Heat

When two bodies of different temperature come into contact, with the result that the temperature of the cooler body is raised while that of the hotter body is reduced, we say that heat has been conveyed from the hotter body to the cooler body. The quantity of heat conveyed is measured against the quantity that would be needed to raise the temperature of a gram of water from 0 degrees centigrade to 1 degree centigrade. This unit of heat is known as the calorie. For example, if a gram of water is placed in contact with a hot radiator, and its temperature increases by one degree, we say that one calorie of heat has passed from the radiator to the water.

Different substances have the ability hold more or less heat at a given temperature. Thus, a gram of iron will be able to convey a greater quanity of heat than a gram of lead when both are heated to the same temperature and, after being placed in contact with a cooler body, their temperatures are equally reduced. We say that the specific heat of the iron is greater than the specific heat of the lead. Specific heat is the quantity of heat required to raise the temperature of a substance one degree centigrade. Thus, the specific heat of water is 1. Heat capacity, on the other hand, is the quantity of heat required to raise the temperature of any body, no matter how big or small, by one degree centigrade.

If a house is heated to a stable temperature in the middle of winter, heat is communicated to the rooms from the heating system, while the rooms lose heat to the air outside. Since the temperature in the room does not change, it must be receiving as much heat from the heating system as it is losing to the atmosphere outside. This condition in which a constant temperature is maintained while the same quantity of heat enters and leaves a body is called thermal equilibrium. While the heat is hardly able to impact the entire body of atmosphere surrounding the house, it does warm the air immediately next to it, causing what is called a heat gradient, or a continuous decline in the temperature from the house to the atmosphere.

LATENT HEAT If mixture of ice and water is heated, the mixture will remain at 0 degrees centigrade until all the ice is melted, after which the temperature of the water will begin to increase. Since the temperature remains the same while the ice is melting, even though heat is added, it is said that the heat is latent. When water is converted to steam, the water remains at 100 degrees centigrade, and the process absorbs heat without affecting any temperature change until all the water is vaporized, after which the vapor will increase in temperature. This is another example of latent heat.

The specific latent heat of a substance in changing states is the heat required to transform a gram of the substance from one state to another.

Heat has been studied since ancient times, beginning with the greek philosophers. It was only during and after the Renaissance, however, when means for measuring temperature accurately was developed, that the scientific study of heat was able to advance. Galileo Galilei (1564-1642)fashioned a thermometer of sorts, while graded thermometers were introduced in the early 1600s. The later 17th century saw decided improvements in instrumentation, spurring research.

Isaac Newton (1642-1727) provided a rudimentary theory of heat flow based on the assumption that the rate at which heat is transferred from one body to another is proportional to their temperature difference, but it was not until the early 1800s that a general equation for heat flow was introduced through the work of Jean Baptiste Joseph Fourier (1768-1830). Using his equations, it was possible to predict the temperatures in solids that would result under various sets of circumstances, called intitial conditions and boundary conditions. For example, a red hot iron ball suspended by a chain will cool if suspended in air. Fourier's equations would yield predictions for the temperature at any point inside the iron ball and at its surface as it cooled.

With the invention of a practical steam engine by James Watt (1736-1819), the relationship between heat and mechanical work came under increased scrutiny. In 1898, Benjamin Thompson (Count Rumford,1753-1814) demonstrated that mechanical work can produce heat, a relationship converse to the one where a steam engine produces work from heat. In an expermiment, he used a dull cannon borer, which when rotated inside a large mass of gun metal, generated appreciable quantities of heat. Finally, James Prescott Joule (1818-1889) and others demonstrated that the conversion of heat to work and visa versa occurs at a fixed rate, and showed that heat is a form of energy that is neither created nor destroyed, but that changes form.

Another scientist, Sadi Carnot (1796-1832), demonstrated an important limitation that exists when heat is used to produce work. He showed that the production of power from an engine is always accompanied by the movement of heat from a hotter to a cooler body, and that there was an upper limit to the efficiency (the ratio of the work produced to the heat transferred) that could be obtained from such action. In pure conduction of heat, none of the heat is transformed into work when it moves from a hotter to a colder body, but the maximum work that can be obtained in such a process is achieved by any process that is reversible, meaning that it can go through all the transformations in reverse. Carnot showed that the efficiency of a reversible process was only dependent on the initial and final temperatures through which the heat flows, and was independent of the substance used to make the transfer.

It was Rudolf Clausius (1822-1888)who took the the two discoveries enunciated by Joule and Carnot, and synthesized them into the modern science of thermodynamics.

The study of thermodynamics was considerably enhanced by the discovery of what are called the ideal gas laws. At a given temperature, the product of the pressure of a sample of gas and its volume remains constant, even if each of those variables undergoes change. Furthermore, if the volume of a gas remains the same, the pressure is proportional to the temperature, while if the pressure remains constant, the volume is proportional to the temperature. It was found that a change in the temperature of a gas of one degree centigrade caused the gas to add an additional 1/273 of its previous volume when the pressure is held constant. It was evident that by reducing the temperature sufficiently, one could reduce the volume of the gas to zero. Taking the final temperature at which the volume of all gases is reduced to zero, as the zero temperature itself, one comes up with the Kelvin scale of temperature, named after Lord Kelvin (William Thomson (1824-1907), who introduced it. A final formula connecting the temperature, pressure and volume of a given sample of gas is given by PV=nRT, where P is the pressure of the sample, V is the volume, T is the temperature in degrees Kelvin, R is a constant, and n is the number of moles (gram molecular weight).

This is called the ideal gas equation because it is not strictly adhered to by all gases at all temperatures and pressures. Monotomic gases such as helium most closely follow in their behavior that predicted by the ideal gas equation.

Carnot's principle demonstrates that the effiency of a reversible engine is dependent on the difference in temperature between the inital and final temperatures of the working substance. In degrees Kelvin, the formula for expressing this efficiency is simply:

T1 -T2/T1, or 1-T2/T1.

where T1 is the hotter body and T2 is the cooler body.

Since heat must flow from a hotter to a cooler body to produce work, T2 is always less than T1, and the efficiency is always less than 1, but approaches 1 (100 percent efficiency) as T2 approaches absolute zero. If it were possible to achieve a temperature of absolute zero, all the heat from the hotter body would theoretically be available for useful work.

Kinetic Theory of Gases: Heat As Motion While Clausius and Joule were working on their respective theories of heat, they also developed the idea that the action of the minutest particles of a gas, called molecules, is responsible for the physical propterties of a gas such as its temperature and pressure. Thus, the collision of countless molecules of gas against the container that holds it was responsible for the pressure against the container. The increase in the pressure of a gas with temperature at constant volume demonstrates that higher temperatures are accompanied by faster molecular motions, according to this theory. Joule was able to derive an expression for the velocity of molecules as a function of pressure and density. From there, it could be shown that the kinetic energy of the molecules (1/2mv(sq), where m is the mass of a molecule, and v is the mean velocity of molecules in the gas), was proportional to the temperature of a gas.

This theory was further developed by James Clerk Maxwell (1831-1879), who was the first to calculate the mean distance that a molecule travels until it hits another molecule. Maxwell's calculations were used by another scientist, Josef Loschmidt (1821-1895), to make the first estimate of the size of a molecule. Ludwig Boltzmann (1844-1906) also worked on the same theory and made additional advances, until the field of statistical mechanics, as it is now called, was able to account for many of the thermodynamic properties of gases.

Heat is generally conveyed by three means: conduction, convection, and radiation. In conduction, heat is transferred from hotter to the bounding cooler portions of a material while the parts of the material remain fixed. This is the chief means by which heat is transmitted in a solid, where parts do not move with respect to one another, although it also applies to liquids and gases where currents are kept to a minimum. On the other hand, liquids and gases often experience currents that transport large portions of material to new locations. This transport is called convection, and when the portions transported are of different temperatures, it can facilitate heat transfer throughout the body. As an example, the air surrounding a radiator in a house is heated through conduction if the air remains still, but if a fan is applied to the radiator, the heat is much more quickly dispersed to the rest of the room through convection.

The steam that fills a metal radiator transmits heat from the furnace primarily through convection, but the heat moves from the inner part of the radiator to the outer part that heats the air, through conduction.

Radiation Even though a heated substance is surrounded by a vaccum, it is found that it will lose heat to its surroundings. Since conduction and convection cannot occur in a vacuum, it is said that the heat is conveyed to its surroundings through radiation. Hot bodies produce radiation in the form of waves similar to that of light that require no medium to transport them. These are called electromagnetic emissions, since it was established by Maxwell that their properties are identical to waves predicted by Maxwell's theory of electricity and magnetism. Radiation obeys the laws of thermodynamics, and as such, heats cooler bodies and is heated by hotter bodies that surround it.

A fire, for example, may heat the surrounding air through conduction and convection, but much of its heat energy is transformed into electromagnetic radiation, including light.

Investigations into the emissions of radiant heat led to the founding of the field of quantum mechanics by Max Plank (Max Planck (1858-1947).

ENTOPY The sums of the increments of heat absorbed or expelled by a substance in the process of undergoing changes in temperature, pressure and volume, divided by the absolute temperature during any one of these incremental changes, is known as entropy. In a reversible cycle, the entropy of the working substance, when returned to the same state after any transformation, is found to be zero. If, however, the process is irreversible, as is generally the case, since the workng substance loses heat to its surroundings and is thus subject to irreversible changes, the entropy is found to increase. It is thus often said that the entropy of the universe is increasing, since irreversible processes are always taking place, and that any process, while it may approach reversiblity, can never achieve it.

Advanced thermodynamics and degrees of freedom Josiah Willard Gibbs (1839-1903)advanced the science of thermodynamics by explaining how a number of different substances will behave under changing conditions of temperature and pressure. His "phase rule," F = C − P + 2, where F is the degrees of freedom (the number of variables from among the set that define the state of the chemical components), C is the number of chemical components, and P is the number of phases (solid, liquid or gas) that can coexist under the given set of variables. Gibbs made many other important contributions to the field of thermodynamics.

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. Generally, heat is a form of energy associated with the motion of atoms, molecules 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 Heat.>>

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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