KHTK Glossary (Physics)

Reference: Course on Subject Clearing

This is the KHTK Glossary for PHYSICS. You can find out more about KHTK at What is KHTK? This glossary is to be used with Subject Clearing.

Key Concepts

SECTION 1: MATHEMATICS

“Something learned.” Mathematics is the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically.

ABSOLUTE VALUE

The value without regards to its sign. It is the magnitude of a number.

FUNCTION

A function relates a dependent variable to independent variable(s). There are linear functions, quadratic functions, exponential functions, etc. The linear functions are represented by straight lines on a graph.

GRAPH

Whenever one has a mathematical relationship between two variables, one can represent the function by a two dimensional graph. [Page 3 – axes, origin, independent variable, dependent variable, slope, intercept]

INTERNATIONAL SYSTEM OF UNITS (SI)

The set of units most commonly used throughout the world, and which is almost exclusively used in scientific work. In mechanics, the units are the meter, the kilogram, and the second, and are what is commonly called the mks system.

INVERSE FUNCTION

A function gives us a y value for every x value. Inverse function turns it around and gives us an x value for every y-value. To get the graph of inverse function, rotate the graph of the function 90 deg clockwise so that y appears along the horizontal.

INVERSE FUNCTION

ONE-DIMENSIONAL

One-dimensional means, in a straight line; in the same direction; along the x-axis.

SCIENTIFIC NOTATION

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power, as 1385.62 written as 1.386 × 10³.

SIGNIFICANT FIGURES

Whenever a measured value is given for a physical quantity, it can only be an approximation, because it is not possible to measure anything with “infinite” accuracy. A scientist or engineer who specifies the numerical value of a physical quantity keeps only as many figures in the number as are justified by the accuracy to which the physical quantity is known. For any measured quantity there is always some uncertainty in the last digit given. The number of significant figures provide a rough measure of percent uncertainty.

SIMULTANEOUS EQUATIONS

When we have two different relationships involving the same two variables, then both relationships can be valid only for specific values of the variables.

STANDARD

The physical specimen, which defines the unit, is called the standard.

TRIGONOMETRIC FUNCTION
Trigonometric Functions are most usually defined in terms of ratios of sides of a right triangle, in which the angle plays the role of the independent variable.

UNITS

Origin: “unity.” Unit is an identity element. We need units of measurement to measure physical quantities, such as, length, area, volume, velocity, acceleration, mass, time and temperature. Not all measurable quantities require their own units. Often, the unit is automatically defined in terms of other units. Such units are called derived units. In the subject of mechanics, only three physical quantities must have their units defined independently. These three quantities are usually taken to be length, mass and time, and their units are called fundamental units. It turns out that units can be treated algebraically in any physics equation.

VARIABLES

Variables are quantities that can take on a range of values.

SECTION 2: MECHANICS

MECHANICS, WORK, ENERGY,

ACCELERATION
Acceleration is the time rate of change of velocity.

BODY
Body is any mass, especially one considered as a whole.

COORDINATE SYSTEM
Origin: “order together.” A coordinate system is a fixed system of directions and angles from an ‘origin point’ that uses numbers to define the position of a point, line, or the like.

DENSITY
DENSITY is the degree of substantiality of substance.

DISPLACEMENT
Displacement is the measure of the position of the object in a coordinate system. Absolute displacement specifies a particle’s location as measured from the origin. It has both a magnitude and a sign. Its magnitude is the straight-line distance from the origin to the location of a particle. Its sign is positive if the particle is on the positive side of the axis, and negative if it is on the negative side. Relative displacement is the location of the particle as measured from an arbitrary point. Like absolute displacement, relative displacement can be either positive or negative. If right is chosen as the positive direction, then the relative displacement is negative when the position of the particle is to the left of the position from which it is measured.

DISTANCE
Distance is the absolute value of the relative displacement. Therefore, the distance traveled is always positive.

ENERGY
The property of a system that diminishes when the system does work on any other system.

In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object. Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed.

ENERGY, KINETIC
In physics, the kinetic energy (KE) of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest. The speed, and thus the kinetic energy of a single object is frame-dependent (relative): it can take any non-negative value, by choosing a suitable inertial frame of reference. For example, a bullet passing an observer has kinetic energy in the reference frame of this observer. The same bullet is stationary to an observer moving with the same velocity as the bullet, and so has zero kinetic energy. By contrast, the total kinetic energy of a system of objects cannot be reduced to zero by a suitable choice of the inertial reference frame, unless all the objects have the same velocity. In any other case, the total kinetic energy has a non-zero minimum, as no inertial reference frame can be chosen in which all the objects are stationary. This minimum kinetic energy contributes to the system’s invariant mass, which is independent of the reference frame.

FORCE
Origin: “strong.” Force is an influence on a body or system, producing or tending to produce a change in movement or in shape or other effects.

Change in momentum over time.

GRAVITY
Gravity is substantial enough to be perceived as force. Therefore, gravity is a substance that is different from matter and energy.

MECHANICS
The branch of physics that deals with the action of forces on bodies and with motion, comprised of kinetics, statics, and kinematics.

MOMENTUM
Momentum is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction.

PARTICLE
A MATERIAL PARTICLE in space is defined by its center of mass. The opposite of particle is CONTINUUM.
An ENERGY PARTICLE is the amount of substance participating in an interaction. It is defined by the interaction.

PARTICLE

In Science, the definition of PARTICLE is missing. This word has been used in very general terms only. A MATERIAL PARTICLE in space is defined by its center of mass. An ENERGY PARTICLE is defined by the amount of substance participating in an interaction. A QUANTUM is a discrete amount drawn from a continuum by an interaction at the atomic level.
In Mechanics, a particle is an infinitesimally small object located at a definite point in a coordinate system. The particle is the representation of the mathematical ‘center of mass’ of an object. If there is no center of mass, as in the case of a “light particle” then the laws of mechanics do not apply.
Originally, a particle was understood to be a small part of matter that obviously had a fixed boundary and a center of mass. Example of this would be a dust particle, or a particle of sand. In Chemistry, a particle was related to the smallest part of substance that took part in chemical reactions. Ultimately, a particle of matter was reduced to the idea of an atom or a molecule. Its boundaries were considered to be well defined and fixed, and it had a center of mass.
This idea of particle shifted as one looked at the sub-atomic region beyond the nucleus. Here the substance is no longer rigidly structured as in the case of matter, or even an atom. This sub-atomic substance is rather thin in consistency and spread out. It appears as a continuum with no definite boundaries and no center of mass. Only definite amount of this substance seem to take part in sub-atomic reactions. Therefore, we fall back to the concept of particle similar to that in Chemistry. It is a definite amount of “energy substance” that takes part in a reaction. At sub-atomic level, this is referred to as a “quantum.”
In atomic physics, a particle is a high-energy pulse with an energy field forming its background. The particle maintains continuity with its background.
In its most basic sense, a particle is defined in terms of its associations; a perceptual element.

PRESSURE
Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

SPEED
Average speed is defined as the total distance traveled in a given time divided by that time interval. Since distance traveled is always positive, the average speed is always positive. Its units are the same as those of velocity. Average speed is either equal to or greater than the average velocity. Instantaneous speed is always the same as instantaneous velocity.

TIME

Time is a measure of when the object is at a certain position in a coordinate system. Time elapsed is always positive.

WORK
The mechanical effort required to change a system from one state to another.

VELOCITY

Velocity is the time rate of change of displacement.

WAVE
WAVES are cycles of oscillations that have the characteristics of a continuum.
A wave can be a disturbance traveling in a stationary medium, such as, the waves on the surface of water in a pond.
A wave can also be a rapidly traveling substance with the characteristics of a continuum, such as, light or the rolling waves of the sea.

WORK
In physics, work is the process of energy transfer to the motion of an object via application of a force, often represented as the product of force and displacement.

SECTION 3: THERMODYNAMICS

THERMODYNAMICS, HEAT, TEMPERATURE

ADIABATIC PROCESS
An adiabatic process occurs without transferring heat or mass between a thermodynamic system and its surroundings. Unlike an isothermal process, an adiabatic process transfers energy to the surroundings only as work. It also conceptually forms the foundation of the theory used to expound the first law of thermodynamics and is therefore a key thermodynamic concept. Q = 0 but ΔT ≠ 0.

CARNOT CYCLE
The Carnot Cycle is a theoretically reversible cycle in which entropy is conserved. The cycle operates between two “heat reservoirs” at temperatures Th and Tc (hot and cold respectively). The reservoirs have such large thermal capacity that their temperatures are practically unaffected by a single cycle.

During the Carnot cycle, an amount of energy ThΔS is extracted from the hot reservoir and a smaller amount of energy TcΔS is deposited in the cold reservoir. The difference in the two energies (Th-Tc)ΔS is equal to the work done by the engine. Thus, heat is converted into work.

ENERGY, INTERNAL
The internal energy keeps account of the gains and losses of energy of the system that are due to changes in its internal state. It is often not necessary to consider all of the system’s intrinsic energies. Internal energy is measured as a difference from a reference zero defined by a standard state. The processes that define the internal energy in the state of interest are transfers of matter, or of energy as heat, or as thermodynamic work. If the containing walls pass neither matter nor energy, the system is said to be isolated and its internal energy cannot change. Microscopically, the internal energy can be analyzed in terms of the kinetic energy of microscopic motion of the system’s particles from translations, rotations, and vibrations, and of the potential energy associated with microscopic forces, including chemical bonds.
Internal energy excludes the kinetic energy of motion of the system as a whole and the potential energy of the system as a whole due to external force fields.

ENERGY, THERMAL
Thermal energy refers to several distinct physical concepts, such as the internal energy of a system; heat or sensible heat, which are defined as types of energy transfer (as is work); or for the characteristic energy of a degree of freedom in a thermal system (kT).

ENTROPY
The word ‘entropy’ comes from the Greek words, `en-tropie’ (intrinsic direction). The concept of entropy came about from investigations into lost energy in heat engines. Entropy was introduced as the concept of ‘transformation-energy’, i.e. energy lost to dissipation and friction. Entropy is a macro state variable for a system that is defined only when the system is in equilibrium.

1789 Count Rumford – heat could be created by friction as when cannon bores are machined.

1803 Lazare Carnot – Losses of moments of activity

1824 Sadi Carnot – Work or motive power can be produced when heat falls through temperature difference

1843 James Joules – expresses the concept of energy and its conservation in all processes. He is unable to quantify the effects of friction and dissipation.

1850s Rudolf Clausius – objected to the supposition that no change occurs in the working body. There is inherent loss of usable heat when work is done, e.g. heat produced by friction. This was in contrast to earlier views, based on the theories of Isaac Newton, that heat was an indestructible particle that had mass.

1877 – Boltzmann – visualized a probabilistic way to measure the entropy of an ensemble of ideal gas particles

Entropy is a state variable. Its thermodynamic definition is “Q/T,” and its statistical mechanics definition is “k ln Ω.” Essential problem in statistical thermodynamics has been to determine the distribution of a given amount of energy E over N identical systems.

FREE ENERGY

The change in the free energy is the maximum amount of work that a thermodynamic system can perform in a process at constant temperature, and its sign indicates whether the process is thermodynamically favorable or forbidden. Free energy is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful.

(Gibbs function) the thermodynamic function of a system that is equal to its enthalpy minus the product of its absolute temperature and entropy: a decrease in the function is equal to the maximum amount of work available exclusive of that due to pressure times volume change during a reversible, isothermal, isobaric process.

(Helmholtz function) the thermodynamic function of a system that is equal to its internal energy minus the product of its absolute temperature and entropy: a decrease in the function is equal to the maximum amount of work available during a reversible isothermal process.

GAS CONSTANT
The gas constant R is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law. It relates the energy scale to the temperature scale, when a mole of particles at the stated temperature is being considered. It is defined as the Avogadro constant multiplied by the Boltzmann constant.

HEAT
A non-mechanical energy transfer with reference to a temperature difference between a system and its surroundings or between two parts of the same system.

In thermodynamics, heat is not the property of an isolated system. It is energy in transfer to or from a thermodynamic system. Heat excludes any thermodynamic work that was done and any energy contained in matter transferred. Heat transfer occurs by the following mechanisms:

(1) Conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter.
(2) Radiation between separated bodies.
(3) Convective circulation that carries energy from a boundary of one to a boundary of the other.
(4) Friction due to work done by the surroundings on the system of interest, such as Joule heating.

Quantity of energy transferred as heat can be measured by its effect on the states of interacting bodies. For example, by the amount of ice melted, or by change in temperature of a body in the surroundings of the system.

HEAT, SENSIBLE
Sensible heat is heat exchanged by a body (or thermodynamic system) in which the exchange of heat changes the temperature of the body, and some macroscopic variables, but leaves unchanged certain other macroscopic variables, such as volume or pressure. The term is used in contrast to a latent heat, which is the amount of heat exchanged that is hidden, meaning it occurs without change of temperature.

IDEAL GAS
The volume of ideal gas is essentially made up of electromagnetic substance. At very high pressures and very low temperatures the Ideal gas approximations are not valid.

IDEAL GAS
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to inter-particle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.

IDEAL GAS LAW
The ideal gas law is the equation of state of a hypothetical ideal gas. It is often written in an empirical form:
PV = nRT
where P, V and T are the pressure, volume and temperature; n is the amount of substance; and R is the ideal gas constant. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations.

ISOTHERMAL PROCESS

An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and the change in the system will occur slowly enough to allow the system to continue to adjust to the temperature of the reservoir through heat exchange. ΔT = 0 but Q ≠ 0.

LAW (ZEROTH) OF THERMODYNAMICS: TEMPERATURE
If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

This law helps define the notion of temperature.
Systems in thermal equilibrium with each other have the same temperature.
Temperature is one-dimensional, that one can conceptually arrange bodies in real number sequence from colder to hotter.
This law allows the definition of temperature in a non-circular way without reference to entropy, its conjugate variable.

LAW (FIRST) OF THERMODYNAMICS: INTERNAL ENERGY
When energy passes, as work, as heat, or with matter, into or out from a system, its internal energy changes in accord with the law of conservation of energy.

The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.

The first law of thermodynamics may be regarded as establishing the existence of the internal energy.

Equivalently, perpetual motion machines of the first kind are impossible.

A perpetual motion machine of the first kind produces work without the input of energy. It thus violates the first law of thermodynamics: the law of conservation of energy.

The internal energy of a system is energy contained within the system… It keeps account of the gains and losses of energy of the system that are due to changes in its internal state.
The internal energy of a system can be changed by transfers: (a) as heat, (b) as work, or (c) with matter.
When matter transfer is prevented by impermeable containing walls, the system is said to be closed. Then the first law of thermodynamics states that the increase in internal energy is equal to the total heat added plus the work done on the system by its surroundings.
If the containing walls pass neither matter nor energy, the system is said to be isolated. Then its internal energy cannot change. The first law of thermodynamics may be regarded as establishing the existence of the internal energy.

The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.

The first law of thermodynamics may be regarded as establishing the existence of the internal energy.

Equivalently, perpetual motion machines of the first kind are impossible.

A perpetual motion machine of the first kind produces work without the input of energy. It thus violates the first law of thermodynamics: the law of conservation of energy.

The internal energy of a system is energy contained within the system… It keeps account of the gains and losses of energy of the system that are due to changes in its internal state.
The internal energy of a system can be changed by transfers: (a) as heat, (b) as work, or (c) with matter.
When matter transfer is prevented by impermeable containing walls, the system is said to be closed. Then the first law of thermodynamics states that the increase in internal energy is equal to the total heat added plus the work done on the system by its surroundings.
If the containing walls pass neither matter nor energy, the system is said to be isolated. Then its internal energy cannot change. The first law of thermodynamics may be regarded as establishing the existence of the internal energy.

The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy.

The first law of thermodynamics may be regarded as establishing the existence of the internal energy.

Equivalently, perpetual motion machines of the first kind are impossible.

A perpetual motion machine of the first kind produces work without the input of energy. It thus violates the first law of thermodynamics: the law of conservation of energy.

The internal energy of a system is energy contained within the system… It keeps account of the gains and losses of energy of the system that are due to changes in its internal state.
The internal energy of a system can be changed by transfers: (a) as heat, (b) as work, or (c) with matter.
When matter transfer is prevented by impermeable containing walls, the system is said to be closed. Then the first law of thermodynamics states that the increase in internal energy is equal to the total heat added plus the work done on the system by its surroundings.
If the containing walls pass neither matter nor energy, the system is said to be isolated. Then its internal energy cannot change. The first law of thermodynamics may be regarded as establishing the existence of the internal energy.

LAW (SECOND) OF THERMODYNAMICS: ENTROPY

Theorem of the equivalence of transformations

In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases.

Equivalently, perpetual motion machines of the second kind are impossible.
Indicates the irreversibility of natural processes. NOTE: The precipitation of order from chaos seems to be irreversible.
When two initially isolated systems in separate but nearby regions of space, each in thermodynamic equilibrium with itself but not necessarily with each other, are then allowed to interact, they will eventually reach a mutual thermodynamic equilibrium. The sum of the entropies of the initially isolated systems is less than or equal to the total entropy of the final combination. Equality occurs just when the two original systems have all their respective intensive variables (temperature, pressure) equal; then the final system also has the same values.
This statement of the second law is founded on the assumption, that in classical thermodynamics, the entropy of a system is defined only when it has reached internal thermodynamic equilibrium (thermodynamic equilibrium with itself).
The second law is applicable to a wide variety of processes, reversible and irreversible. All natural processes are irreversible. Reversible processes are a useful and convenient theoretical fiction, but do not occur in nature.
A prime example of irreversibility is in the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies initially of different temperatures come into thermal connection, then heat always flows from the hotter body to the colder one.
The second law tells also about kinds of irreversibility other than heat transfer, for example those of friction and viscosity, and those of chemical reactions. The notion of entropy is needed to provide that wider scope of the law.
Heat Q is proportional to the total kinetic energy (K.E.) of microscopic particles in a system. Temperature T is proportional to the average K.E. of the system. Therefore, the ratio Q/T (entropy) shall be constant for a closed system, being the ratio of total to average K.E. Thus, it would represent the total number of particles in a system. Q reduces as does T when heat energy converts to the mechanical work done.
Conversion of Heat to mechanical Work is essentially the kinetic energy of microscopic particles converting to kinetic energy of large objects.
Not all K.E. of microscopic particles can be converted to K.E. of large objects. As long as temperature is not zero (K), the microscopic particles retain some of their K.E.
When heat is added to a system in which the number of microscopic particles do not change, then both Q and T increase in the same proportion. It is incorrect to assume that T remains constant.
When Q is converted to mechanical work in a system in which the number of microscopic particles do not change, then both Q and T decrease in the same proportion. It is incorrect to assume that Q remains constant.

Q1 = Q2 + W with a decrease in temperature from T1 to T2.
or, W = Q1 – Q2
or, W = n (T1 – T2), where n is proportional to the number of particles in the system

Mechanical work done should be proportional to the difference in temperatures in a reversible process. In an irreversible process where losses occur, work w is less than W.

Efficiency = w/W x 100% = w/[n(T1-T2)] x 100%

Entropy increases when Q remains constant while T decreases. How is Q defined here?

LAW (THIRD) OF THERMODYNAMICS
The entropy of a system approaches a constant value as the temperature approaches absolute zero. The entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero.

At zero temperature the system must be in a state with the minimum thermal energy. This statement holds true if the perfect crystal has only one state with minimum energy.
The constant value (not necessarily zero) is called the residual entropy of the system.

LAWS OF THERMODYNAMICS

FIRST LAW: Energy cannot be created or destroyed, only transformed.

MOLE (AVOGADRO CONSTANT)
The mole is the unit of measurement for amount of substance. A mole of particles is defined as 6.022 × 10^23 particles, which may be atoms, molecules, ions, or electrons. The mass of one mole of a chemical compound, in grams, is numerically equal (for all practical purposes) to the average mass of one molecule of the compound, in atomic mass units).

SPECIFIC HEAT CAPACITY
The specific heat capacity of a substance is the amount of energy that must be added, in the form of heat, to one unit of mass of the substance in order to cause an increase of one unit in its temperature. The SI unit of specific heat is joule per kelvin per kilogram, J/(K kg). Liquid water has one of the highest specific heats among common substances, about 4182 J/(K kg) at 20 °C. The specific heat often varies with temperature, and is different for each state of matter.

TEMPERATURE
Temperature is a physical property of matter that quantitatively expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source of the occurrence of heat, a flow of energy, when a body is in contact with another that is colder.

TEMPERATURE
A measure of the warmth or coldness of an object or substance with reference to some standard value.

TEMPERATURE, THERMODYNAMIC
Thermodynamic temperature is defined by the third law of thermodynamics in which the theoretically lowest temperature is the null or zero point. At this point, absolute zero, the particle constituents of matter have minimal motion and can become no colder. Thermodynamic temperature is often also called absolute temperature, for two reasons: the first, proposed by Kelvin, that it does not depend on the properties of a particular material; the second, that it refers to an absolute zero according to the properties of the ideal gas.

THERMODYNAMICS (“force or power of heat”)
The science concerned with the relations between heat and mechanical energy or work, and the conversion of one into the other.

THERMODYNAMIC CYCLE
Every single thermodynamic system exists in a particular state. When a system is taken through a series of different states and finally returned to its initial state, a thermodynamic cycle is said to have occurred. In the process of going through this cycle, the system may perform work on its surroundings, for example by moving a piston, thereby acting as a heat engine.

THERMODYNAMIC EQUILIBRIUM
Macrostates are not changing, but microstates are constantly changing. When a system changes state, the beginning and final states may be well-defined, but the intermediate states may not be defined because the system is not in equilibrium. However, if we can maintain equilibrium the whole time by making the changes very slowly and in very small steps (quasi-static process). Then we can describe the path from beginning and final states. Most quasi-static processes are reversible because there is no loss of energy. In real world there is no perfectly reversible process.

THERMODYNAMIC STATE
A thermodynamic system is a macroscopic object, the microscopic details of which are not explicitly considered in its thermodynamic description.

WORK (Thermodynamic)
In thermodynamics, work performed by a system is energy transferred by the system to its surroundings, by a mechanism through which the system can spontaneously exert macroscopic forces on its surroundings, where those forces, and their external effects, can be measured.

SECTION 4: STATISTICAL MECHANICS

BOLTZMANN CONSTANT
It is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas.

The Boltzmann constant (k_B or k), which is named after Ludwig Boltzmann, is a physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas. It is the gas constant R divided by the Avogadro constant NA.

MACROSTATES

Pressure, temperature and volume are macrostates of a system.

MAXWELL-BOLTZMANN DISTRIBUTION

A Maxwell–Boltzmann Distribution is a probability distribution used for describing the speeds of various particles within a stationary container at a specific temperature. The distribution is often represented with a graph, with the y-axis defined as the number of molecules and the x-axis defined as the speed.

MICROSTATES
State of every atom and molecule.

STATE VARIABLE
Internal energy, enthalpy, and entropy are state quantities or state functions because they describe quantitatively an equilibrium state of a thermodynamic system, irrespective of how the system arrived in that state. In contrast, mechanical work and heat are process quantities or path functions, because their values depend on the specific transition (or path) between two equilibrium states.

STATISTICAL MECHANICS
Statistical mechanics involves dynamics, Where the attention is focused on statistical equilibrium (steady state). Statistical equilibrium does not mean that the particles have stopped moving (mechanical equilibrium), rather, only that the ensemble is not evolving.

STATISTICAL THERMODYNAMICS (equilibrium statistical mechanics)
The primary goal of statistical thermodynamics is to derive the classical thermodynamics of materials in terms of the properties of their constituent particles and the interactions between them. In other words, statistical thermodynamics provides a connection between the macroscopic properties of materials in thermodynamic equilibrium, and the microscopic behaviors and motions occurring inside the material.

STATISTICS
We can’t keep track of trillions of molecules individually, so we track the average.

SECTION 5: QUANTUM MECHANICS

ATOM
A particle of matter that cannot be divided further. Faraday saw atom as the center of force. The concentrated force appears as mass. Maxwell and other physicists, however, saw atom as the smallest, indivisible unit of matter.

The ATOM is a whirlpool of substance that is thinning in density and increasing in speed as it spreads out from the nucleus. The highly dense nucleus appears as the “stationary” center of mass. The immediate substance surrounding the nucleus is the rapidly whirling continuum of electrons.
A unit of matter.

ATOMIC NUMBER
The atomic number of a chemical element is the number of protons found in the nucleus of every atom of that element. The atomic number uniquely identifies a chemical element. It is identical to the charge number of the nucleus. In an uncharged atom, the atomic number is also equal to the number of electrons.

Black-body radiation (Notes)
1. Black Body
2. Thermodynamic Equilibrium
3. Equipartition Theorem
4. Rayleigh-Jeans Law
5. Ultraviolet Catastrophe
6. Black-body Radiation

CHARGE:
Charge is the dynamic motion of field-substance. (See MASS)

Classical to Quantum Mechanics
1. Field-Matter Interactions
2. Derivation of Planck’s Radiation Law

FIELD-SUBSTANCE
This is the non-structured aspect of substance that starts as a wave of disturbance. This wave congeals into greater substantial-ness as it follows paths of smaller and smaller radius. This leads to a pattern similar to a “whirlpool”. The substantial-ness increases as one approaches the center of this whirlpool formation. The electromagnetic spectrum provides the progression of substantial-ness of field-substance. The substantial-ness of field-substance is measured in terms of QUANTIZATION.
The field-substance, as electromagnetic phenomenon, is identified as “energy” as in “mass-energy equivalence” but it is not the same thing as the classical notion of energy. This mis-identification of field-substance as “energy” generates confusion.

MANIFOLD
A manifold is basically a set of points that can be represented by one or more coordinate systems. The plane is a manifold, the surface of a sphere is a manifold, three-dimensional space is a manifold, and yes, so is four-dimensional spacetime. Each of these can be covered by a finite number of coordinate charts.

MANIFOLD, EINSTEIN
The physical significance of what is called an Einstein manifold is that it’s a mathematical representation of a spacetime that is dominated by a cosmological constant, aka. “vacuum energy”. If our current views of accelerating expansion due to vacuum energy are correct, then the far distant future of our universe will appear increasingly closely represented by an Einstein manifold.

METRIC
In physics, a metric is a numerical value derived from measurements to be used in math equations for calculating and predicting outcomes.

PHOTON
A photon is an energy particle, meaning it is the energy of an interaction within the electromagnetic spectrum. A photon does not exist in the absence of interaction.

SPACE
Space is the metric of distances.

SPACETIME
Spacetime is, according to Einstein’s description, a mathematical construct and has no material properties. Spacetime is a metric.

TIME
Time is the metric of the rate and duration of an observed action.

QUANTA
Newton’s mechanics dealt only with material particles. Maxwell’s equations introduced continuous fields. Thus, there was an inconsistency that was bridged over by the discovery of quanta. Quanta provides a gradient from continuous field to discrete material particles.

QUANTIZATION
QUANTIZATION is the process of congealing through which the field-substance gradually becomes more substantial and discrete. Quantization parallels the increasing frequency of the elecromagnetic spectrum.
When the field-substance transitions into material-substance with the formation of nucleus at the upper end of the spectrum, the process of quantization appears as increasing INERTIA of the material-substance.

QUANTUM
A QUANTUM is an energy particle. It is the discrete amount drawn from a continuum for an interaction at the atomic level.

QUANTUM “PARTICLES”
Quantum “particles” are not really discrete particles; but they have a very high consistency like syrup. Quantum “particles” participate in discrete interactions like matter.

WORK (Electrodynamics)
Electrical work is the work done on a charged particle by an electric field. The electrical work per unit of charge, when moving a negligible test charge between two points, is defined as the voltage between those points.

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