# Second law of thermodynamics

The second law of thermodynamics states that whenever energy is transformed from one form to another form, entropy increases and energy decreases. In other words: over time, differences in temperature, pressure, and density tend to even out in a horizontal plane, but not in a vertical plane due to the force of gravity. For example, density and pressure do not even out in a vertical plane, and nor does temperature because gravity acts on individual molecules, and this means molecular kinetic energy interchanges with gravitational potential energy in free path motion between collisions.

Entropy is a measure of progression towards the state of thermodynamic equilibrium which has the greatest entropy among the states accessible by the system. In a vertical plane in a gravitational field, thermodynamic equilibrium exhibits a non-zero gradient in pressure, density and temperature, each being less at the top of a planet's troposphere.

The most common wording for the second law of thermodynamics is essentially due to Rudolf Clausius:

 “ The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. ”

In layman's terms: everything tries to maintain the same temperature over time.

There are many statements of the second law which use different terms, but are all equal. Another statement by Clausius is:

Heat cannot of itself pass from a colder to a hotter body.

This, however, is strictly only correct in a horizontal plane where the state of thermodynamic equilibrium has uniform temperature. When that state exhibits a thermal gradient in a vertical plane, then temperature inversions can occur in which the upper, cooler region is warmer than normal, even though cooler than lower regions. In such instances there can be heat transfers from cooler to warmer regions because such transfers are increasing entropy and restoring thermodynamic equilibrium. This is how energy absorbed in the cooler Venus troposphere is transferred into (and warms) the surface.

An equivalent statement by Lord Kelvin is:

A transformation whose only final result is to convert heat, extracted from a source at constant temperature, into work, is impossible.

The second law is only applicable to macroscopic systems. The second law is actually a statement about the probable behavior of an isolated system. As larger and larger systems are considered, the probability of the second law being practically true becomes more and more certain. For any isolated system with a mass of more than a few picograms, the second law is true to within a few parts in a million.[1]

A simple stylized diagram of a heat pump's vapor-compression refrigeration cycle: 1) condenser, 2) expansion valve, 3) evaporator, 4) compressor.

## Overview

In a general sense, the second law says that temperature differences between systems in contact with each other tend to even out and that work can be obtained from these non-equilibrium differences, but that loss of thermal energy occurs, when work is done and entropy increases.[2] Pressure, density and temperature differences in an isolated system, all tend to equalize (in a horizontal plane) if given the opportunity. A heat engine is a mechanical device that provides useful work from the difference in temperature of two bodies.

## Quotes

 “ The law that entropy always increases, holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations — then so much the worse for Maxwell's equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. ”
--Sir Arthur Stanley Eddington, The Nature of the Physical World (1927)
 “ The tendency for entropy to increase in isolated systems is expressed in the second law of thermodynamics -- perhaps the most pessimistic and amoral formulation in all human thought. ”
--Greg Hill and Kerry Thornley, Principia Discordia (1965)
 “ There are almost as many formulations of the second law as there have been discussions of it. ”
--Philosopher / Physicist P.W. Bridgman, (1941)

## Miscellany

• Flanders and Swann produced a setting of a statement of the Second Law of Thermodynamics to music, called "First and Second Law".
• The economist Nicholas Georgescu-Roegen showed the significance of the Entropy Law in the field of economics (see his work The Entropy Law and the Economic Process (1971), Harvard University Press).

## References

1. Landau, L.D.; Lifshitz, E.M. (1996). Statistical Physics Part 1. Butterworth Heinemann. .
2. Mendoza, E. (1988). Reflections on the Motive Power of Fire – and other Papers on the Second Law of Thermodynamics by E. Clapeyron and R. Clausius. New York: Dover Publications. .
• Fermi, Enrico (1956) [1936]. Thermodynamics. New York: Dover Publications, Inc.
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