ideal gas constant; universal molar gas constant; R
The constant that appears in the ideal gas equation. It is equal to 8.314 34 J/K/mol.
ideal gas equation
An equation which sums up the ideal gas laws in one simple equation,
P V = n R T,
where P is the pressure, V is the volume, n is the number of moles present, and T is the temperature of the
ideal gas laws
The pressure of an ideal gas is inversely proportional to the volume of the gas at constant
The volume of an ideal gas is directly proportional to the thermodynamic temperature at constant
The pressure of an ideal gas is directly proportional to the thermodynamic temperature at constant
joule; J (after J.P. Joule, 1818-1889)
The derived SI unit of energy defined as the amount of work done by moving an object through a distance
of 1 m by applying a force of 1 N; it thus has units of N m.
Joule-Thomson effect; Joule-Kelvin effect (J.P. Joule, W. Thomson [later Lord Kelvin])
The change in temperature that occurs when a gas expands into a region of lower pressure.
Joule's laws (J.P. Joule)
Joule's first law:
The heat Q produced when a current I flows through a resistance R for a specified time t is given
Q = I2 R t
Joule's second law:
The internal energy of an ideal gas is independent of its volume and pressure, depending only on its
Josephson effects (B.D. Josephson; 1962)
Electrical effects observed when two superconducting materials are separated by a thin layer of insulating
kelvin; K (after Lord Kelvin, 1824-1907)
The fundamental SI unit of thermodynamic temperature defined as 1/273.16 of the thermodynamic
temperature of the triple point of water.
Kepler's 1-2-3 law
Another formulation of Kepler's third law, which relates the mass m of the primary to a secondary's
angular velocity omega and semimajor axis a:
m o= omega2 a3.
Kepler's laws (J. Kepler)
Kepler's first law:
A planet orbits the Sun in an ellipse with the Sun at one focus.
Kepler's second law:
A ray directed from the Sun to a planet sweeps out equal areas in equal times.
Kepler's third law:
The square of the period of a planet's orbit is proportional to the cube of that planet's semimajor
axis; the constant of proportionality is the same for all planets.
Kerr effect (J. Kerr; 1875)
The ability of certain substances to differently refract light waves whose vibrations are in different
directions when the substance is placed in an electric field.
Kirchhoff's law of radiation (G.R. Kirchhoff)
The emissivity of a body is equal to its absorptance at the same temperature.
Kirchhoff's laws (G.R. Kirchhoff)
Kirchhoff's first law:
An incandescent solid or gas under high prssure will produce a continuous spectrum.
Kirchhoff's second law:
A low-density gas will radiate an emission-line spectrum with an underlying emission continuum.
Kirchhoff's third law:
Continuous radiation viewed through a low-density gas will produce an absorption-line spectrum.
Kirchhoff's rules (G.R. Kirchhoff)
The sum of the potential differences encountered in a round trip around any closed loop in a circuit
The sum of the currents toward a branch point is equal to the sum of the currents away from the
same branch point.
Kirkwood gaps (Kirkwood)
Gaps in the asteroid belt, caused by resonance effects from Jupiter. Similar gaps exist in Saturn's rings,
due to the resonance effects of shepherd moons.
Kohlrausch's law (F. Kohlrausch)
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 (J.H. Lambert)
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
Points in the vicinity of two massive bodies (such as the Earth and the Moon) where each others'
respective gravities balance. There are five, labelled L1 through L5. L1, L2, and L3 lie along the
centerline between the centers of mass between the two masses; L1 is on the inward side of the
secondary, L2 is on the outward side of the secondary; and L3 is on the outward side of the primary. L4
and L5, the so-called Trojan points, lie along the orbit of the secondary around the primary, sixty degrees
ahead and behind of the secondary.
L1 through L3 are points of unstable equilibrium; any disturbance will move a test particle there out of the
Lagrange point. L4 and L5 are points of stable equilibrium, provided that the mass of the secondary is less
than about 1/24.96 the mass of the primary. These points are stable because centrifugal pseudoforces
work against gravity to cancel it out.
A principle which states that it doesn't explicitly take energy to compute data, but rather it takes energy to
erase any data, since erasure is an important step in computation.
Laplace equation (P. Laplace)
For steady-state 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;
d2 T/dr2 = 0.
Laue pattern (M. von Laue)
The pattern produced on a photographic film when high-frequency electromagnetic waves (such as
x-rays) are fired at a crystalline solid.
Lawson criterion (J.D. Lawson)
A condition for the release of energy from a thermonuclear reactor. It is usually stated as the minimum
value for the product of the density of the fuel particles and the energy confinement time for energy
breakeven. For a half-and-half mixture of deuterium and tritium at ignition temperature, nG tau is
between 1014 and 1015 s/cm3.
Le Chatelier's principle (H. Le Chatelier; 1888)
If a system is in equilibrium, then any change imposed on the system tends to shift the equilibrium to
reduce the effect of that applied change.
The opposite-chirality version of the right-hand rule.
Lenz's law (H.F. Lenz; 1835)
An induced electric current always flows in such a direction that it opposes the change producing it.
Loschmidt constant; Loschmidt number; NL
The number of particles per unit volume of an ideal gas at standard temperature and pressure. It has the
value 2.687 19 x 1025 m-3.
The derived SI unit of luminous flux, defined as the luminous flux emitted by a uniform point source of 1
cd emitting its luminous energy over a solid angle of 1 sr; it thus has units of cd sr.
A substance, which filled all the empty spaces between matter, which was used to explain what medium
light was "waving" in. Now it has been discredited, as Maxwell's equations imply that electromagnetic
radiation can propagate in a vacuum, since they are disturbances in the electromagnetic field rather than
traditional waves in some substance, such as water waves.
The derived SI unit of illuminance equal to the illuminance produced by a luminous flux of 1 lm distributed
uniformly over an area of 1 m2; it thus has units of lm/m2.
A particle which travels solely at c (the speed of light in vacuum). All luxons have a rest mass of exactly
zero. Though they are massless, luxons do carry momentum. Photons are the prime example of luxons
(the name itself is derived from the Latin word for light).
Compare tardon, tachyon.
The series which describes the emission spectrum of hydrogen when electrons are jumping to the ground
state. All of the lines are in the ultraviolet.
Mach number (E. Mach)
The ratio of the speed of an object in a given medium to the speed of sound in that medium.
Mach's principle (E. Mach; c. 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.
See permeability of free space.
A hypothetical particle which constitutes sources and sinks of the magnetic field. Magnetic monopoles
have never been found, but would only cause fairly minor modifications to Maxwell's equations. They also
seem to be predicted by some grand-unified theories. If magnetic monopoles do exist, they do not seem to
be very common in our Universe.
A rotating cylinder in a moving fluid drags some of the fluid around with it, in its direction of rotation. This
increases the speed in that region, and thus the pressure is lower. Consequently, there is a net force on
the cylinder in that direction, perpendicular to the flow of the fluid. This is called the Magnus effect.
Malus' law (E.L. Malus)
The light intensity I of a ray with initial intensity I0 travelling through a polarizer at an angle theta between
the polarization of the light ray and the polarization axis of the polarizer is given by
I = I0 cos2 theta.
Maxwell's demon (J.C. Maxwell)
A thought experiment illustrating the concepts of entropy. We have a container of gas which is partitioned
into two equal sides; each side is in thermal equilibrium with the other. The walls and the partition of the
container are perfect insulators.
Now imagine there is a very small demon who is waiting at the partition next to a small trap door. He can
open and close the door with negligible work. Let's say he opens the door to allow a fast-moving molecule
to travel from the left side to the right, or for a slow-moving molecule to travel from the right side to the
left, and keeps it closed for all other molecules. The net effect would be a flow of heat -- from the left
side to the right -- even though the container was in thermal equilibrium. This is clearly a violation of the
second law of thermodynamics.
So where did we go wrong? It turns out that information has to do with entropy as well. In order to sort
out the molecules according to speeds, the demon would be having to keep a memory of them -- and it
turns out that increase in entropy of the maintenance of this simple memory would more than make up for
the decrease in entropy due to the heat flow.
Maxwell's equations (J.C. Maxwell; 1864)
Four elegant equations which describe classical electromagnetism in all its splendor. They are:
The electric flux normal to 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 normal to a closed surface is zero; no magnetic charges exist. In
div B = 0.
The line integral of the electric flux 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 d/dt here represents partial differentation.
Ampere's law, modified form:
The line integral of the magnetic flux 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,
where d/dt here represents partial differentiation.
In addition to describing electromagnetism, his equations also predict that waves can propagate through
the electromagnetic field, and would always propagate at the same speed -- these are electromagnetic
waves; the speed can be found by computing (epsilon0 mu0)-1/2, which is c, the speed of light in vacuum.
The principle that there is nothing particularly interesting about our place in space or time, or about
ourselves. This principle probably first made its real appearance in the scientific community when Shapley
discovered that the globular clusters center around the center of the Galaxy, not around the solar system.
The principle can be considered a stronger form of the uniformity principle; instead of no place being
significantly different than any other, the mediocrity principle indicates that, indeed, where you are is not
any more special than any other.
Meissner effect (W. Meissner; 1933)
The decrease of the magnetic flux within a superconducting metal when it is cooled below the transition
temperature. That is, superconducting materials reflect magnetic fields.
Michelson-Morley experiment (A.A. Michelson, E.W. Morley; 1887)
Possibly the most famous null-experiment of all time, designed to verify the existence of the proposed
"lumeniferous aether" through which light waves were thought to propagate. Since the Earth moves
through this aether, a lightbeam fired in the Earth's direction of motion would lag behind one fired
sideways, where no aether effect would be present. This difference could be detected with the use of an
The experiment showed absolutely no aether shift whatsoever, where one should have been quite
detectable. Thus the aether concept was discredited as was the idea that one measures the velocity of
light as being added vectorially to the velocity of the emitter.
See constancy principle.
Millikan oil drop experiment (R.A. Millikan)
A famous experiment designed to measure the electronic charge. Drops of oil were carried past a
uniform electric field between charged plates. After charging the drop with x-rays, he adjusted the
electric field between the plates so that the oil drop was exactly balanced against the force of gravity.
Then the charge on the drop would be known. Millikan did this repeatedly and found that all the charges
he measured came in integer multiples only of a certain smallest value, which is the charge on the
An experiment which demonstrates verifies the prediction of time dilation by special relativity. Muons,
which are short-lived subatomic particles, are created with enormous energy in the upper atmosphere by
the interaction of energetic cosmic rays. Muons have a very short halflife in their own reference frame,
about 2.2 us. Since they are travelling very close to c, however, time dilation effects should become
important. A naive calculation would indicate that, without special relativistic effects, the muons would
travel on the average only about 700 m before decaying, never reaching the surface of the Earth.
Observations reveal, however, that significant numbers of muons do reach the Earth. The explanation is
that muon is in a moving frame of reference, and thus time is slowed down for the muons relative to the
Earth, effectively extending the halflife of the muons relative to the Earth, allowing some of them to reach
negative feedback principle
The idea that in a system where there are self-propagating circumstances, those new circumstances tend
to act against previously existing circumstances. Such a principle is really a restatement of a conservation
Example Lenz's law.
newton; N (after Sir I. Newton, 1642-1727)
The derived SI unit of force, defined as the force required to give a mass of 1 kg an acceleration of 1
m/s2; it thus has units of kg m/s2.
Newton's law of universal gravitation (Sir I. Newton)
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; mathematically,
F = (G m M/r2) 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 (Sir I. Newton)
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
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.
Noether theorem (Noether)
A theorem which demonstrates that symmetries are what gives rise to conserved quantities. For instance,
translational symmetry (the fact that the laws of physics work the same in all places) gives rise to
conservation of momentum, since position and momentum are complementary. Additionally, conservation
of energy is indicated by time symmetry, and conservation of angular momentum is indicated by isotropy.
no-hair conjecture (1960s)
The conjecture (proved in the 1970s and 1980s) within general relativity that a black hole has only three
salient external characteristics: mass, angular momentum, and electric charge. All other properties
(including baryon number, lepton number, strangeness, etc.) are destroyed as matter falls into the horizon.
Note that there is some indication that quantum mechanical considerations in quantum gravity will result in
a "quantum hair" coming into play. However, that 1. would constitute a prediction of a theory which does
not yet formally exist, and 2. is utterly insignificant for solar-massed black holes, the only types that can
be formed today.
An experiment which, after being executed, yields no result. Null experiments are just as meaningful as
non-null experiments; if current theory predicts an observable effect (or predicts there should be no
observable effect), and experimentation (within the required accuracy) does not yield said effect, then the
null experiment has told us something about our theory.