|work]] <math> W </math> done by the system by the [[first law of thermodynamics]]:
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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. A second, smaller term is needed to complete the expression for low-temperature metals having conduction electrons, an example of [[Fermi Dirac statistics|Fermi-Dirac statistics]].
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:<math>\Delta U = Q - W \ </math>
 
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which means that the energy of the system can change either via work or via heat.
 
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Whereas <math> U </math>, internal energy, is a [[state function]] and therefore returns to its initial state upon completion of a cyclic process as in a [[heat engine]], neither <math>Q </math> nor <math> W </math> is conserved. The infinitesimal expression for heat, <math>\delta Q </math>, forms an [[inexact differential]] for processes involving work. However, for processes involving no change in volume, applied magnetic field, or other external parameters, <math>\delta Q </math>, forms an [[exact differential]].
 
  
 
==Changes of phase==
 
==Changes of phase==
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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:
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The boiling point of [[water]], at [[sea level]] and normal atmospheric pressure, will always be at 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:
 
  
 
:<math>L = \frac{Q}{\Delta m} \,\!</math>
 
:<math>L = \frac{Q}{\Delta m} \,\!</math>
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:<math>Q = \int_{M_0}^{M} L\,dm \,\!</math>
 
:<math>Q = \int_{M_0}^{M} L\,dm \,\!</math>
  
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For example, turning 1 pound of water into one pound of steam at  100 °C and at normal atmospheric pressure would be: 1000 BTU = (1000 BTU/lb)(1 lb). Note that as pressure increases, the ''L'' rises slightly. Here, <math>M_o</math> 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,
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Note that as pressure increases, the ''L'' rises slightly. Here, <math>M_o</math> 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:
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''L'' generally doesn't depend on the amount of mass that changes phase, so the equation can normally be written:
 
  
 
:<math>Q = L\Delta m \,\!</math>
 
:<math>Q = L\Delta m \,\!</math>
  
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Sometimes ''L'' can be time-dependent if pressure and volume are time-varying, so that the integral can be handled:
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Sometimes ''L'' can be time-dependent if pressure and volume are changing with time, so that the integral can be written as:
  
 
:<math>Q = \int L\frac{dm}{dt}dt \,\!</math>
 
:<math>Q = \int L\frac{dm}{dt}dt \,\!</math>
  
 
==Heat transfer mechanisms==
 
==Heat transfer mechanisms==
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{{main|Heat transfer}}
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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 [[heat conduction|conduction]] and [[Thermal radiation|radiation]]. In [[engineering]], the term "[[convection|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.
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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 [[heat conduction|conduction]] and [[Thermal radiation|radiation]]. In [[engineering]], the term ''[[convection|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===
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[[heat conduction|Conduction]] is the most common means of heat transfer in a solid. On a microscopic scale, conduction occurs as hot, rapidly moving or vibrating atoms and [[molecule]]s interact with neighboring atoms and molecules, transferring some of their energy (heat) to these neighboring atoms. In [[thermal insulation|insulators]] the heat flux is carried almost entirely by [[phonon]] vibrations.
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[[heat 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 [[molecule]]s interact with neighboring atoms and molecules, transferring some of their energy (heat) to these neighboring atoms.
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The "electron fluid" of a [[conductor (material)|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 conductivity|thermal]] and [[electrical conductivity|electrical conductivities]] of most [[metal]]s 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===  
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[[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. [[buoyancy|Buoyant]] convection is heavily affected by gravity, and so does not occur in [[microgravity]] environments.
−
[[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. [[buoyancy|Buoyant]] convection is due to the effects of gravity, and hence does not occur in [[microgravity]] environments.
 
  
 
===Radiation===
 
===Radiation===
 +
[[Thermal radiation|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 ([[proton]]s and [[electron]]s), 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.
  
−
[[Thermal radiation|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 ([[proton]]s and [[electron]]s), 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.
+
==Notes==
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<references />
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For room temperature objects (~300 K), the majority of photons emitted (and involved in radiative heat transfer) are in the [[infrared]] spectrum, but this is by no means the only frequency range involved in radiation.  The frequencies emitted are partially related to [[black-body radiation]].  Hotter objects&mdash;a light bulb filament at [[color temperature|3000K]] for instance&mdash;transfer heat in the visible spectrum or beyond.  Whenever EM radiation is emitted and then absorbed, heat is transferred.  This principle is used in [[microwave oven]]s, [[laser cutting]], and [[Electrolysis (cosmetology)|RF hair removal]].
 
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===Other heat transfer mechanisms===
 
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*[[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 computer]]s.
 
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==Heat dissipation==
 
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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 sake 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.
 
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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==
 
==References==
−
<div class="references-small">
+
* Baierlein, Ralph. 2003. ''Thermal Physics''. Cambridge: Cambridge University Press. ISBN 0521658381
−
<references />
+
* Halliday, David, Robert Resnick, and Jearl Walker. 1993. ''Fundamentals of Physics.'' New York: Wiley. ISBN 0471524611
−
<!-- No longer referenced:  #{{note|smith}}{{cite book|author= Smith, J.M., Van Ness, H.C., Abbot, M.M.|title=Introduction to Chemical Engineering Thermodynamics|publisher=McGraw-Hill|year=2005|id=ISBN 0073104450}}—>
+
* Massey, B. S. 1983. ''Mechanics of Fluids''. UK: Van Nostrand Reinhold. ISBN 0-442-30552-4
−
<!-- No longer referenced: #{{note|baierlein}}{{cite book|author= Baierlein, Ralph|title=Thermal Physics|publisher=Cambridge University Press|year=2003|id=ISBN 0521658381}}—>
+
* Myers, Rusty L. 2006. ''The Basics of Physics''. Westport, CT: Greenwood Press. ISBN 0313328579
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<!-- No longer referenced:  #{{note|schroeder}}{{cite book|author= Schroeder, Daniel, R.|title=Thermal Physics|location=New York | publisher=Addison Wesley Longman|year=2000|id=ISBN 0201380277}}-->
+
* Perrot, Pierre. 1998. ''A to Z of Thermodynamics''. Oxford: Oxford University Press. ISBN 0198565526
−
<!— No longer referenced:  #{{note|4}}[http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heat.html Discourse on Heat and Work] - Department of Physics and Astronomy, Georgia State University: Hyperphysics (online) —>
+
* Serway, Raymond A. and John W. Jewett. 2004. ''Physics for Scientists and Engineers.'' Belmont, CA: Thomson-Brooks/Cole. ISBN 0534408427
−
<!-- No longer referenced:  #{{note|perrot}}{{cite book | author=Perrot, Pierre | title=A to Z of Thermodynamics | publisher=Oxford University Press | year=1998 | id=ISBN 0198565526}}—>
+
* Smith, J.M., H.C. Van Ness, and M.M. Abbot. 2005. ''Introduction to Chemical Engineering Thermodynamics''. New York: McGraw-Hill. ISBN 0073104450
−
<!-- No longer referenced:  #{{note|clark}}{{cite book | author=Clark, John, O.E. | title=The Essential Dictionary of Science | publisher=Barnes & Noble Books | year=2004 | id=ISBN 0760746168}}-->
+
* Young, Hugh D. and Roger A. Freedman. 2003. ''Physics for Scientists and Engineers''. San Fransisco, CA: Pearson. ISBN 080538684X
−
</div>
 
−
 
 
−
== See also ==
 
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* [[Temperature]]
 
−
* [[Thermometer]]
 
−
* [[Heat death of the Universe]]
 
−
* [[Heat equation]]
 
−
* [[Heat transfer]]
 
−
* [[Heat exchanger]]
 
−
* [[Heat pump]]
 
−
* [[Heat transfer coefficient]]
 
−
* [[Effect of sun angle on climate]]
 
−
* [[Internal energy]]
 
−
* [[Shock heating]]
 
  
 
== External links ==
 
== External links ==
−
*[http://www.foxnews.com/story/0,2933,187464,00.html Plasma heat at 2 gigakelvins] - Article about extremely high heat generated by scientists (Foxnews.com)
+
All links retrieved December 12, 2017.
−
*[http://hyperphysics.phy-astr.gsu.edu/hbase/heacon.html#heacon Heat and Thermodynamics] - Georgia State University
+
* [http://hyperphysics.phy-astr.gsu.edu/hbase/heacon.html#heacon Heat and Thermodynamics] - Georgia State University.
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*[http://www.cheresources.com/convection.shtml Correlations for Convective Heat Transfer] - ChE Online Resources
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* [http://www.cheresources.com/convection.shtml Correlations for Convective Heat Transfer] - ChE Online Resources.
  
 
[[Category:Physical sciences]]
 
[[Category:Physical sciences]]
 
[[Category:Physics]]
 
[[Category:Physics]]
  
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{{credit|67610422}}
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{{credit|141123823}}

Latest revision as of 17:30, 12 December 2017

When water is boiled, heat is transferred from the flame to the pot of water.

In thermodynamics, heat is energy transferred from one object to another.[1] Heat spontaneously flows from an object with a high temperature to an object with a lower temperature. The transfer of heat from an object, to another object with an equal or higher temperature, however, can happen only with the aid of a heat pump.

Heat is transferred between objects by radiation, conduction, or convection. Temperature 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). The temperature and state of a substance subject to heat transfer are determined by latent heat and heat capacity. A related term, thermal energy, is loosely defined as the energy in a body that increases with its temperature.

Overview

Heat is the transfer of energy caused by temperature difference. The first law of thermodynamics states that the energy of a closed system is conserved. Therefore, to change the energy of a system, energy must be transferred to or from the system. Heat and work are the only two mechanisms by which energy can be transferred to or from a control mass. The unit for the amount of energy transferred by heat in International System of Units (SI) is the Joule—though the British Thermal Unit and calorie are still occasionally used in the United States—and the unit for the rate of heat transfer is the Watt (J/s).

Heat transfer is a path function (process quantity), as opposed to a point function (state quantity). Heat flows between systems that are not in thermal equilibrium with each other; it spontaneously flows from the areas of high temperature to areas of low temperature. When two bodies of different temperature come into thermal contact, they will exchange internal energy until their temperatures are equalized (thermal equilibrium). 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.

Specific heat of a substance is the amount of energy that has to be transferred to or from one unit of mass or mole of a substance to change its temperature by one degree. Specific heat is a property, which means that it depends on the substance under consideration and its state as specified by its properties. Fuels, when burned, release much of the energy in the chemical bonds of their molecules. Upon changing from one phase to another, a pure substance releases or absorbs heat without its temperature changing. The amount of heat transfer during a phase change is known as latent heat and depends primarily on the substance and its state.

History

The first recorded to have put forward a theory on heat was the Greek philosopher Heraclitus, who lived around 500 B.C.E. 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 principal elements in nature were fire, earth, and water. Of these three, he proposed fire to be the central element that controlled and modified the other two. He postulated the universe to be in a permanent condition of change as a result of transformations of fire; his philosophy could be summarized as: "All things are an exchange for fire." As early as 460 B.C.E., Hippocrates, the father of medicine, postulated that heat was, "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 twelfth 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-seventeenth century view of English scientist Robert Hooke, who stated that heat was, "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 had become latent. Between 1759 and 1763, he developed the theory of "latent heat," on which his scientific fame chiefly rests, and also showed that different substances have different specific heats.

The ability to use heat transfer to generate work allowed for the invention and development of the steam engine by such persons as Thomas Newcomen and James Watt. In 1797, 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.[2]

Several theories on the nature of heat were developed. In the seventeenth 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 refuted by Lavoisier, who demonstrated the importance of oxygen in burning in 1783. He proposed instead 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 from 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.[3]

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 can be felt.[4] 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 high internal energy, to those with less energetic molecules and 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 considered rather than the movement of a substance, and stated the First Law of Thermodynamics.

Thermodynamics

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. First, it is “something which may be transferred from one body to another,” as per the second law of thermodynamics. Second, 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, such as mechanical work. Lastly, it is “one of the forms of energy.”

The total amount of energy moved through heat transfer is conventionally abbreviated as Q. The conventional sign 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:

.

This 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 meter squared, though slightly different notation conventions can be used.

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

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 (that is, 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" (such as shaft work performed by a compressor fan), yields the following:

This combined quantity is enthalpy, , one of the thermodynamic potentials. Both enthalpy, , and internal energy, 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 nor are properties of a system and need not sum to zero over the steps of a cycle. The infinitesimal expression for heat, , forms an inexact differential for processes involving work. However, for processes involving no change in volume, applied magnetic field, or other external parameters, , 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, , required to change the temperature of a gas from an initial temperature, T0, to a final temperature, Tf depends on the relationship:

for constant pressure, whereas at constant volume:

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, , and specific heat capacity, according to:

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

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 (for example, helium) are nearly constant with temperature. Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (forxample, carbon dioxide) still more.

In liquids at sufficiently low temperatures, quantum effects become significant. An example is the behavior of bosons such as helium-4. For such substances, the behavior of heat capacity with temperature is discontinuous at the 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. A second, smaller term is needed to complete the expression 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:

and

Note that as pressure increases, the L rises slightly. Here, 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:

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

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.

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 heavily affected by gravity, and so does not occur in microgravity environments.

Radiation

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.

Notes

  1. ↑ J.M. Smith, H.C. Van Ness, M.M. Abbot, Introduction to Chemical Engineering Thermodynamics (McGraw-Hill, 2005). ISBN 0073104450
  2. ↑ H.C von Baeyer, Warmth Disperses and Time Passes—the History of Heat (New York: The Modern Library, 1998). ISBN 0-375-75372-9
  3. ↑ E. Mendoza, Reflections on the Motive Power of Fire—and other Papers on the Second Law of Thermodynamics (New York: Dover Publications, 1988). ISBN 0-486-44641-7
  4. ↑ Basil Mahon, The Man Who Changed Everything—the Life of James Clerk Maxwell (Hoboken, NJ: Wiley, 2003). ISBN 0-470-86171-1

References
ISBN links support NWE through referral fees

  • Baierlein, Ralph. 2003. Thermal Physics. Cambridge: Cambridge University Press. ISBN 0521658381
  • Halliday, David, Robert Resnick, and Jearl Walker. 1993. Fundamentals of Physics. New York: Wiley. ISBN 0471524611
  • Massey, B. S. 1983. Mechanics of Fluids. UK: Van Nostrand Reinhold. ISBN 0-442-30552-4
  • Myers, Rusty L. 2006. The Basics of Physics. Westport, CT: Greenwood Press. ISBN 0313328579
  • Perrot, Pierre. 1998. A to Z of Thermodynamics. Oxford: Oxford University Press. ISBN 0198565526
  • Serway, Raymond A. and John W. Jewett. 2004. Physics for Scientists and Engineers. Belmont, CA: Thomson-Brooks/Cole. ISBN 0534408427
  • Smith, J.M., H.C. Van Ness, and M.M. Abbot. 2005. Introduction to Chemical Engineering Thermodynamics. New York: McGraw-Hill. ISBN 0073104450
  • Young, Hugh D. and Roger A. Freedman. 2003. Physics for Scientists and Engineers. San Fransisco, CA: Pearson. ISBN 080538684X

External links

All links retrieved December 12, 2017.

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