Heat

For other uses, see Heat (disambiguation).

Heat generated from the nuclear fusion in the Sun, and transported to Earth as electromagnetic radiation, is one of the driving forces of life on Earth.

In physics, chemistry, engineering, especially in thermodynamics, a quantity of heat is an amount of energy produced or transferred from one body, region of space, set of components, or thermodynamic system to another in any way other than as work. Thus, heat always means "heat transfer" and is synonymous with it. This definition is the carefully developed fruit of the finding from experiments in physics that in general a definite statement cannot be made of "the amount of heat in a body"—although ordinary language appears to suggest that such a statement could be made.

Quantity of heat transferred (or simply quantity of heat) can be estimated either by measurement of temperature increase by amount heat generated by a reference source, as in calorimetry, or indirectly, by calculations based on other quantities, relying on the law of conservation of energy, or on the first law of thermodynamics.

Heat is primarily of macroscopic character, but it has a good explanation in the motion of microscopic particles.

In ordinary language, as distinct from technical language, heat has a broader meaning. This can lead to confusion if the diversity of usage of words is forgotten.

Thermodynamically, energy can be produced or transferred as heat by thermal conduction, by thermal radiation, by friction and viscosity, and by chemical dissipation.

Heat transfer by conduction and by radiation from a hotter to a colder body is spontaneous. The second law of thermodynamics requires that the transfer of energy from one body to another with an equal or higher temperature can only occur with the aid of a heat pump by mechanical work, or by some other similar process in which entropy is increased in the universe in a manner that compensates for the decrease of entropy in the cooled body, due to the removal of the heat from it. For example, energy may be removed against a temperature gradient by spontaneous evaporation of a liquid.

The engineering discipline of heat transfer recognizes heat transfer by conduction, by convective circulation, by net mass transfer, and by radiation.

In physics, especially in calorimetry, and in meteorology, the concepts of latent heat and of sensible heat are used. Latent heat is associated with phase changes, while sensible heat is associated with temperature change, and is equivalent to thermal energy when stored in an object or system.

The term thermal energy, defined as the internal energy of a body that increases with its temperature, is not a term that is defined in thermodynamics but is often used in engineering, as it is naturally related to heat capacity. The thermal energy of an object consists of all the heat energy entering the object or system, that is later stored as atomic translations, rotations and vibrations that serve to store heat in ways that increase the mean atomic kinetic energy (temperature) of the system.

Overview

Heat may flow across the boundary of the system and thus change its internal energy.

Heat flows spontaneously only from systems of higher temperature to systems of lower temperature. When two systems come into thermal contact, they always exchange thermal energy due to the microscopic interactions of their particles. When the systems are at different temperatures, the net flow of thermal energy is not zero and is directed from the hotter region to the cooler region, until their temperatures are equal and the flow of heat ceases. Then they have reached a state of thermal equilibrium, exchanging thermal energy at an equal rate in both directions.

The first law of thermodynamics requires that the energy of an isolated system is conserved. To change the energy of a system, energy must be transferred to or from the system. For a closed system, heat and work are the mechanisms by which energy can be transferred. For an open system, total energy can be changed also by transfer of matter.

Work performed on a system is, by definition , an energy transfer to the system that is due to a change to external or mechanical parameters of the system, such as the volume, magnetization, center of mass in a gravitational field.

For a closed system (with no external transfer of matter), heat is defined as energy transferred to the system in any way other than as work. Heat transfer is an irreversible process, which leads to the systems coming closer to mutual thermodynamic equilibrium. In the case of systems close to thermodynamic equilibrium where temperature can be defined, some heat transfer can be related to temperature difference between systems. Heat transfer can also arise by friction and by viscosity. For an open system, far from thermodynamic equilibrium, where temperature cannot be defined, there the distinction between heat and work may not be feasible.

Human notions such as hot and cold are relative terms and are generally used to compare one system’s temperature to another or its surroundings.

In a thermodynamic sense, heat is never regarded as being stored within a system. Like work, it exists only as energy in transit from one system to another or between a system and its surroundings. When energy in the form of heat is added to a system, it is stored as kinetic and potential energy of the atoms and molecules in the system.

There are two elements to physicists' definition of quantity of heat. One is that it requires a differentiation from work. The other is that it requires transfer. The requirement for transfer is because "the amount of heat in a body" would be determined not only by the amount of heat entering or leaving the body, but also by work which may be done on the body and would not be heat entering or leaving the body. Nevertheless, this definition does not presume the law of conservation of energy or the first law of thermodynamics and does not presume how quantities of energy are measured empirically.

Definitions

Scottish physicist James Clerk Maxwell, in his 1871 classic Theory of Heat, was one of many who began to build on the already established idea that heat was something to do with matter in motion, this was the same idea put forwards by Sir Benjamin Thompson in 1798 who said he was only following on from the work of many others. One of Maxwell's recommended books was by John Tyndall Heat as a Mode of Motion. Maxwell outlined four stipulations for the definition of heat:

• It is something which may be transferred from one body to another, according to the second law of thermodynamics.
• It is a measurable quantity, and thus treated mathematically.
• It cannot be treated as a substance, because it may be transformed into something that is not a substance, e.g., mechanical work.
• Heat is one of the forms of energy.

Two main streams of definition

There is variation between respected authors as to how they approach the definition of quantity of heat transferred. There are two main streams of thinking. One is from an empirical viewpoint, to define heat transfer as occurring by specified macroscopic mechanisms. The other is from a theoretical viewpoint, to define it as a residual quantity after transfers as macroscopic work have been determined for a process, so as to conform with the principle of conservation of energy or the first law of thermodynamics.

Specified mechanisms of heat transfer

Specified mechanisms of heat transfer are conduction and radiation. These mechanisms presuppose recognition of temperature; empirical temperature is enough for this purpose, though absolute temperature can also serve. In this stream of thinking, quantity of heat is defined primarily through calorimetry.^{[citation needed]}

Referring to conduction, Partington writes: "If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a quantity of heat has passed from the hot body to the cold body." The reader may see that this concise statement does not amount to a complete definition. Though continuing at length on the subject, Partington does not provide an explicit concise and complete definition of heat.

Referring to radiation, Maxwell writes: "In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself thereby become hot."

From these empirically based ideas of heat and from other empirical observations, the notions of internal energy and of entropy can be derived, so as to lead to the recognition of the first and second laws of thermodynamics. This was the way of the historical pioneers of thermodynamics.

Heat transfer as a residual quantity

Heat transfer as a residual quantity is a concept of theoretical character. There are four main elements of the underlying theory.

• The existence of states of thermodynamic equilibrium.
• The universality of the law of conservation of energy.
• The recognition of work as a form of energy transfer.
• The universal irreversibility of natural processes.

From these four elements is theoretically distilled an idea of heat as a form of energy transfer other than by work. Also theoretically distilled from them is the idea of absolute or thermodynamic temperature. From here it is deduced that heat transfer is often related to temperature differences.

Notation and units

As a form of energy heat has the unit joule (J) in the International System of Units (SI). However, in many applied fields in engineering the British Thermal Unit (BTU) and the calorie are often used. The standard unit for the rate of heat transferred is the watt (W), defined as joules per second.

The total amount of energy transferred as heat is conventionally written as Q for algebraic purposes. Heat released by a system into its surroundings is by convention a negative quantity (Q < 0); when a system absorbs heat from its surroundings, it is positive (Q > 0). Heat transfer rate, or heat flow per unit time, is denoted by

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

Heat flux is defined as rate of heat transfer per unit cross-sectional area, resulting in the unit watts per square metre.

Estimation of quantity of heat

Quantity of heat transferred can be estimated either by direct measurement as heat, or indirectly, through calculations based on other quantities.

Direct measurement is by calorimetry and is the primary empirical basis of the idea of quantity of heat. The transferred heat is measured by changes in a body of known properties, for example, temperature rise, change in volume or length, or phase change, such as melting of ice.

Indirect estimation of quantity of heat relies on the law of conservation of energy, and in particular cases on the first law of thermodynamics. Indirect estimation is the primary approach of many theoretical studies of heat.

Semantics

Heat

There is some diversity of usage of the word heat, even in technical scientific writings. In current scientific usage, the language surrounding the term can be conflicting and even misleading. One study showed that several popular textbooks used language that implied several meanings of the term, that heat is the process of transferring energy, that it is the transferred energy (i.e., as if it were a substance), and that is an entity contained within a system, among other similar descriptions. The study determined it was not uncommon for a combination of these representations to appear within the same text. They found the predominant use among physicists to be as if it were a substance.

"Thermal energy"

A potentially confusing term is thermal energy, loosely defined as the energy of a body that increases with its temperature. The term "thermal energy" is not one that has a definite meaning in thermodynamics. Thermal energy, even when not in transit or motion, is sometimes referred to as heat or heat content, while the strict thermodynamic definition of heat requires heat energy to be in transfer between two systems (or in motion of flow in response to a temperature gradient), or otherwise in production in a dissipative process such as friction, viscosity, or chemical reaction. In this technical usage, whenever heat passes into a system, or stops moving within a system, it ceases to be heat (even "heat content"), but its energy remains, re-termed, as "thermal energy content."^{[citation needed]}

Internal energy and enthalpy

In the case where the number of particles in the system is constant, the first law of thermodynamics states that the differential change in internal energy dU of a system is given by the differential heat flow δQ into the system minus the differential work δW exerted by the system:

$\mathrm{d} U = \delta Q_\text{in} - \delta W_\text{out} \quad{\rm{(first\,\,law)}}$.

The differential transfer of heat, $\delta Q_\text{in}$, makes differential contributions, not only to internal energy, but also to the work done by the system:

$\delta Q_\text{in} = \mathrm{d} U + \delta W_\text{out} \$.

The work done by the system includes boundary work, which causes the boundaries of the system to expand, in addition to other work (e.g. shaft work performed by a compressor fan):

$\delta Q_\text{in} = \mathrm{d} U + \delta W_\text{boundary} + \delta W_\text{other} \$.^{[citation needed]}

$\mathrm{d} U + \delta W_\text{boundary}\$ is equal to the differential enthalpy change (dH) of the system. Substitution gives:

$\delta Q_\text{in} = \mathrm{d} H + \delta W_\text{other} \$.

Both enthalpy, $H$, and internal energy, $U$, are state functions. In cyclical processes, such as the operation of a heat engine, state functions return to their initial values. Thus, the differentials for enthalpy and energy are exact differentials, which are $dH$ and $dU$, respectively. The symbol for exact differentials is the lowercase letter d.

In contrast, neither $Q$ nor $W$ represents the state of the system (i.e. they need not return to their original values when returning to same step in the following cycle). Thus, the infinitesimal expressions for heat and work are inexact differentials, $\delta Q$ and $\delta W$, respectively. The lowercase Greek letter delta, $\delta$, is the symbol for inexact differentials. The integral of any inexact differential over the time it takes to leave and return to the same thermodynamic state does not necessarily equal zero. However, for slow enough processes involving no change in volume (i.e. $dV = 0$), applied magnetic field, or other external parameters (i.e. $\delta W_\text{out} = 0$ and $\delta W_\text{in} = 0$), $\delta Q$ forms the exact differential, $dS = \frac{\delta Q_\text{rev}}{T}$, wherein the following relation applies:

$dU = TdS = \delta Q_\text{rev}$.

Likewise, for an isentropic process (i.e. $\delta Q = 0$ and $dS = 0$), $\delta W$ forms the exact differential, $dV = \frac{\delta W_\text{rev}}{p}$, wherein the following relation applies:

$dU = - pdV = - \delta W_\text{rev}$.

Path-independent examples for an ideal gas

For a simple compressible system such as an ideal gas inside a piston, the internal energy change $\Delta U$ at constant volume and the enthalpy change $\Delta H$ at constant pressure are modeled by separate heat capacity values, which are $C_v$ and $C_p$, 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 this formula:

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

Removing the volume constraint and allowing the system to expand or contract at constant pressure, the heat, $Q$, required to change its temperature from an initial temperature, T₀, to a final temperature, T_f, is given by this formula:

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

Note that when integrating an exact differential (e.g. $\mathrm{d} U$), the lowercase letter d is substituted for $\Delta$ (e.g. $\Delta U$), and when integrating an inexact differential (e.g. $\delta W_{boundary}$), the lowercase Greek letter $\delta$ is removed with no replacement (e.g. $W_{boundary}$).

Incompressible substances

For incompressible substances, such as solids and liquids, the distinction between the two types of heat capacity (i.e. $C_p$ which is based on constant pressure and $C_v$ which is based on constant volume) disappears, as no work is performed.

Latent and sensible heat

Joseph Black

In an 1847 lecture entitled On Matter, Living Force, and Heat, James Prescott Joule characterized the terms latent heat and sensible heat as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively. He described latent energy as the energy possessed via a distancing of particles where attraction was over a greater distance , i.e. a form of potential energy, and the sensible heat as an energy involving the motion of particles or what was known as a living force. At the time of Joule kinetic energy either held 'invisibly' internally or held 'visibly' externally was known as a living force.

Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature. Such a process may be a phase transition, such as the melting of ice or the boiling of water. The term was introduced around 1750 by Joseph Black as derived from the Latin latere (to lie hidden), characterizing its effect as not being directly measurable with a thermometer.

Sensible heat, in contrast to latent heat, is the heat exchanged by a thermodynamic system that has as its sole effect a change of temperature. Sensible heat therefore only increases the thermal energy of a system.

Consequences of Black's distinction between sensible and latent heat are examined in the Wikipedia article on calorimetry.

Specific heat

Specific heat, also called specific heat capacity, is defined as the amount of energy that has to be transferred to or from one unit of mass (kilogram) or amount of substance (mole) to change the system temperature by one degree. Specific heat is a physical property, which means that it depends on the substance under consideration and its state as specified by its properties.

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.

Motion of microscopic particles explains heat

Heat is primarily of macroscopic character, but it has a good explanation in the motion of microscopic particles. An early and vague expression of this explanation was by Francis Bacon. Precise and detailed versions of it were developed in the nineteenth century. It is nowadays covered in the subject of statistical mechanics.

Entropy

Main article: Entropy

Rudolf Clausius

In 1856, German physicist Rudolf Clausius defined the second fundamental theorem (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): "if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat Q from work at the temperature T, has the equivalence-value:"

${} \frac {Q}{T}$

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 inexact differential) are defined as quantities of TdS (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.

To be precise, this equality is only valid, if the heat $\delta Q$ is applied reversibly. If, in contrast, irreversible processes are involved, e.g. some sort of friction, then instead of the above equation one has

$\delta Q \leq T dS \quad{\rm{(second\,\,law)}}\,.$

This is the second law of thermodynamics.

Heat transfer in engineering

A red-hot iron rod from which heat transfer to the surrounding environment will be primarily through radiation.

The discipline of heat transfer, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system. Although the definition of heat implicitly means the transfer of energy, the term heat transfer encompasses this traditional usage in many engineering disciplines and laymen language.

Heat transfer includes the mechanisms of heat conduction, thermal radiation, and mass transfer. In engineering, the term convective heat transfer is used to describe the combined effects of conduction and fluid flow and is often regarded as an additional mechanism of heat transfer. Although distinct physical laws may describe the behavior of each of these methods, real systems often exhibit a complicated combination which are often described by a variety of complex mathematical methods.

Application

In accordance with the first law, heat may be converted to or from work by so-called heat engines, e.g. the steam engine. Heat engines achieve maximum efficiency when the difference between initial and final temperature is largest, resulting in minimal loss. Heat pumps on the other hand operate at a small temperature difference, transferring heat at low temperatures from a reservoir, e.g. from the soil, and deliver it by means of electrical work for heating purposes. Now the temperature difference should be small, to keep the lost electrical work small.

See also

• Effect of sun angle on climate
• Heat death of the Universe
• Heat diffusion
• Heat equation
• Heat exchanger
• Heat flux sensor
• Heat transfer coefficient
• History of heat
• Sigma heat
• Shock heating
• Thermal management of electronic devices and systems
• Thermometer
• Relativistic heat conduction
• Waste heat

References

Bibliography

• Beattie, J.A., Oppenheim, I. (1979). Principles of Thermodynamics, Elsevier, Amsterdam, ISBN 0–444–41806–7.
• Bryan, G.H. (1907). Thermodynamics. An Introductory Treatise dealing mainly with First Principles and their Direct Applications, B.G. Teubner, Leipzig.
• Guggenheim, E.A. (1967) [1949], Thermodynamics. An Advanced Treatment for Chemists and Physicists (fifth ed.), Amsterdam: North-Holland Publishing Company. 
• Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of Thermodynamics, pages 1–97 of volume 1, ed. W. Jost, of Physical Chemistry. An Advanced Treatise, ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.
• Kondepudi, D. (2008), Introduction to Modern Thermodynamics, Chichester UK: Wiley, ISBN 978–0–470–01598–8. 
• Kondepudi, D., Prigogine, I. (1998). Modern Thermodynamics: From Heat Engines to Dissipative Structures, John Wiley & Sons, Chichester, ISBN 0–471–97393–9.
• Maxwell, J.C. (1871), Theory of Heat (first ed.), London: Longmans, Green and Co. 
• Partington, J.R. (1949), An Advanced Treatise on Physical Chemistry., volume 1, Fundamental Principles. The Properties of Gases, London: Longmans, Green and Co. 
• Planck, M. (1903) [1897] (in English), Treatise on Thermodynamics (first ed.), London: Longmans, Green and Co., http://www.onread.com/reader/145819 
• Planck, M. (1927) [1923] (in English), Treatise on Thermodynamics (third ed.), London: Longmans, Green and Co. 
• Reif, F. (1965). Fundamentals of Statistical and Thermal Physics. New York: McGraw-Hll, Inc.. 
• Truesdell, C. (1980). The Tragicomical History of Thermodynamics 1822-1854, Springer, New York, ISBN 0–387–90403–4.

External links

• Heat on In Our Time at the BBC. (listen now)
• Plasma heat at 2 gigakelvins - Article about extremely high temperature generated by scientists (Foxnews.com)
• Correlations for Convective Heat Transfer - ChE Online Resources
• An Introduction to the Quantitative Definition and Analysis of Heat written for High School Students