This article is a summary of common
equation
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in ...
s and
quantities
Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit ...
in
thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
(see
thermodynamic equations
Thermodynamics is expressed by a mathematical framework of ''thermodynamic equations'' which relate various thermodynamic quantities and physical properties measured in a laboratory or production process. Thermodynamics is based on a fundamental ...
for more elaboration).
Definitions
Many of the definitions below are also used in the thermodynamics of
chemical reaction
A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
s.
General basic quantities
General derived quantities
Thermal properties of matter
Thermal transfer
Equations
The equations in this article are classified by subject.
Thermodynamic processes
Kinetic theory
Ideal gas
Entropy
*
, where ''k''
B is the
Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic 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 Ω denotes the volume of
macrostate
In statistical mechanics, a microstate is a specific microscopic configuration of a thermodynamic system that the system may occupy with a certain probability in the course of its thermal fluctuations. In contrast, the macrostate of a system refe ...
in the
phase space
In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually ...
or otherwise called thermodynamic probability.
*
, for reversible processes only
Statistical physics
Below are useful results from the
Maxwell–Boltzmann distribution
In physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann.
It was first defined and used ...
for an ideal gas, and the implications of the Entropy quantity. The distribution is valid for atoms or molecules constituting ideal gases.
Corollaries of the non-relativistic Maxwell–Boltzmann distribution are below.
Quasi-static and reversible processes
For
quasi-static and
reversible processes, the
first law of thermodynamics
The first law of thermodynamics is a formulation of the law of conservation of energy, adapted for thermodynamic processes. It distinguishes in principle two forms of energy transfer, heat and thermodynamic work for a system of a constant amoun ...
is:
:
where δ''Q'' is the heat supplied ''to'' the system and δ''W'' is the work done ''by'' the system.
Thermodynamic potentials
The following energies are called the
thermodynamic potentials
A thermodynamic potential (or more accurately, a thermodynamic potential energy)ISO/IEC 80000-5, Quantities an units, Part 5 - Thermodynamics, item 5-20.4 Helmholtz energy, Helmholtz functionISO/IEC 80000-5, Quantities an units, Part 5 - Thermod ...
,
:
and the corresponding
fundamental thermodynamic relation
In thermodynamics, the fundamental thermodynamic relation are four fundamental equations which demonstrate how four important thermodynamic quantities depend on variables that can be controlled and measured experimentally. Thus, they are essentiall ...
s or "master equations"
[Physical chemistry, P.W. Atkins, Oxford University Press, 1978, ] are:
Maxwell's relations
The four most common
Maxwell's relations are:
More relations include the following.
Other differential equations are:
Quantum properties
*
*
Indistinguishable Particles
where ''N'' is number of particles, ''h'' is
Planck's constant, ''I'' is
moment of inertia
The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceler ...
, and ''Z'' is the
partition function, in various forms:
Thermal properties of matter
Thermal transfer
Thermal efficiencies
See also
*
Antoine equation
The Antoine equation is a class of semi-empirical correlations describing the relation between vapor pressure and temperature for pure substances. The Antoine equation is derived from the Clausius–Clapeyron relation. The equation was presented ...
*
Bejan number There are two different Bejan numbers (Be) used in the scientific domains of thermodynamics and fluid mechanics. Bejan numbers are named after Adrian Bejan.
Thermodynamics
In the field of thermodynamics the Bejan number is the ratio of heat transfe ...
*
Bowen ratio The Bowen ratio is used to describe the type of heat transfer for a surface that has moisture. Heat transfer can either occur as sensible heat (differences in temperature without evapotranspiration) or latent heat (the energy required during a chan ...
*
Bridgman's equations
*
Clausius–Clapeyron relation
The Clausius–Clapeyron relation, named after Rudolf Clausius and Benoît Paul Émile Clapeyron, specifies the temperature dependence of pressure, most importantly vapor pressure, at a discontinuous phase transition between two phases of matter ...
*
Departure function
In thermodynamics, a departure function is defined for any thermodynamic property as the difference between the property as computed for an ideal gas and the property of the species as it exists in the real world, for a specified temperature ''T'' ...
s
*
Duhem–Margules equation The Duhem–Margules equation, named for Pierre Duhem and Max Margules, is a thermodynamic statement of the relationship between the two components of a single liquid where the vapour mixture is regarded as an ideal gas:
: \left ( \frac \right ) ...
*
Ehrenfest equations Ehrenfest equations (named after Paul Ehrenfest) are equations which describe changes in specific heat capacity and derivatives of specific volume in second-order phase transitions. The Clausius–Clapeyron relation does not make sense for second-o ...
*
Gibbs–Helmholtz equation
The Gibbs–Helmholtz equation is a thermodynamic equation used for calculating changes in the Gibbs free energy of a system as a function of temperature. It was originally presented in an 1882 paper entitled " Die Thermodynamik chemischer Vorgang ...
*
Gibbs' phase rule
In thermodynamics, the phase rule is a general principle governing "pVT" systems, whose thermodynamic states are completely described by the variables pressure (), volume () and temperature (), in thermodynamic equilibrium. If is the number of ...
*
Kopp's law
Kopp's law can refer to either of two relationships discovered by the German chemist Hermann Franz Moritz Kopp (1817–1892).
#Kopp found "that the molecular heat capacity of a solid compound is the sum of the atomic heat capacities of the elemen ...
*
Kopp–Neumann law
*
Noro–Frenkel law of corresponding states
*
Onsager reciprocal relations
In thermodynamics, the Onsager reciprocal relations express the equality of certain ratios between flows and forces in thermodynamic systems out of equilibrium, but where a notion of local equilibrium exists.
"Reciprocal relations" occur betw ...
*
Stefan number
The Stefan number (St or Ste) is defined as the ratio of sensible heat to latent heat. It is given by the formula
\mathrm = \frac,
where
* ''cp'' is the specific heat,
** cp is the specific heat of solid phase in the freezing process while cp ...
*
Triple product rule
*
Exact differential
In multivariate calculus, a differential or differential form is said to be exact or perfect (''exact differential''), as contrasted with an inexact differential, if it is equal to the general differential dQ for some differentiable function&nbs ...
References
*
Atkins, Peter and de Paula, Julio ''Physical Chemistry'', 7th edition, W.H. Freeman and Company, 2002 .
** Chapters 1–10, Part 1: "Equilibrium".
*
*Landsberg, Peter T.
Thermodynamics and Statistical Mechanics. New York: Dover Publications, Inc., 1990. ''(reprinted from Oxford University Press, 1978)''.
* Lewis, G.N., and Randall, M., "Thermodynamics", 2nd Edition, McGraw-Hill Book Company, New York, 1961.
*
Reichl, L.E., ''A Modern Course in Statistical Physics'', 2nd edition, New York: John Wiley & Sons, 1998.
*Schroeder, Daniel V. ''Thermal Physics''. San Francisco: Addison Wesley Longman, 2000 .
*Silbey, Robert J., et al. ''Physical Chemistry'', 4th ed. New Jersey: Wiley, 2004.
*Callen, Herbert B. (1985). ''Thermodynamics and an Introduction to Themostatistics'', 2nd edition, New York: John Wiley & Sons.
External links
Thermodynamic equation calculator
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Thermodynamic equations