• Pranav Nandurkar

Do you know: Some theories which changed the world

Logarithm functions :

Logarithms were introduced by John Napier in 1614 as a means to simplify calculations. In mathematics, Logarithm is termed as an inverse of an exponential function. The logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x. In simple language, the logarithm counts the number of occurrences of the same factor in repeated manner. More generally, exponentiation allows any positive real number as a base to be raised to any real power, always producing a positive result, so logb(x) for any two positive real numbers b and x, where b is not equal to 1, is always a unique real number y. The 2 most common bases that we use are base 10 and base e, which are often termed as Logs to base 10 and Natural log with base e.

The logarithmic function has many real-life applications, in acoustics, electronics, earthquake analysis and population prediction.

Second Law of Thermodynamics : The second law may be expressed in many ways, some of the prominent statements are given by Rudolf Clausius, Lord Kelvin and Constantin Carathéodory.

Various statements of the second law are:

Clausius statement - By examining the relation between heat transfer and work, the German scientist Rudolf Clausius laid the foundation for the second law of thermodynamics in 1850. But the Clausius statement was published in German in 1854. Clausius stated the second law as follows : "Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time."

Planck's statement - Planck stated the second law as follows: "Every process occurring in nature proceeds in the sense in which the sum of the entropies of all bodies taking part in the process is increased. In the limit, i.e. for reversible processes, the sum of the entropies remains unchanged."

Kelvin statement - Wordings of Lord Kelvin are : "It is impossible for a self-acting machine,  unaided by any external agency, to convey heat from one body to another at a higher temperature." "It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects."

Newton's Law of Universal gravitation : Newton's law of universal gravitation is stated as every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. This law was formulated by Newton in his work Philosophiæ Naturalis Principia Mathematica on 5 July 1687. In modern times it can be stated as every point mass attracts every single other point mass by a force acting along the line intersecting both points.

where: -F is the force between the masses; -G is the gravitational constant; -m1 is the first mass; -m2 is the second mass; -r is the distance between the centres of the masses.

Einstein's theory of relativity: The theory of relativity is based on two interrelated theories of Einstein First- special relativity Second- General relativity It introduced concepts including spacetime as a unified entity of space and time, relativity of simultaneity, kinematic and gravitational time dilation, and length contraction. Special Relativity - Special relativity applies to all physical phenomena in the absence of gravity. It is based on two postulates : 1-The laws of physics are the same for all observers in any inertial frame of reference relative to one another. 2-The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the light source. General Relativity - General relativity explains the law of gravitation and its relation to other forces of nature. Its development began with the equivalence principle, under which the states of accelerated motion and being at rest in a gravitational field are physically identical. It has many consequences.

Moreover, the theory has many surprising and counterintuitive consequences.

Maxwell's Equations : Maxwell's equations are a set of partial differential equations. Maxwell's equations and Lorentz force law together led the foundation of classical optics, electric circuits, and classical electromagnetism. Set of partial differential equations are-

-Gauss's  law : The electric flux across a closed surface is proportional to the charge enclosed.

-Gauss's law for magnetism :

The magnetic flux across a closed surface is zero.

-Faraday's law:

Time-varying magnetic fields produce an electric field.

-Amperes law:

Steady currents and time-varying electric field produce a magnetic field.