Heat

In physics, heat, symbolized by Q, is defined as energy in transit. Generally, heat is a form of energy associated with the motion of atoms, molecules and other particles which comprise matter. Heat can be created by chemical reactions (such as burning), nuclear reactions (such as fusion taking place inside the Sun), electromagnetic dissipation (as in electric stoves), or mechanical dissipation (such as friction). Heat can be transferred between objects by radiation, conduction and convection. Temperature, defined as the measure of an object to spontaneously give up energy, is used 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).

Heat emanating from a red-hot iron rod.

History

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 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."

As early as 460 B.C.E., 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."

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. 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."

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.

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...”

In 1824, French engineer 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.

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).

Overview

By common knowledge, the term heat has been used in connection with the warmth, or hotness, 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 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.

The amount of heat exchanged by an object when its temperature varies by one degree is called heat capacity. Heat capacity is specific to each and every object. When referred to a quantity unit (such as mass or moles), the heat exchanged per degree is termed specific heat, and depends primarily on the composition and physical state (phase) of objects. Fuels 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.

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

Infrared radiation is often linked to heat, since objects at room temperature or above will emit radiation mostly concentrated in the mid-infrared band (see black body).

Notation

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 < 0 (-). When a body absorbs heat from its surroundings, Q > 0 (+). Heat transfer rate, or heat flow per unit time, is labeled:

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

to indicate a change per unit time. It is measured in watts. 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″ or q″ or ${\dot {Q}}''$.

Thermodynamics

The amount of heat , $Q$, required to change the temperature of a material from an initial temperature, T₀, to a final temperature, T_f depends on the heat capacity of that material according to the relationship:

$Q=\int _{T_{0}}^{T_{f}}C_{p}\,dT\,\!$

for constant pressure, whereas at constant volume:

$Q=\int _{T_{0}}^{T_{f}}C_{v}\,dT\,\!$

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

$C_{p}=mc_{s}\,\!$

or is dependent on the number of moles and the molar heat capacity, $c_{n}\,\!$ according to:

$C_{p}=nc_{n}\,\!$

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

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

For 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 discontinuos at the Bose-Einstein condensation point.

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.

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

$\Delta U=Q-W\$

which means that the energy of the system can change either via work or via heat. Whereas $U$, 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 $Q$ nor $W$ is conserved. The infinitesimal expression for heat, $\delta Q$, forms an inexact differential for processes involving work. However, for processes involving no change in volume, applied magnetic field, or other external parameters, $\delta Q$, forms an exact differential.

Changes of phase

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:

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

and

$Q=\int _{M_{0}}^{M}L\,dm\,\!$

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, $M_{o}$ 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 doesn't depend on the amount of mass that changes phase, so the equation can normally be written:

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

Sometimes L can be time-dependent if pressure and volume are time-varying, so that the integral can be handled:

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

Heat transfer mechanisms

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

Conduction

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

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

Convection

Convection is usually the dominant form of heat transfer in liquids and gases. This is a term used to characterize the combined effects of conduction and fluid flow. In convection, enthalpy transfer occurs by the movement of hot or cold portions of the fluid together with heat transfer by conduction. For example, when water is heated on a stove, hot water from the bottom of the pan rises, heating the water at the top of the pan. Two types of convection are commonly distinguished, free convection, in which gravity and buoyancy forces drive the fluid movement, and forced convection, where a fan, stirrer, or other means is used to move the fluid. Buoyant convection is due to the effects of gravity, and hence 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.

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—a light bulb filament at 3000K for instance—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 ovens, laser cutting, and RF hair removal.

Other heat transfer mechanisms

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

Heat dissipation

In cold climates, houses with their heating systems form dissipative systems. In spite of efforts to insulate such houses, to reduce heat losses to their exteriors, considerable heat is lost, or dissipated, from them which can make their interiors uncomfortably cool or cold. Furthermore, the interior of the house must be maintained out of thermal equilibrium with its external surroundings for the 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.

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.

See also

• 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

• Plasma heat at 2 gigakelvins - Article about extremely high heat generated by scientists (Foxnews.com)
• Heat and Thermodynamics - Georgia State University
• Correlations for Convective Heat Transfer - ChE Online Resources

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