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Thermodynamic Equilibrium

Thermodynamic equilibrium

In thermodynamics, a thermodynamic system is in thermal equilibrium or thermodynamic equilibrium when its macroscopic observables have ceased to change with time -- for example, an ideal gas whose distribution function has stabilised to a Maxwell-Boltzmann distribution. This allows a single temperature to be attributed to the whole system. (See also chemical equilibrium). The process that leads to a thermodynamic equilibrium is called thermalisation. An example of this is a system of interacting particles that is left undisturbed by outside influences. By interacting, they will share energy/momentum among themselves and reach a state where the global statistics are unchanging in time. In thermodynamics, the local state of a system at thermodynamic equilibrium is determined by the values of its intensive parameters (examples of intensive parameters include pressure,temperature etc.).

Local Thermodynamic Equilibrium (LTE)

It is useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by intensive parameters (for example, temperature controls heat exchanges). Global thermodynamic equilibrium means that those intensive parameters are homogeneous throughout the whole system, while local thermodynamic equilibrium (LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that for any point, one can assume thermodynamic equilibrium in some neighborhood about that point. If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the very concept of temperature breaks down, and the temperature becomes undefined. It is important to note that this local equilibrium applies only to massive particles. In a radiating gas, the photons being emitted and absorbed by the gas need not be in thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist. As an example, let us take a glass of water which contains a melting ice cube. LTE will exist in this case. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If we look at the energies of the molecules located near a given point, they will be distributed according to the Maxwell-Boltzmann distribution for a certain temperature. If we look at the energies of the molecules located near another point, they will be distributed according to the Maxwell-Boltzmann distribution for another temperature. Local thermodynamic equilibrium is not a stable state, unless it is maintained by exchanges between the system and the outside(for example, it could be maintained inside the glass of water by regularly adding ice into it in order to compensate for the melting). Transport phenomena are processes which lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.

Thermodynamics

Thermodynamics (from the Greek thermos meaning heat and dynamis meaning power) is a branch of physics that studies the effects of temperature, pressure, and volume changes on physical systems at the macroscopic scale. In simpler terms, heat means ‘energy in transit’ and dynamics relates to ‘movement’. Thus, in essence thermodynamics studies how energy instills movement. The starting point for most thermodynamic considerations are the laws of thermodynamics. These laws postulate that energy can be exchanged between physical systems in the form of heat and work, as well as the existence of a quantity named entropy, which can be associated with every system. From its inception, thermodynamics developed out of the need to increase the efficiency of early steam engines. The first engine constructed was the 1698 Savery engine as shown below: steam engines]

Overview

Thermodynamics in most regards is held to be a difficult subject. In chemical engineering for example, which teaches one of the more rigorous variations of such, thermodynamics is considered a weeder course. One of the better ways to learn thermodynamics is to follow a ground up development of its concepts and principles, beginning with units as SI and English, parameters as pressure, temperature, and volume, etc., properties of substances as gas, vapor, liquid, and solid, etc., phase diagrams, the laws of thermodynamics, equations of state, continuing onward through such advanced subjects as multi-phase reaction thermodynamics, high-speed gas flow thermodynamics, or molecular thermodynamics, etc. A difficult concept in thermodynamics is that of "entropy". In particular, the entropy of a system exchanging no heat with the outside can never decrease with time. As such, entropy allows predictions on the transformations and energy exchanges that are accessible to a given system. Related to entropy, Statistical mechanics or statistical thermodynamics is one of the underlying theories that sustain thermodynamics; it provides a way to predict the entropy of a thermodynamic system, based on the statistical analysis of the fluctuations the system experiences over a set of microstates

History

microstate A short history of thermodynamics begins with the British physicist and chemist Robert Boyle who in 1656, in coordination with English scientist Robert Hooke, invented the air pump. Using this pump, Boyle and Hooke noticed the pressure-temperature-volume correlation. In time, the ideal gas law was formulated. Soon thereafter, in 1679, based on these concepts, an associate of Boyle's named Denis Papin built a bone digester, which is a closed vessel with a tightly fitting lid that confines steam until a high pressure is generated. Later designs implemented a steam release valve to keep the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a piston and cylinder engine. He did not however follow through with his design. Nevertheless, in 1698, based on Papin’s designs, engineer Thomas Savery built the first engine. These early engines being crude and inefficient attracted the attention of the leading scientists of the time. One such scientist was Sadi Carnot, the “father of thermodynamics”, who in 1824 published “Reflections on the Motive Power of Fire”, a discourse on heat, power, and engine efficiency. This marks the start of thermodynamics as a modern science.

Thermodynamic systems

Of most importance in thermodynamics is the concept of the “system”. A system is the region of the universe under study. A system is separated from the remainder of the universe by a boundary which may be imaginary or not, but which, by convention delimits a finite volume. The possible exchanges of work, heat, or matter between the system and the surroundings take place across this boundary. There are four dominate classes of systems: matter #Isolated Systems – matter and energy may not cross the boundary. #Adiabatic Systems – heat and matter may not cross the boundary. #Closed Systems – matter may not cross the boundary. #Open Systems – heat, work, and matter may cross the boundary. For closed systems, as time goes by, internal differences in the system tend to even out; pressures and temperatures tend to equalize, as do density differences. A system in which all equalizing processes have gone practically to completion, is considered to be in a state of thermodynamic equilibrium. In thermodynamic equilibrium, a system's properties are, by definition, unchanging in time. Systems in equilibrium are much simpler and easier to understand than systems which are not in equilibrium. Often, when analyzing a thermodynamic process, it can be assumed that each intermediate state in the process is at equilibrium. This will also considerably simplify the situation. Thermodynamic processes which develop so slowly as to allow each intermediate step to be an equilibrium state are said to be reversible processes.

Thermodynamic parameters

The central concept of thermodynamics is that of energy, the ability to do work. As stipulated by the first law, the total energy of the system and its surroundings is conserved. It may be transferred into a body by heating, compression, or addition of matter, and extracted from a body either by expansion, cooling, or extraction of matter. Just as in mechanics, energy transfer is effected by a force causing a displacement, with the product of the two being the amount of energy transferred. In a similar way, thermodynamic systems can be thought of as transferring energy as the result of a generalized force causing a generalized displacement, with the product of the two being the amount of energy transferred. These thermodynamic force-displacement pairs are known as conjugate variables. The most common conjugate thermodynamic variables are pressure-volume (mechanical parameters), temperature-entropy (thermal parameters), and chemical potential-particle number (material parameters).

Thermodynamic instruments

There are two types of thermodynamic instruments, the meter and the reservoir. A thermodynamic meter is any device which measures any parameter of a thermodynamic systems. In some cases, the thermodynamic parameter is actually defined in terms of an idealized measuring instrument. For example, the zeroth law states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted by James Maxwell in 1872, asserts that it is possible to measure temperature. An idealized thermometer is a sample of an ideal gas at constant pressure. From the ideal gas law PV=NRT, the volume of such a sample can be used as an indicator of temperature; in this manner it defines temperature. Although pressure is defined mechanically, a pressure-measuring device, called a barometer may also be constructed from a sample of an ideal gas held at a constant temperature. A calorimeter is a device which is used to measure and define the internal energy of a system. A thermodynamic reservoir is a system which is so large that it does not appreciably alter its state parameters when brought into contact with the test system. It is used to impose a particular value of a state parameter upon the system. For example, a pressure reservoir is a system at a particular pressure, which imposes that pressure upon any test system that it is mechanically connected to. The earths atmosphere is often used as a pressure reservoir.

Thermodynamic states

When a system is at equilibrium under a given set of conditions, it is said to be in a definite state. The state of the system can be described by a number of intensive variables and extensive variables. The properties of the system can be described by an equation of state which specifies the relationship between these variables. State may be thought of as the instantaneous quantitative description of a system with a set number of variables held constant.

Thermodynamic processes

A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. Typically, each thermodynamic process is distinguished from other processes, in energetic character, according to what parameters, as temperature, pressure, or volume, etc., are held fixed. Furthermore, it is useful to group these processes into pairs, in which each variable held constant is one member of a conjugate pair. The five most common thermodynamic processes are shown below: #An isobaric process occurs at constant pressure. #An isochoric process occurs at constant volume. #An isothermal process occurs at a constant temperature. #An isentropic process occurs at a constant entropy. #An adiabatic process occurs without loss or gain of heat.

The laws of thermodynamics

In thermodynamics, there are four laws of very general validity, and as such they do not depend on the details of the interactions or the systems being studied. Hence, they can be applied to systems about which one knows nothing other than the balance of energy and matter transfer. Examples of this include Einstein's prediction of spontaneous emission around the turn of the 20th century and current research into the thermodynamics of black holes. The four laws are:
- Zeroth law of thermodynamics, about the transitivity of thermodynamic equilibrium
- If systems A and B are in thermal equilibrium, and systems B and C are in thermal equilibrium, then A and C are also in thermal equilibrium.
- Two systems in thermal equilibrium with a third system, all must be in equilibrium with each other.
- First law of thermodynamics, or a statement about the conservation of energy
- The work exchanged in an adiabatic process depends only on the initial and the final state and not on the details of the process.
- The heat energy flowing into a system is equal to the sum of the increase in the internal energy of the system and the work done by the system.
- The change in internal energy of a system is

\Delta

U = q + w, where q is heat flow and w is work.
- Second law of thermodynamics, about entropy
- The entropy of an isolated system never decreases (see Maxwell's demon)
- A system operating in contact with a thermal reservoir cannot produce positive work in its surroundings (Kelvin)
- A system operating in a cycle cannot produce a positive heat flow from a colder body to a hotter body (Clausius)
- Third law of thermodynamics, about absolute zero temperature
- All processes cease as temperature approaches zero.
- As temperature goes to 0, the entropy of a system approaches a constant

Thermodynamic potentials

As derived from the energy balance equation on a thermodynamic system there exist energetic quantities called thermodynamic potentials, being the quantitative measure of the stored energy in the system. The four most well known potentials are: Potentials are used to measure energy changes in systems as they evolve from an initial state to a final state. The potential used depends on the constraints of the system, such as constant temperature or pressure. Internal energy is the internal energy of the system, enthalpy is the internal energy of the system plus the energy related to pressure-volume work, and Helmholtz and Gibbs free energy are the energies available in a system to do useful work when the temperature and volume or the pressure and temperature are fixed, respectively.

Thermodynamic evolution

In 1875 Austrian physicist Ludwig Boltzmann declared: "the general struggle for existence of animate beings is a struggle for entropy". Ever since, there has been a continuous search to elucidate the thermodynamic mechanism behind evolution. As it is generally agreed that life evolved from non-life, a process called abiogenesis, by some form of chemical evolution, and as it is understood that both life and non-life abide by the laws of thermodynamics, then, in theory, it is reasoned that there should exist a functionable model of thermodynamic evolution. This line of research defines the field of thermodynamic evolution.

Quotes & humor

- A common scientific joke expresses the three laws simply and surprisingly accurately as: : Zeroth: "You must play the game." : First: "You can't win." : Second: "You can't break even." : Third: "You can't quit the game."

References

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External links

- [http://thermohistory.com/ History of Thermodynamics]
- [http://www.shakespeare2ndlaw.com Shakespeare & Thermodynamics]
- [http://www.wiley.com/legacy/college/boyer/0470003790/reviews/thermo/thermo_intro.htm Biochemistry Thermodynamics]

Laws

- [http://www.humanthermodynamics.com/0th-Law-Variations.html 10+ Variations of the 0th Law]
- [http://www.humanthermodynamics.com/1st-Law-Variations.html 30+ Variations of the 1st Law]
- [http://www.humanthermodynamics.com/2nd-Law-Variations.html 110+ Variations of the 2nd Law]
- [http://www.humanthermodynamics.com/3rd-Law-Variations.html 20+ Variations of the 3rd Law]
- [http://www.humanthermodynamics.com/4th-Law-Variations.html 10+ Variations of the 4th Law] ko:열역학 ja:熱力学 th:อุณหพลศาสตร์

Ideal gas

An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of negligible volume, with no intermolecular forces. Additionally, the constituent atoms or molecules undergo perfectly elastic collisions with the walls of the container. The real gases that actually exist do not exhibit these exact properties, although the approximation is often good enough to treat real gases as ideal gases. There are basically three types of ideal gas:
- the classical or Maxwell-Boltzmann ideal gas,
- the ideal quantum Bose gas, composed of bosons, and
- the ideal quantum Fermi gas, composed of fermions.

Classical ideal gas

The thermodynamic properties of an ideal gas can be described by two equations: The equation of state of a classical ideal gas is given by the ideal gas law. :

PV = nRT = NkT\,

The internal energy of an ideal gas is given by: :

U = \hat_V nRT = \hat_V NkT

where

\hat_V

is a constant (e.g. equal to 3/2 for a monatomic gas) and: (with SI units appended) :
- U is internal energy (joule) :
- P is the pressure (pascal) :
- V is the volume (cubic meter) :
- n is the amount of gas (mole) :
- R is the ideal gas constant (joule per kelvin per mole) :
- T is the absolute temperature (kelvin) :
- N is the number of particles :
- k is the Boltzmann constant (joule per kelvin per particle), :
- nR=Nk is the amount of gas (joule per kelvin). The probability distribution of particles by velocity or energy is given by the Boltzmann distribution. The ideal gas law is an extension of experimentally discovered gas laws. Real fluids at low density and high temperature, approximate the behavior of a classical ideal gas. However, at lower temperature or higher density, a real fluid deviates strongly from the behavior of an ideal gas, particularly as it condenses from a gas into a liquid or solid.

Heat capacities of an ideal gas

The heat capacity at constant volume of an ideal gas is: :

C_V = \left(\frac\right)_V =  \hat_V Nk

It is seen that the constant

\hat_V

is just the dimensionless specific heat capacity at constant volume. It is equal to half the number of degrees of freedom per particle. For a monatomic gas this is just

\hat_V=3/2

while for a diatomic gas it is

\hat_V=5/2

. It is seen that macroscopic measurements on heat capacity provide information on the microscopic structure of the molecules. The heat capacity at constant pressure of an ideal gas is: :

C_P = \left(\frac\right)_P = (\hat_V+1) Nk

where

H=U+PV

is the enthalpy of the gas. It is seen that

\hat_P

is also a constant and that the dimensionless heat capacities are related by: :

\hat_P-\hat_V=1

The entropy of an ideal gas

Using the results of thermodynamics only, we can go a long way in determining the expression for the entropy of an ideal gas. This is an important step since, according to the theory of thermodynamic potentials, of which the internal energy U is one, if we can express the entropy as a function of U and the volume V, then we will have a complete statement of the thermodynamic behavior of the ideal gas. We will be able to derive both the ideal gas law and the expression for internal energy from it. Since the entropy is an exact differential, using the chain rule, the change in entropy when going from a reference state 0 to some other state with entropy S may be written as

\Delta S

where: :

\Delta S = \int_^dS
=\int_^ \left(\frac\right)_V\!dT
+\int_^ \left(\frac\right)_T\!dV

Using the definition of the heat capacity at constant volume for the first differential and the appropriate Maxwell relation for the second we have: :

\Delta S
=\int_^ \frac\,dT+\int_^\left(\frac\right)_VdV

Using the expressions for an ideal gas and integrating yields: :

\Delta S
= Nk\ln\left(\frac\right)

where all constants have been incorporated into the logarithm as f(N) which is some function of the particle number N having the same dimensions as

VT^

in order that the argument of the logarithm be dimensionless. We now impose the constraint that the entropy be extensive. This will mean that when the extensive parameters (V and N) are multiplied by a constant, the entropy will be multiplied by the same constant. Mathematically: :

\Delta S(T,aV,aN)=a\Delta S(T,V,N)\,

From this we find an equation for the function f(N) :

af(N)=f(aN)\,

Differentiating this with respect to a, setting a equal to unity, and then solving the differential equation yields f(N): :

f(N)=\phi N\,

where φ is some constant with the dimensions of

VT^/N

. Substituting into the equation for the change in entropy: :

\frac = \ln\left(\frac\right)\,

This is about as far as we can go using thermodynamics alone. Note that the above equation is flawed - as the temperature approaches zero, the entropy approaches negative infinity, in contradiction to the third law of thermodynamics. In the above "ideal" development, there is a critical point, not at absolute zero, at which the argument of the logarithm becomes unity, and the entropy becomes zero. This is unphysical. The above equation is a good approximation only when the argument of the logarithm is much larger than unity - the concept of an ideal gas breaks down at low values of V/N. Nevertheless, there will be a "best" value of the constant in the sense that the predicted entropy is as close as possible to the actual entropy, given the flawed assumption of ideality. It remained for quantum mechanics to introduce a reasonable value for the value of φ which yields the Sackur-Tetrode equation for the entropy of an ideal gas. It too suffers from a divergent entropy at absolute zero, but is a good approximation to an ideal gas over a large range of densities.

Thermodynamic potentials of an ideal gas

Since the dimensionless heat capacity at constant pressure

\hat_P

is a constant we can express the entropy in what will prove to be a more convenient form: :

\frac=\ln\left( \frac\right)+\hat_P

where Φ is now the undetermined constant. The chemical potential of the ideal gas is calculated from the corresponding equation of state (see thermodynamic potential): :

\mu=\left(\frac\right)_

where G is the Gibbs free energy and is equal to U+PV-TS so that: :

\mu(T,V,N)=-kT\ln\left(\frac\right)

The thermodynamic potentials for an ideal gas can now be written as functions of T, V, and N as: : The most informative way of writing the potentials is in terms of their natural variables, since each of these equations can be used to derive all of the other thermodynamic variables of the system. In terms of their natural variables, the thermodynamic potentials of a single-specie ideal gas are: :

U(S,V,N)=\hat_V Nk\left(\frac\right)^

A(T,V,N)=-NkT\left(1+\ln\left(\frac\right)\right)

H(S,P,N)=\hat_P Nk\left(\frac\right)^

G(T,P,N)=-NkT\ln\left(\frac\right)

Ideal quantum gases

In the above mentioned Sackur-Tetrode equation, the best choice of the entropy constant was found to be proportional to the quantum thermal wavelength of a particle, and the point at which the argument of the logarithm becomes zero is roughly equal to the point at which the average distance between particles becomes equal to the thermal wavelength. In fact, quantum theory itself predicts the same thing. Any gas behaves as an ideal gas at high enough temperature and low enough density, but at the point where the Sackur-Tetrode equation begins to break down, the gas will begin to behave as a quantum gas, composed of either bosons or fermions. Just as there is a classical ideal gas, there are ideal quantum gases. An ideal gas of bosons will be governed by Bose-Einstein statistics and the distribution of energy will be in the form of a Bose-Einstein distribution. An ideal gas of fermions will be governed by Fermi-Dirac statistics and the distribution of energy will be in the form of a Fermi-Dirac distribution. Category:Gases ko:이상기체 ja:理想気体

Distribution function

:This article describes the distribution function as used in physics. You may be looking for the related mathematical concepts of probability density function or cumulative distribution function. In molecular kinetic theory in physics, a particle's distribution function is a function of seven variables,

f(x,y,z,t;v_x,v_y,v_z)

, which gives the number of particles per unit volume in phase space. It is the number of particles having approximately the velocity

(v_x,v_y,v_z)

near the place

(x,y,z)

and time

(t)

. The usual normalization of the distribution function is :

n(x,y,z,t) = \int f \,dv_x \,dv_y \,dv_z

N(t) = \int n \,dx \,dy \,dz

Here, N is the total number of particles and n is the number density of particles - the number of particles per unit volume, or the density divided by the mass of individual particles. Particle distribution functions are often used in plasma physics to describe wave-particle interactions and velocity-space instabilities. Distribution functions are also used in fluid mechanics and statistical mechanics. The basic distribution function uses the Boltzmann constant

k

and temperature

T

with the number density to modify the normal distribution: :

f = \frac e^

Related distribution functions may allow bulk fluid flow, in which case the velocity origin is shifted, so that the exponent's numerator is

(m(v_x - u_x)^2 + (v_x - u_x)^2 + (v_x - u_x)^2)

;

(u_x, u_y, u_z)

is the bulk velocity of the fluid. Distribution functions may also feature non-isotropic temperatures, in which each term in the exponent is divided by a different temperature. Plasma theories such as magnetohydrodynamics may assume the particles to be in thermodynamic equilibrium. In this case, the distribution function is Maxwellian. This distribution function allows fluid flow and different temperatures in the directions parallel to, and perpendicular to, the local magnetic field. More complex distribution functions may also be used since plasmas are rarely in thermal equilibrium.

Temperature

Temperature is the physical property of a system which underlies the common notions of "hot" and "cold"; the material with the higher temperature is said to be hotter. Physically, temperature is a measure of the random agitation of matter and ambiant photons, under the effect of thermal fluctuations. It is a fundamental parameter in thermodynamics and it is conjugate to entropy. More quantitatively, the order of magnitude of the fluctuations of the energy associated with an atom, molecule or another elementary constituant of a physical system is

k_B T

, where

k_B

is Boltzmann's constant, and T is temperature, expressed in Kelvins.

Overview

The formal properties of temperature are studied in thermodynamics and statistical mechanics. The temperature of a system at thermodynamic equilibrium is defined by a relation between the amount of heat

\delta Q

incident on the system during an infinitesimal quasistatic transformation, and the variation

\delta S

of its entropy during this transformation. :

\delta S = \frac

Contrarly to entropy and heat, whose microscopic definitions are valid even far away from thermodynamic equilibrium temperature can only be defined at thermodynamic equilibrium, or local thermodynamic equilibrium (see below). As a system receives heat its temperature rises, similarly a loss of heat from the system tends to decrease its temperature (at the - uncommon - exception of negative temperature, see below). When two systems are at the same temperature, no heat transfer occurs between them. When a temperature difference does exist, heat will tend to move from the higher-temperature system to the lower-temperature system, until they are at thermal equilibrium. This heat transfer may occur via conduction, convection or radiation (see heat for additional discussion of the various mechanisms of heat transfer). Temperature is also related to the amount of internal energy and enthalpy of a system. The higher the temperature of a system, the higher its internal energy and enthalpy are. Temperature is an intensive property of a system, meaning that it does not depend on the system size or the amount of material in the system. Other intensive properties include pressure and density. By contrast, mass and volume are extensive properties, and depend on the amount of material in the system.

Role of temperature in nature

Temperature plays an important role in almost all fields of science, including physics, chemistry, and biology. Many physical properties of materials including the phase (solid, liquid, gaseous or plasma), density, solubility, vapor pressure, and electrical conductivity depend on the temperature. Temperature also plays an important role in determining the rate and extent to which chemical reactions occur. This is one reason why the human body has several elaborate mechanisms for maintaining the temperature at 37 °C, since temperatures only a few degrees higher can result in harmful reactions with serious consequences. Temperature also controls the type and quantity of thermal radiation emitted from a surface. One application of this effect is the incandescent light bulb, in which a tungsten filament is electrically heated to a temperature at which significant quantities of visible light are emitted. Temperature-dependence of the speed of sound in air c, density of air ρ and acoustic impedance Z vs. temperature °C

Temperature measurement

Main article: Temperature measurement Temperature measurement using modern scientific thermometers and temperature scales goes back at least as far as the early 18th century, when Gabriel Fahrenheit adapted a thermometer (switching to mercury) and a scale both developed by Ole Christensen Rømer. Fahrenheit's scale is still in use, alongside the Celsius scale and the Kelvin scale.

Units of temperature

The basic unit of temperature (symbol: T) in the International System of Units (SI) is the kelvin (K). One kelvin is formally defined as 1/273.16 of the temperature of the triple point of water (the point at which water, ice and water vapor exist in equilibrium). The temperature 0 K is called absolute zero and corresponds to the point at which the molecules and atoms have the least possible thermal energy. An important unit of temperature in theoretical physics is the Planck temperature (1.4 × 10³² K). In the field of plasma physics, because of the high temperatures encountered and the electromagnetic nature of the phenomena involved, it is customary to express temperature in electronvolts (eV) or kiloelectronvolts (keV), where 1 eV = 11,605 K. In the study of QCD matter one routinely meets temperatures of the order of a few hundred MeV, equivalent to about 10¹² K. For everyday applications, it is often convenient to use the Celsius scale, in which 0 °C corresponds to the temperature at which water freezes and 100 °C corresponds to the boiling point of water at sea level. In this scale a temperature difference of 1 degree is the same as a 1 K temperature difference, so the scale is essentially the same as the kelvin scale, but offset by the temperature at which water freezes (273.15 K). Thus the following equation can be used to convert from degrees Celsius to kelvins. :

\mathrm

In the United States, the Fahrenheit scale is widely used. On this scale the freezing point of water corresponds to 32 °F and the boiling point to 212 °F. The following formula can be used to convert from Fahrenheit to Celsius: :

\mathrm

See temperature conversion formulas for conversions between most temperature scales. ¹ Only the kelvin, Celsius, Fahrenheit, and Rankine scales are in use today.
² Some numbers in this table have been rounded off.
³ Normal human body temperature is 36.8 °C ±0.7 °C, or 98.2 °F ±1.3 °F.

Negative temperatures

:See main article: Negative temperature. For some systems and specific definitions of temperature, it is possible to obtain a negative temperature. A system with a negative temperature is not colder than absolute zero, but rather it is, in a sense, hotter than infinite temperature (sic).

Articles about temperature ranges:

- 10⁻¹² K = 1 picokelvin (pK)
- 10⁻⁹ K = 1 nanokelvin (nK)
- 10⁻⁶ K = 1 microkelvin (µK)
- 10⁻³ K = 1 millikelvin (mK)
- 10⁰ K = 1 kelvin
- 10¹ K = 10 kelvins
- 10² K = 100 kelvins
- 10³ K = 1,000 kelvin = 1 kilokelvin (kK)
- 10⁴ K = 10,000 kelvins = 10 kK
- 10⁵ K = 100,000 kelvins = 100 kK
- 10⁶ K = 1 megakelvin (MK)
- 10⁹ K = 1 gigakelvin (GK)
- 10¹² K = 1 terakelvin (TK) See Orders of magnitude (temperature).

Theoretical foundation of temperature

Zeroth-law definition of temperature

While most people have a basic understanding of the concept of temperature, its formal definition is rather complicated. Before jumping to a formal definition, let us consider the concept of thermal equilibrium. If two closed systems with fixed volumes are brought together, so that they are in thermal contact, changes may take place in the properties of both systems. These changes are due to the transfer of heat between the systems. When a state is reached in which no further changes occur, the systems are in thermal equilibrium. Now a basis for the definition of temperature can be obtained from the so-called zeroth law of thermodynamics which states that if two systems, A and B, are in thermal equilibrium and a third system C is in thermal equilibrium with system A then systems B and C will also be in thermal equilibrium (being in thermal equilibrium is a transitive relation; moreover, it is an equivalence relation). This is an empirical fact, based on observation rather than theory. Since A, B, and C are all in thermal equilibrium, it is reasonable to say each of these systems shares a common value of some property. We call this property temperature. Generally, it is not convenient to place any two arbitrary systems in thermal contact to see if they are in thermal equilibrium and thus have the same temperature. Also, it would only provide an ordinal scale. Therefore, it is useful to establish a temperature scale based on the properties of some reference system. Then, a measuring device can be calibrated based on the properties of the reference system and used to measure the temperature of other systems. One such reference system is a fixed quantity of gas. The ideal gas law indicates that the product of the pressure and volume (P · V) of a gas is directly proportional to the temperature: :

P \cdot V = n \cdot R \cdot T

(1) where 'T is temperature, n is the number of moles of gas and R is the gas constant. Thus, one can define a scale for temperature based on the corresponding pressure and volume of the gas: the temperature in kelvins is the pressure in pascals of one mole of gas in a container of one cubic metre, divided by 8.31... In practice, such a gas thermometer is not very convenient, but other measuring instruments can be calibrated to this scale. Equation 1 indicates that for a fixed volume of gas, the pressure increases with increasing temperature. Pressure is just a measure of the force applied by the gas on the walls of the container and is related to the energy of the system. Thus, we can see that an increase in temperature corresponds to an increase in the thermal energy of the system. When two systems of differing temperature are placed in thermal contact, the temperature of the hotter system decreases, indicating that heat is leaving that system, while the cooler system is gaining heat and increasing in temperature. Thus heat always moves from a region of high temperature to a region of lower temperature and it is the temperature difference that drives the heat transfer between the two systems.

Temperature in gases

As mentioned previously for a monatomic ideal gas the temperature is related to the translational motion or average speed of the atoms. The kinetic theory of gases uses statistical mechanics to relate this motion to the average kinetic energy of atoms and molecules in the system. For this case 7736 K = 7463 degrees Celsius corresponds to an average kinetic energy of one electronvolt; to take room temperature (300 K) as an example, the average energy of air molecules is 300/7736 eV, or 0.0388 electronvolt. This average energy is independent of particle mass, which seems counterintuitive to many people. Although the temperature is related to the average kinetic energy of the particles in a gas, each particle has its own energy which may or may not correspond to the average. However, after an examination of some basic physics equations it makes perfect sense. The second law of thermodynamics states that any two given systems when interacting with each other will later reach the same average energy. Temperature is a measure of the average kinetic energy of a system. The formula for the kinetic energy of an atom is:
:

K_t = \begin \frac \end mv^2

(Note that a calculation of the kinetic energy of a more complicated object, such as a molecule, is slightly more involved. Additional degrees of freedom are available, so molecular rotation or vibration must be included.)

Thus, particles of greater mass (say a neon atom relative to a hydrogen molecule) will move slower than lighter counterparts, but will have the same average energy. This average energy is independent of the mass because of the nature of a gas, all particles are in random motion with collisions with other gas molecules, solid objects that may be in the area and the container itself (if there is one). A visual illustration of this [http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm from Oklahoma State University] makes the point more clear. Not all the particles in the container have different velocities, regardless of whether there are particles of more than one mass in the container, but the average kinetic energy is the same because of the ideal gas law. In a gas the distribution of energy (and thus speeds) of the particles corresponds to the Boltzmann distribution. An electronvolt is a very small unit of energy, approximately 1.602×10^-19 joule.

Temperature of the vacuum

When a satellite in empty space is heated by sunshine and cooled by radiating energy away it is not in thermodynamic equilibrium and has no well-defined temperature. A system in a vacuum will radiate its thermal energy, i.e. convert heat into electromagnetic waves. If vacuum is filled with electromagnetic waves (say, radiation from walls of vacuum chamber, or relic microwave radiation in space) then the system will exchange by energy with these waves and thermally equilibrates at some finite (non zero) temperature. Cosmic microwave background radiation being remnant of radiation of hot early universe when radiation was in thermal equilibrium with matter has Planck spectrum (black body spectrum) with the temperature (at present) of about 2.7 K.

Second-law definition of temperature

In the previous section temperature was defined in terms of the Zeroth Law of thermodynamics. It is also possible to define temperature in terms of the second law of thermodynamics, which deals with entropy. Entropy is a measure of the disorder in a system. The second law states that any process will result in either no change or a net increase in the entropy of the universe. This can be understood in terms of probability. Consider a series of coin tosses. A perfectly ordered system would be one in which every coin toss would come up either heads or tails. For any number of coin tosses, there is only one combination of outcomes corresponding to this situation. On the other hand, there are multiple combinations that can result in disordered or mixed systems, where some fraction are heads and the rest tails. As the number of coin tosses increases, the number of combinations corresponding to imperfectly ordered systems increases. For a very large number of coin tosses, the number of combinations corresponding to ~50% heads and ~50% tails dominates and obtaining an outcome significantly different from 50/50 becomes extremely unlikely. Thus the system naturally progresses to a state of maximum disorder or entropy. Now, we have stated previously that temperature controls the flow of heat between two systems and we have just shown that the universe, and we would expect any natural system, tends to progress so as to maximize entropy. Thus, we would expect there to be some relationship between temperature and entropy. In order to find this relationship let's first consider the relationship between heat, work and temperature. A heat engine is a device for converting heat into mechanical work and analysis of the Carnot heat engine provides the necessary relationships we seek. The work from a heat engine corresponds to the difference between the heat put into the system at the high temperature, q_H and the heat ejected at the low temperature, q_C. The efficiency is the work divided by the heat put into the system or: :

\textrm = \frac  = \frac = 1 - \frac

(2) where w_cy is the work done per cycle. We see that the efficiency depends only on q_C/q_H. Because q_C and q_H correspond to heat transfer at the temperatures T_C and T_H, respectively, q_C/q_H should be some function of these temperatures: :

\frac = f(T_H,T_C)

(3) Carnot's theorem states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, a heat engine operating between T₁ and T₃ must have the same efficiency as one consisting of two cycles, one between T₁ and T₂, and the second between T₂ and T₃. This can only be the case if: :

q_ = \frac

which implies: :

q_13 = f(T_1,T_3) = f(T_1,T_2)f(T_2,T_3)

Since the first function is independent of T₂, this temperature must cancel on the right side, meaning f(T₁,T₃) is of the form g(T₁)/g(T₃) (i.e. f(T₁,T₃) = f(T₁,T₂)f(T₂,T₃) = g(T₁)/g(T₂)· g(T₂)/g(T₃) = g(T₁)/g(T₃)), where g is a function of a single temperature. We can now choose a temperature scale with the property that: :

\frac = \frac

(4) Substituting Equation 4 back into Equation 2 gives a relationship for the efficiency in terms of temperature: :

\textrm = 1 - \frac = 1 - \frac

(5) Notice that for T_C = 0 K the efficiency is 100% and that efficiency becomes greater than 100% below 0 K. Since an efficiency greater than 100% violates the first law of thermodynamics, this implies that 0 K is the minimum possible temperature. In fact the lowest temperature ever obtained in a macroscopic system was 20 nK, which was achieved in 1995 at NIST. Subtracting the right hand side of Equation 5 from the middle portion and rearranging gives: :

\frac  - \frac = 0

where the negative sign indicates heat ejected from the system. This relationship suggests the existence of a state function, S, defined by: :

dS = \frac

(6) where the subscript indicates a reversible process. The change of this state function around any cycle is zero, as is necessary for any state function. This function corresponds to the entropy of the system, which we described previously. We can rearranging Equation 6 to get a new definition for temperature in terms of entropy and heat: :

T = \frac

(7) For a system, where entropy S may be a function S(E) of its energy E, the temperature T is given by: :

\frac = \frac

(8) The reciprocal of the temperature is the rate of increase of entropy with energy.

References

External links

- [http://www.unitconversion.org/unit_converter/temperature.html Online Temperature Converter] - convert between various units of temperature, such as kelvin, Celsius, Fahrenheit, Rankine, Reaumur, and even Triple point of water
- [http://www.unitconversion.org/unit_converter/temperature-v.html Interactive Temperature Conversion Table] - convert selected unit to all other units of temperature
- [http://www.indiana.edu/~animal/fun/conversions/temperature.html Temperature Conversions: Celsius, Fahrenheit, Kelvin, Réaumur and Rankine]
- [http://www.unidata.ucar.edu/staff/blynds/tmp.html An elementary introduction to temperature aimed at a middle school audience]
- [http://www.straightdope.com/mailbag/mtempscales.html Why do we have so many temperature scales?]
- [http://thermodynamics-information.net A Brief History of Temperature Measurement] Category:Meteorology Category:Physical quantity Category:Thermodynamics Category:Heat ko:온도 ja:温度 th:อุณหภูมิ

Thermalisation

In physics, thermalisation (in American English thermalization) is the process of particles reaching thermal equilibrium through mutual interaction. Examples of thermalisation include:
- the achievement of equilibrium in a plasma
- the process undergone by high-energy neutrons as they lose energy by collision.
- and many other physical processes

External links

- [http://sdphca.ucsd.edu/coll_therm.html Collisions and thermalization]
- [http://www.nrc.gov/reading-rm/basic-ref/glossary/thermalization.html U.S. Nuclear Regulatory Commission Glossary]

Intensive

:In physics, intensive may refer to an intensive quantity. In grammar, an intensive form of a word is one which denotes stronger or more forceful action as compared with the root which the intensive is built on. Intensives are usually lexical formations, but there may be a regular process for forming intensives from a base root. Intensive formations, for example, existed in Proto-Indo-European, and in many of the Semitic languages. In Classical Arabic, Form II (fa99al) can form intensives, in addition to causatives; while form IV (af9al) forms only causitives. Hebrew has a similar distinction between the "pi`el" (intensive) and "hiph`il" (causative) binyans. Some Germanic languages have intensive prefixes or particles that can be attached to verbs; consider German zer-, which adds the meaning of "... into pieces", e.g. reißen "to rip" zerreißen "to rip to pieces". Latin had verbal prefixes e- and per- that could be more or less freely added onto any verb and variously added such meanings as "to put a great deal of effort into doing something". When the same prefixes (per especially) were added onto adjectives, the resulting meaning was "very X" or "extremely X". Category:Grammar Category:Grammatical aspects Category:Verb types

Temperature

k_B T

, where

k_B

is Boltzmann's constant, and T is temperature, expressed in Kelvins.

Overview

\delta Q

incident on the system during an infinitesimal quasistatic transformation, and the variation

\delta S

of its entropy during this transformation. :

\delta S = \frac

Role of temperature in nature

Temperature measurement

Units of temperature

\mathrm

\mathrm

Negative temperatures

Articles about temperature ranges:

Theoretical foundation of temperature

Zeroth-law definition of temperature

P \cdot V = n \cdot R \cdot T

Temperature in gases

K_t = \begin \frac \end mv^2

Temperature of the vacuum

Second-law definition of temperature

\textrm = \frac  = \frac = 1 - \frac

\frac = f(T_H,T_C)

q_ = \frac

which implies: :

q_13 = f(T_1,T_3) = f(T_1,T_2)f(T_2,T_3)

\frac = \frac

(4) Substituting Equation 4 back into Equation 2 gives a relationship for the efficiency in terms of temperature: :

\textrm = 1 - \frac = 1 - \frac

\frac  - \frac = 0

where the negative sign indicates heat ejected from the system. This relationship suggests the existence of a state function, S, defined by: :

dS = \frac

T = \frac

(7) For a system, where entropy S may be a function S(E) of its energy E, the temperature T is given by: :

\frac = \frac

(8) The reciprocal of the temperature is the rate of increase of entropy with energy.

References

External links

Temperature

k_B T

, where

k_B

is Boltzmann's constant, and T is temperature, expressed in Kelvins.

Overview

\delta Q

incident on the system during an infinitesimal quasistatic transformation, and the variation

\delta S

of its entropy during this transformation. :

\delta S = \frac

Role of temperature in nature

Temperature measurement

Units of temperature

\mathrm

\mathrm

Negative temperatures

Articles about temperature ranges:

Theoretical foundation of temperature

Zeroth-law definition of temperature

P \cdot V = n \cdot R \cdot T

Temperature in gases

K_t = \begin \frac \end mv^2

Temperature of the vacuum

Second-law definition of temperature

\textrm = \frac  = \frac = 1 - \frac

\frac = f(T_H,T_C)

q_ = \frac

which implies: :

q_13 = f(T_1,T_3) = f(T_1,T_2)f(T_2,T_3)

\frac = \frac

(4) Substituting Equation 4 back into Equation 2 gives a relationship for the efficiency in terms of temperature: :

\textrm = 1 - \frac = 1 - \frac

\frac  - \frac = 0

where the negative sign indicates heat ejected from the system. This relationship suggests the existence of a state function, S, defined by: :

dS = \frac

T = \frac

(7) For a system, where entropy S may be a function S(E) of its energy E, the temperature T is given by: :

\frac = \frac

(8) The reciprocal of the temperature is the rate of increase of entropy with energy.

Thermodynamic equilibrium

Local Thermodynamic Equilibrium (LTE)

Further reading

Thermodynamics

Overview

History

Thermodynamic systems

Thermodynamic parameters

Thermodynamic instruments

Thermodynamic states

Thermodynamic processes

The laws of thermodynamics

Thermodynamic potentials

Thermodynamic evolution

Quotes & humor

See also

Related lists and timelines

Related fields

Wikibooks

References

External links

Laws

Ideal gas

Classical ideal gas

Heat capacities of an ideal gas

The entropy of an ideal gas

Thermodynamic potentials of an ideal gas

Ideal quantum gases

Distribution function

Temperature

Overview

Role of temperature in nature

Temperature measurement

Units of temperature

Negative temperatures

Articles about temperature ranges:

Theoretical foundation of temperature

Zeroth-law definition of temperature

Temperature in gases

Temperature of the vacuum

Second-law definition of temperature

See also

References

External links

Thermalisation

External links

Intensive

Temperature

Overview

Role of temperature in nature

Temperature measurement

Units of temperature

Negative temperatures

Articles about temperature ranges:

Theoretical foundation of temperature

Zeroth-law definition of temperature

Temperature in gases

Temperature of the vacuum

Second-law definition of temperature

See also

References

External links

Temperature

Overview

Role of temperature in nature

Temperature measurement

Units of temperature

Negative temperatures

Articles about temperature ranges:

Theoretical foundation of temperature

Zeroth-law definition of temperature

Temperature in gases

Temperature of the vacuum

Second-law definition of temperature

See also

References

External links