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Maxwell's relations are a set of equations in thermodynamics which are derivable from the symmetry of second derivatives and from the definitions of the thermodynamic potentials. These relations are named for the nineteenth-century physicist James Clerk Maxwell .
The term "Maxwell's equations" is often also used for equivalent alternative formulations. Versions of Maxwell's equations based on the electric and magnetic scalar potentials are preferred for explicitly solving the equations as a boundary value problem, analytical mechanics, or for use in quantum mechanics.
The placement and relation among the variables serves as a key to recall the relations they constitute. A mnemonic used by students to remember the Maxwell relations (in thermodynamics ) is " G ood P hysicists H ave S tudied U nder V ery F ine T eachers", which helps them remember the order of the variables in the square, in clockwise direction.
Thus, we use more complex relations such as Maxwell relations, the Clapeyron equation, and the Mayer relation. Maxwell relations in thermodynamics are critical because they provide a means of simply measuring the change in properties of pressure, temperature, and specific volume, to determine a change in entropy. Entropy cannot be measured ...
The discontinuity in , and other properties, e.g. internal energy, , and entropy,, of the substance, is called a first order phase transition. [12] [13] In order to specify the unique experimentally observed pressure, (), at which it occurs another thermodynamic condition is required, for from Fig.1 it could clearly occur for any pressure in the range .
[24] [25] Maxwell deals with the motion-related aspect of electromagnetic induction, v × B, in equation (77), which is the same as equation (D) in Maxwell's original equations as listed below. It is expressed today as the force law equation, F = q ( E + v × B ) , which sits adjacent to Maxwell's equations and bears the name Lorentz force ...
Thus, there is another Euler relation, based on the expression of entropy as a function of internal energy and other extensive variables. Yet other Euler relations hold for other fundamental equations for energy or entropy, as respective functions of other state variables including some intensive state variables. [17]
At constant pressure the above equation produces a Maxwell relation that links the change in open cell voltage with temperature T (a measurable quantity) to the change in entropy S when charge is passed isothermally and isobarically. The latter is closely related to the reaction entropy of the electrochemical reaction that lends the battery its ...