ReferenceA Logical Approach to Theoretical Physics

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PHYSICS (General)

Matter is any substance that has mass and takes up space by having volume. Physics has no definition for “substance”. It simply defines certain physical properties mathematically.

An extremely small particle of matter.

All objects are persisting on their own; nothing else is making them persist. ENERGY, therefore, is the impulse innate to the object, which makes it persist. That persistence expresses itself further as motion and/or tension. This was Faraday’s view. Maxwell saw ENERGY as “the power a thing has of doing work arising either from its own motion or from the tension subsisting between it and other things.” Unlike Faraday, Maxwell did not relate it to something innate. Therefore, in physics, neither motion nor tension has innate origins.

Mass is condensed energy. (Also see under Newton’s Mechanics).

We perceive objects and their substance by how they impact our senses. This impact is always in the form of FORCE. Therefore, we may consider FORCE to be synonymous with substance. This was Faraday’s view. Maxwell, however, saw force only as “the tendency of a body to pass from one place to another,” which depends upon “the amount of change of tension which that passage would produce.” Thus, he saw force as change in energy over distance. Here distance is not defined but considered subjectively only. Unlike Faraday, Maxwell did not relate force directly to the nature of substance.

Faraday conceived lines of force as the force extending between atoms that forms the fabric of space between them. These lines of force carry the vibrations of the radiative phenomena. Maxwell and other physicists postulated space consisting of mysterious aether instead.

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.

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. 



Mass is both a property of a physical body and a measure of its resistance to change in its state of motion when a net force is applied. An object’s mass also determines the strength of its gravitational attraction to other bodies.

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. 

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.

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

Change in momentum over time.

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

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. 



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

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

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.

The Boltzmann constant (kB 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.

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. 

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.

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.  

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.


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.


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.


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?


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.

The mass number is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It is approximately equal to the atomic mass of the atom expressed in atomic mass units. 

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).

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. 

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.

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).

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

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.

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. 



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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