Petrophysical Training
Petrophysical Consulting


Publication History:
This article was
prepared especially for "Crain's Petrophysical Handbook" by
E. R. (Ross) Crain, P.Eng. in 2005 based on numerous
Internet Sources.
This webpage version is the copyrighted intellectual
property of the author.
Do not copy or distribute in any form without explicit
permission. 
LAWS OF PHYSICS
The
basic laws of physics fall into two categories: classical physics
that deals with the observable world (classical mechanics), and
atomic physics that deals with the interactions between elementary
and sub atomic particles (quantum mechanics). The basic laws of both
are listed here in alphabetical order. Some laws apply only to one
or the other category; some belong to both. A few of the laws listed
may have little impact on petrophysics and some may have been left
off the list for any number of reasons.

Ampere's Law

The line integral of the magnetic
flux around a closed curve is proportional to the algebraic sum
of electric currents flowing through that closed curve; or, in
differential form curl
B = J.
This was later
modified to add a second term when
it was incorporated into Maxwell's equations.
Archimedes' Principle

A body that is submerged in a fluid
is buoyed up by a force equal in magnitude to the weight of the
fluid that is displaced, and directed upward along a line
through the center of gravity of the displaced fluid.
Avogadro's Hypothesis (1811)

Equal volumes of all gases at the
same temperature and pressure contain equal numbers of
molecules. It is, in fact, only true for ideal gases.
Bernoulli's Equation
 In an irrotational fluid, the
sum of the static pressure, the weight of the fluid per unit
mass times the height, and half the density times the velocity
squared is constant throughout the fluid.
BiotSavart Law
 A law which describes the
contributions to a magnetic field by an electric current. It is
analogous to
Coulomb's law.
Boyle's Law (1662); Mariotte's law (1676)
 The product of the pressure
and the volume of an ideal gas at constant temperature is a
constant.
Bragg's Law (1912)
 When a beam of Xrays
strikes a crystal surface in which the layers of atoms or ions
are regularly separated, the maximum intensity of the reflected
ray occurs when the complement of the angle of incidence,
theta, the wavelength of the Xrays, lambda,
and the distance between layers of atoms or ions, d, are
related by the equation 2 d sin theta = n
lambda,
Brownian Motion (1827)
 The continuous random motion
of solid microscopic particles when suspended in a fluid medium
due to the consequence of ongoing bombardment by atoms and
molecules.
Casimir Effect
 A quantum mechanical effect,
where two very large plates placed close to each other will
experience an attractive force, in the absence of other forces.
The cause is virtual particleantiparticle pair creation in the
vicinity of the plates. Also, the speed of light will be
increased in the region between the two plates, in the direction
perpendicular to them.
Causality Principle
 The principle that cause must
always preceed effect. More formally, if an event A ("the
cause") somehow influences an event B ("the effect")
which occurs later in time, then event B cannot in turn
have an influence on event A. That is, event B
must occur at a later time t than event A, and
further, all frames must agree upon this ordering.
Centrifugal Pseudoforce
 A
pseudoforce on an object when it is moving in uniform
circular motion. The "force" is directed outward from the center
of motion.
Charles' Law (1787)
 The volume of an ideal gas at
constant pressure is proportional to the thermodynamic
temperature of that gas.
Cherenkov Radiation
 Radiation emitted by a
massive particle which is moving faster than light in the medium
through which it is traveling. No particle can travel faster
than light
in vacuum, but the speed of light in other media, such as water,
glass, etc., are considerably lower. Cherenkov radiation is the
electromagnetic analogue of the sonic boom, though Cherenkov
radiation is a shockwave set up in the electromagnetic field.
Complementarity Principle
 The principle that a given
system cannot exhibit both
wavelike behavior
and particlelike behavior at the
same time. That is, certain experiments will reveal the
wavelike nature of a system, and certain experiments will
reveal the particlelike nature of a system, but no experiment
will reveal both simultaneously.
Compton Effect (1923)
 An effect that demonstrates
that photons (the quantum of electromagnetic radiation) have
momentum. A photon fired at a stationary particle, such as an
electron, will impart momentum to the electron and, since its
energy has been decreased, will experience a corresponding
decrease in frequency.
Conservation Laws


Conservation of massenergy
 The total massenergy
of a closed system remains constant.

Conservation of electric charge
 The total electric
charge of a closed system remains constant.

Conservation of linear momentum
 The total linear
momentum of a closed system remains constant.

Conservation of angular momentum
 The total angular
momentum of a closed system remains constant.
There are several other laws
that deal with particle physics, such as conservation of baryon
number, of strangeness, etc., which are conserved in some
fundamental interactions (such as the electromagnetic
interaction) but not others (such as the weak interaction).
Constancy Principle
 One of the postulates of A.
Einstein's special theory of relativity, which puts forth that
the speed of
light in vacuum is measured as the
same speed to all observers, regardless of their relative
motion.

Continuity
Equation
 An equation which states that
a fluid flowing through a pipe flows at a rate which is
inversely proportional to the crosssectional area of the pipe.
It is in essence a restatement of the conservation of mass during
constant flow.
Copernican Principle (1624)
 The idea, suggested by
Copernicus, that the Sun, not the Earth, is at the center of the
Universe. We now know that neither idea is correct.
Coriolis Pseudoforce (1835)
 A
pseudoforce which arises because of motion relative to a
frame of reference which is itself rotating relative to a
second, inertial frame. The magnitude of the Coriolis "force" is
dependent on the speed of the object relative to the noninertial
frame, and the direction of the "force" is orthogonal to the
object's velocity.
Correspondence Principle
 The principle that when a
new, more general theory is put forth, it must reduce to the
more specialized (and usually simpler) theory under normal
circumstances. There are correspondence principles for general
relativity to special relativity and special relativity to
Newtonian mechanics, but the most widely known correspondence
principle is that of quantum mechanics to classical mechanics.
Coulomb's Law
 The primary law for
electrostatics, analogous to
Newton's law of universal
gravitation. It states that the force
between two point charges is proportional to the algebraic
product of their respective charges as well as proportional to
the inverse square of the distance between them.
Curie's Law
 The susceptibility of an
isotropic paramagnetic substance is related to its thermodynamic
temperature T by the equation KHI =
C /
T.
CurieWeiss Law
 A more general form of
Curie's Law,
which states that the susceptibility of a paramagnetic substance
is related to its thermodynamic temperature T by the
equation
KHI =
C/T 
W, where W is the Weiss constant.


Dalton's Law of partial
pressures
 The total pressure of a
mixture of ideal gases is equal to the sum of the partial
pressures of its components; that is, the sum of the pressures
that each component would exert if it were present alone and
occupied the same volume as the mixture.
Doppler Effect
 Waves emitted by a moving
object as received by an observer will be blueshifted
(compressed) if approaching, redshifted (elongated) if receding.
It occurs both in sound as well as electromagnetic phenomena.
DulongPetit Law (1819)
 The molar heat capacity is
approximately equal to the three times the
ideal gas constant:

Einstein Field Equation
 The cornerstone of Einstein's
general theory of relativity, relating the gravitational tensor
G to the
stressenergy tensor T by the
simple equation G = 8 pi T.

Einstein's MassEnergy Equation
 The energy E of a particle
is equal to its mass M times the square of the speed of light c,
giving rise to the best known physics equation in the Universe:
E = M c^{2}.
Equivalence
Principle
 The basic postulate of A.
Einstein's general theory of relativity, which posits that an
acceleration is fundamentally indistinguishable from a
gravitational field.

Faraday's Law
 The line integral of the
electric field around a closed curve is proportional to the
instantaneous time rate of change of the magnetic flux through a
surface bounded by that closed curve; in differential form
curl E = dB/dt, where
here d/dt represents partial differentiation.
Faraday's Laws
of electrolysis


Faraday's first law of electrolysis
 The amount of chemical
change during electrolysis is proportional to the charge
passed.

Faraday's second law of electrolysis
 The charge Q
required to deposit or liberate a mass m is
proportional to the charge z of the ion, the mass,
and inversely proportional to the relative ionic mass M;
mathematically Q =
F m z / M,

Faraday's first law of electromagnetic induction
 An electromotive force is
induced in a conductor when the magnetic field surrounding
it changes.
Faraday's second law of electromagnetic induction
 The magnitude of the
electromotive force is proportional to the rate of change of
the field.
Faraday's third law of electromagnetic induction
 The sense of the induced
electromotive force depends on the direction of the rate of
the change of the field.
Fermat's Principle
 The principle states that the
path taken by a ray of light between any two points in a system
is always the path that takes the least time.

Gauss' Law
 The electric flux through a
closed surface is proportional to the algebraic sum of electric
charges contained within that closed surface; in differential
form div E =
rho, where rho
is the charge density.
Gauss' Law for magnetic
fields
 The magnetic flux through a
closed surface is zero; no magnetic charges exist; in
differential form
div B = 0.
Hall Effect
 When charged particles flow
through a tube which has both an electric field and a magnetic
field (perpendicular to the electric field) present in it, only
certain velocities of the charged particles are preferred, and
will make it undeviated through the tube; the rest will be
deflected into the sides.
Hooke's Law
 The stress applied to any
solid is proportional to the strain it produces within the
elastic limit for that solid. The constant of that
proportionality is the Young modulus of elasticity for that
substance.
Huygens' Principle
 The mechanical propagation of
a wave (specifically, of light) is equivalent to assuming that
every point on the wavefront acts as point source of wave
emission

Ideal Gas Law
 An equation which sums up the
ideal gas laws in one simple equation
P V = n R T,

JouleThomson Effect; JouleKelvin Effect
 The change in temperature
that occurs when a gas expands into a region of lower pressure.
Joule's Laws


Joule's first law
 The heat Q
produced when a current I flows through a resistance
R for a specified time t is given by Q
= I^{2} R t .
Kirchhoff's Rules


loop rule
 The sum of the
potential differences encountered in a round trip around
any closed loop in a circuit is zero.

point rule
 The sum of the
currents toward a branch point is equal to the sum of
the currents away from the same branch point.


Kohlrausch's Law
 If a salt is dissolved in
water, the conductivity of the solution is the sum of two
values  one depending on the positive ions and the other
on the negative ions
Lambert's Laws


Lambert's
first law
 The illuminance on a
surface illuminated by light falling on it
perpendicularly from a point source is proportional to
the inverse square of the distance between the surface
and the source.

Lambert's
second law
 If the rays meet the
surface at an angle, then the illuminance is
proportional to the cosine of the angle with the normal.

Lambert's
third law
 The luminous
intensity of light decreases exponentially with distance
as it travels through an absorbing medium.
Laplace Equation
 For steadystate heat
conduction in one dimension, the temperature distribution is
the solution to Laplace's equation, which states that the
second derivative of temperature with respect to
displacement is zero.
Lenz's Law (1835)
 An induced electric
current always flows in such a direction that it opposes the
change producing it.

 Mach Number
 The ratio of the speed of an
object in a given medium to the speed of sound in that medium.
Mach's Principle (1870)
 The inertia of any particular
particle or particles of matter is attributable to the
interaction between that piece of matter and the rest of the
Universe. Thus, a body in isolation would have no inertia.
Maxwell's Equations (1864)

 Gauss' law
 The electric flux
through a closed surface is proportional to the
algebraic sum of electric charges contained within that
closed surface; in differential form
div E = rho,
where rho is the charge density.
 Gauss' law
for magnetic fields
 The magnetic flux
through a closed surface is zero; no magnetic charges
exist. In differential form
div B
= 0.
 Faraday's
law
 The line integral of
the electric field around a closed curve is proportional
to the instantaneous time rate of change of the magnetic
flux through a surface bounded by that closed curve; in
differential form
curl E = dB/dt,..

Ampere's law, modified form
 The line integral of
the magnetic field around a closed curve is proportional
to the sum of two terms: first, the algebraic sum of
electric currents flowing through that closed curve; and
second, the instantaneous time rate of change of the
electric flux through a surface bounded by that closed
curve; in differential form
curl H = J
+ dD/dt,.
In addition to describing
electromagnetism, his equations also predict that waves can
propagate through the electromagnetic field, and would always
propagate at the the speed of light in vacuum.
Murphy's
Law (1942)
 If anything can go wrong, it
will.
Newton's Law of universal
gravitation
 Two bodies attract each other
with equal and opposite forces; the magnitude of this force is
proportional to the product of the two masses and is also
proportional to the inverse square of the distance between the
centers of mass of the two bodies;
F
= (G
m M/r^{2})
e, where m and M are the masses of the two
bodies, r is the distance between. the two, and e is a
unit vector directed from the test mass to the second.
Newton's Laws of motion


Newton's
first law of motion
 A body continues in its
state of constant velocity (which may be zero) unless it is
acted upon by an external force.

Newton's
second law of motion
 For an unbalanced force
acting on a body, the acceleration produced is proportional
to the force impressed; the constant of proportionality is
the inertial mass of the body.

Newton's
third law of motion
 In a system where no
external forces are present, every action force is always
opposed by an equal and opposite reaction force.

Occam's Razor (1340)
 If two theories predict
phenomena to the same accuracy, then the one which is simpler is
the better one. Moreover, additional aspects of a theory which
do not lend it more powerful predicting ability are unnecessary
and should be stripped away.
Ohm's
Law (1827)
 The ratio of the potential
difference between the ends of a conductor to the current
flowing through it is constant; the constant of proportionality
is called the resistance, and is different for different
materials.

Pascal's Principle
 Pressure applied to an
enclosed incompressible static fluid is transmitted undiminished
to all parts of the fluid.
Peter
Principle
 In a hierarchy, every
employee tends to rise to his level of incompetence.
Planck Equation
 The quantum mechanical
equation relating the energy of a photon E to its
frequency nu:
E =
h nu.

Reflection Law,
Snell's Law
 For a wavefront intersecting
a reflecting surface, the angle of incidence is equal to the
angle of reflection, in the same plane defined by the ray of
incidence and the normal.


Refraction Law
 For a wavefront traveling
through a boundary between two media, the first with a
refractive index of n_{1}, and the other with one
of n_{2}, the angle of incidence theta is
related to the angle of refraction phi by n_{1}
sin theta = n_{2} sin phi.


Relativity Principle
 The principle, employed by
Einstein's relativity theories, that the laws of physics are the
same, at least qualitatively, in all frames. That is, there is
no frame that is better (or qualitatively any different) from
any other. This principle, along with the
constancy principle, constitute the founding principles of
special relativity.

StefanBoltzmann Law
 The radiated power P
(rate of emission of electromagnetic energy) of a hot body is
proportional to the radiating surface area, A, and the
fourth power of the thermodynamic temperature, T. The
constant of proportionality is the
StefanBoltzmann constant.
Mathematically P = e
sigma A T^{4},.where the efficiency rating e
is called the emissivity of the object.


Superposition Principle
 The general idea that, when a
number of influences are acting on a system, the total influence
on that system is merely the sum of the individual influences;
that is, influences governed by the superposition principle add
linearly.

Thermodynamic Laws


First law
of thermodynamics
 The change in internal
energy of a system is the sum of the heat transferred to or
from the system and the work done on or by the system.

Second
law of thermodynamics
 The entropy  a measure
of the unavailability of a system's energy to do useful work
 of a closed system tends to increase with time.

Third law
of thermodynamics
 For changes involving
only perfect crystalline solids at absolute zero, the change
of the total entropy is zero.

Zeroth
law of thermodynamics
 If two bodies are each in
thermal equilibrium with a third body, then all three bodies
are in thermal equilibrium with each other.

Uncertainty Principle (1927)
 A principle, central to
quantum mechanics, which states that two complementary
parameters (such as position and momentum, energy and time, or
angular momentum and angular displacement) cannot both be known
to infinite accuracy; the more you know about one, the less you
know about the other.

van der Waals force
 Forces responsible for the
nonideal behavior of gases, and for the lattice energy of
molecular crystals. There are three causes: dipoledipole
interaction; dipoleinduced dipole moments; and dispersion
forces arising because of small instantaneous dipoles in atoms.
WaveParticle Duality
 The principle of quantum
mechanics which implies that light (and, indeed, all other
subatomic particles) sometimes act like a wave, and sometime act
like a particle, depending on the experiment you are performing.
For instance, low frequency electromagnetic radiation tends to
act more like a wave than a particle; high frequency
electromagnetic radiation tends to act more like a particle than
a wave.


WiedemannFranz Law
 The ratio of the thermal
conductivity of any pure metal to its electrical conductivity is
approximately constant for any given temperature. This law holds
fairly well except at low temperatures.

