KT (energy)

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Approximate values of kT at 298 KUnits
kT = 4.11×10−21 J
kT = 4.114pN⋅nm
kT = 9.83×10−22 cal
kT = 25.7 meV
kT = −174 dBm/Hz
Related quantities (also at 298 K)
kT/hc207 [1] cm−1
kT/e = 25.7 mV
RT = kTNA = 2.479 kJ⋅mol−1
RT = 0.592 kcal⋅mol−1
h/kT = 0.16 ps

kT (also written as kBT) is the product of the Boltzmann constant, k (or kB), and the temperature, T. This product is used in physics as a scale factor for energy values in molecular-scale systems (sometimes it is used as a unit of energy), as the rates and frequencies of many processes and phenomena depend not on their energy alone, but on the ratio of that energy and kT, that is, on E / kT (see Arrhenius equation, Boltzmann factor). For a system in equilibrium in canonical ensemble, the probability of the system being in state with energy E is proportional to e−ΔE / kT. [2]

More fundamentally, kT is the amount of heat required to increase the thermodynamic entropy of a system by k.

In physical chemistry, as kT often appears in the denominator of fractions (usually because of Boltzmann distribution), sometimes β = 1/kT is used instead of kT, turning e−ΔE / kT into e−βΔE. [2]

RT

RT is the product of the molar gas constant, R, and the temperature, T. This product is used in physics and chemistry as a scaling factor for energy values in macroscopic scale (sometimes it is used as a pseudo-unit of energy), as many processes and phenomena depend not on the energy alone, but on the ratio of energy and RT, i.e. E/RT. The SI units for RT are joules per mole (J/mol).

It differs from kT only by a factor of the Avogadro constant, NA. Its dimension is energy or ML2T2, expressed in SI units as joules (J):

kT = RT/NA

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In thermodynamics, the specific heat capacity of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity or as the specific heat. Informally, it is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg−1⋅K−1. For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg−1⋅K−1.

<span class="mw-page-title-main">Activation energy</span> Minimum amount of energy that must be provided for a system to undergo a reaction or process

In the Arrhenius model of reaction rates, activation energy is the minimum amount of energy that must be available to reactants for a chemical reaction to occur. The activation energy (Ea) of a reaction is measured in kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol). Activation energy can be thought of as the magnitude of the potential barrier (sometimes called the energy barrier) separating minima of the potential energy surface pertaining to the initial and final thermodynamic state. For a chemical reaction to proceed at a reasonable rate, the temperature of the system should be high enough such that there exists an appreciable number of molecules with translational energy equal to or greater than the activation energy. The term "activation energy" was introduced in 1889 by the Swedish scientist Svante Arrhenius.

<span class="mw-page-title-main">Thermodynamic temperature</span> Measure of absolute temperature

Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.

In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 that the van 't Hoff equation for the temperature dependence of equilibrium constants suggests such a formula for the rates of both forward and reverse reactions. This equation has a vast and important application in determining the rate of chemical reactions and for calculation of energy of activation. Arrhenius provided a physical justification and interpretation for the formula. Currently, it is best seen as an empirical relationship. It can be used to model the temperature variation of diffusion coefficients, population of crystal vacancies, creep rates, and many other thermally induced processes and reactions. The Eyring equation, developed in 1935, also expresses the relationship between rate and energy.

<span class="mw-page-title-main">Boltzmann constant</span> Physical constant relating particle kinetic energy with temperature

The Boltzmann constant is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy. It is named after the Austrian scientist Ludwig Boltzmann.

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<span class="mw-page-title-main">Gibbs free energy</span> Type of thermodynamic potential

In thermodynamics, the Gibbs free energy is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy is expressed as

<span class="mw-page-title-main">Thermal energy</span> Energy that is measured by temperature

The "thermal energy" is used loosely in various contexts in physics and engineering, generally related to the kinetic energy of vibrating and colliding atoms in a substance. It can refer to several different well-defined physical concepts. These include the internal energy or enthalpy of a body of matter and radiation; heat, defined as a type of energy transfer ; and the characteristic energy of a degree of freedom, , in a system that is described in terms of its microscopic particulate constituents.

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Collision theory is a principle of chemistry used to predict the rates of chemical reactions. It states that when suitable particles of the reactant hit each other with the correct orientation, only a certain amount of collisions result in a perceptible or notable change; these successful changes are called successful collisions. The successful collisions must have enough energy, also known as activation energy, at the moment of impact to break the pre-existing bonds and form all new bonds. This results in the products of the reaction. The activation energy is often predicted using the Transition state theory. Increasing the concentration of the reactant brings about more collisions and hence more successful collisions. Increasing the temperature increases the average kinetic energy of the molecules in a solution, increasing the number of collisions that have enough energy. Collision theory was proposed independently by Max Trautz in 1916 and William Lewis in 1918.

In chemical kinetics, a reaction rate constant or reaction rate coefficient is a proportionality constant which quantifies the rate and direction of a chemical reaction by relating it with the concentration of reactants.

Many letters of the Latin alphabet, both capital and small, are used in mathematics, science, and engineering to denote by convention specific or abstracted constants, variables of a certain type, units, multipliers, or physical entities. Certain letters, when combined with special formatting, take on special meaning.

<span class="mw-page-title-main">Thermodynamic beta</span> Measure of the coldness of a system

In statistical thermodynamics, thermodynamic beta, also known as coldness, is the reciprocal of the thermodynamic temperature of a system:

Energy is defined via work, so the SI unit of energy is the same as the unit of work – the joule (J), named in honour of James Prescott Joule and his experiments on the mechanical equivalent of heat. In slightly more fundamental terms, 1 joule is equal to 1 newton metre and, in terms of SI base units

In chemical kinetics, an Arrhenius plot displays the logarithm of a reaction rate constant, (, ordinate axis) plotted against reciprocal of the temperature (, abscissa). Arrhenius plots are often used to analyze the effect of temperature on the rates of chemical reactions. For a single rate-limited thermally activated process, an Arrhenius plot gives a straight line, from which the activation energy and the pre-exponential factor can both be determined.

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  1. Between the logarithm of the pre-exponential factors and the activation energies where the series of closely related reactions are indicated by the index i, Ai are the preexponential factors, Ea,i are the activation energies, R is the gas constant, and α, β are constants.
  2. Between enthalpies and entropies of activation where H
    i
    are the enthalpies of activation and S
    i
    are the entropies of activation.
  3. Between the enthalpy and entropy changes of a series of similar reactions where Hi are the enthalpy changes and Si are the entropy changes.
<span class="mw-page-title-main">Temperature</span> Physical quantity of hot and cold

Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making up a substance.

<span class="mw-page-title-main">2019 redefinition of the SI base units</span> Definition of the units kg, A, K and mol

In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144th anniversary of the Metre Convention, the kilogram, ampere, kelvin, and mole are now defined by setting exact numerical values, when expressed in SI units, for the Planck constant, the elementary electric charge, the Boltzmann constant, and the Avogadro constant, respectively. The second, metre, and candela had previously been redefined using physical constants. The four new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research.

References

  1. "Google Unit Converter" . Retrieved 10 November 2018.
  2. 1 2 Atkins, Peter (2010). Atkins' Physical Chemistry (9th ed.). OUP Oxford. pp. 564–591. ISBN   978-0-19-954337-3.