In
thermodynamics
Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
, Bridgman's thermodynamic equations are a basic set of thermodynamic equations, derived using a method of generating multiple thermodynamic identities involving a number of thermodynamic quantities. The equations are named after the American physicist
Percy Williams Bridgman
Percy Williams Bridgman (April 21, 1882 – August 20, 1961) was an American physicist who received the Nobel Prize in Physics in 1946 for his work on the physics of high pressures. He also wrote extensively on the scientific method and on other ...
. (See also the
exact differential
In multivariate calculus, a differential (infinitesimal), 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 som ...
article for general differential relationships).
The extensive variables of the system are fundamental. Only the
entropy
Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the micros ...
''S'' , the
volume
Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...
''V'' and the four most common thermodynamic potentials will be considered. The four most common thermodynamic potentials are:
:
The first derivatives of the internal energy with respect to its (extensive) natural variables ''S'' and ''V'' yields the intensive parameters of the system - The
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
''P'' and the
temperature
Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
''T'' . For a simple system in which the
particle number
In thermodynamics, the particle number (symbol ) of a thermodynamic system is the number of constituent particles in that system. The particle number is a fundamental thermodynamic property which is conjugate to the chemical potential. Unlike m ...
s are constant, the second derivatives of the thermodynamic potentials can all be expressed in terms of only three
material properties
A material property is an intensive property of a material, i.e., a physical property or chemical property that does not depend on the amount of the material. These quantitative properties may be used as a metric by which the benefits of one ma ...
:
Bridgman's equations are a series of relationships between all of the above quantities.
Introduction
Many thermodynamic equations are expressed in terms of partial derivatives. For example, the expression for the heat capacity at constant pressure is:
:
which is the partial derivative of the enthalpy with respect to temperature while holding pressure constant. We may write this equation as:
:
This method of rewriting the partial derivative was described by Bridgman (and also Lewis & Randall), and allows the use of the following collection of expressions to express many thermodynamic equations. For example from the equations below we have:
:
and
:
Dividing, we recover the proper expression for C
P.
The following summary restates various partial terms in terms of the thermodynamic potentials, the state parameters S, T, P, V, and the following three
material properties
A material property is an intensive property of a material, i.e., a physical property or chemical property that does not depend on the amount of the material. These quantitative properties may be used as a metric by which the benefits of one ma ...
which are easily measured experimentally.
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Bridgman's thermodynamic equations
Note that Lewis and Randall use F and E for the Gibbs energy and internal energy, respectively, rather than G and U which are used in this article.
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See also
*
Table of thermodynamic equations
*
Exact differential
In multivariate calculus, a differential (infinitesimal), 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 som ...
References
*
*{{cite book , last=Lewis , first=G.N. , authorlink=Gilbert N. Lewis , author2=Randall, M. , authorlink2=Merle Randall , title=Thermodynamics , url=https://archive.org/details/thermodynamics00lewi , url-access=registration , year=1961 , publisher=McGraw-Hill Book Company , location=New York, edition=2nd
Thermodynamic equations
Equations