MEDICAL ENGINEERING DEPT SECOND YEAR
THERMODYNAMICS LECTURE TWELVE
INTRODUCTION PART ONE BY:
PROF. MOHAMED REFAAT DIAB
Maxwell Equations (Thermodynamics)
In thermodynamics, the Maxwell equations are a set of equations derived by application of Euler's reciprocity relation to the thermodynamic characteristic functions. The Maxwell relations, first derived by James Clerk Maxwell, are the following expressions between partial differential quotients:
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Maxwell Equations (Continue…)
The characteristic functions are:
U (internal energy), A (Helmholtz free energy), H (enthalpy), and G ( Gibbs free energy). The thermodynamic parameters are: T (
temperature), S (entropy), P (pressure), and V (volume)
As an example of a derivation, consider Euler's reciprocity relation reads:
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Maxwell Equations (Continue…)
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Maxwell Equations (Continue…)
Maxwell's equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ... Maxwell first used the equations to propose that light is an electromagnetic phenomenon.
They describe how electric charges and electric currents create electric and magnetic fields. They describe how an electric field can generate a magnetic field, and vice versa. ... The second allows one to calculate the magnetic field.
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Maxwell Equations (Continue…)
According to Lenz's law, when an electromagnetic field is generated by a change in magnetic flux, the polarity of the induced electromagnetic field produces an induced current whose magnetic field opposes the initial changing magnetic field which produced it.
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Maxwell's Equations
Maxwell's equations represent one of the most elegant and concise ways to state the fundamentals of electricity and magnetism. From them one can develop most of the working relationships in the field. Because of their
concise statement, they embody a high level of mathematical sophistication and are therefore not generally introduced in an
introductory treatment of the subject, except perhaps as summary relationships.
These basic equations of electricity and magnetism can be used as a
starting point for advanced courses, but are usually first encountered as unifying equations after the study of electrical and magnetic phenomena
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Maxwell Equations (Continue…)
Symbols Used
E = Electric field ρ = charge density i = electric current
B = Magnetic field ε0 = permittivity J = current density
D = Electric displacement μ0 = permeability c = speed of light
H =
Magnetic field strength M = Magnetization P = Polarization
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Maxwell's Equations (Continue..)
Integral form in the absence of magnetic or polarizable media
: I. Gauss' law for electricity9
II. Gauss' law for magnetism
Maxwell's Equations (Continue..)
III. Faraday's law of induction
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IV. Ampere's law
Maxwell's Equations (Continue..)
I. Gauss' law for electricity
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II. Gauss' law for magnetism
III. Faraday's law of induction
Maxwell's Equations (Continue..)
IV. Ampere's law
12 here represent the vector operations
divergence and curl, respectively
Maxwell's Equations (Continue..)
Differential form with magnetic and/or polarizable media
I. Gauss' law for electricity
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II. Gauss' law for magnetism
Maxwell's Equations (Continue..)
III. Faraday's law of induction
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IV. Ampere's law
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