Description of the second law of thermodynamics

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The second law of thermodynamics Photograph: Observer

Alok Jha

Sunday 1 December 2013 08.00 GMT

Thermodynamics is the study of heat and energy. At its heart are laws that describe how energy moves around within a system, whether an atom, a hurricane or a black hole. The first law describes how energy cannot be created or destroyed, merely transformed from one kind to another. The second law, however, is probably better known and even more profound because it describes the limits of what the universe can do. This law is about inefficiency, degeneration and decay. It tells us all we do is inherently wasteful and that there are irreversible processes in the universe. It gives us an arrow for time and tells us that our universe has a inescapably bleak, desolate fate.

Despite these somewhat deflating ideas, the ideas of thermodynamics were formulated in a time of great technological optimism – the Industrial Revolution. In the mid-19th century, physicists and engineers were building steam engines to mechanise work and transport and were trying to work out how to make them more powerful and efficient.

Many scientists and engineers – including Rudolf Clausius, James Joule and Lord Kelvin – contributed to the development of thermodynamics, but the father of the discipline was the French physicist Sadi Carnot. In 1824 he published Reflections on the Motive Power of Fire, which laid down the basic principles, gleaned from observations of how energy moved around engines and how wasted heat and useful work were related.

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The second law can be expressed in several ways, the simplest being that heat will naturally flow from a hotter to a colder body. At its heart is a property of thermodynamic systems called entropy – in the equations above it is represented by "S" – in loose terms, a measure of the amount of disorder within a system. This can be represented in many ways, for example in the arrangement of the molecules – water molecules in an ice cube are more ordered than the same molecules after they have been heated into a gas. Whereas the water molecules were in a well-defined lattice in the ice cube, they float unpredictably in the gas. The entropy of the ice cube is, therefore, lower than that of the gas. Similarly, the entropy of a plate is higher when it is in pieces on the floor compared with when it is in one piece in the sink.

A more formal definition for entropy as heat moves around a system is given in the first of the equations. The infinitesimal change in entropy of a system (dS) is calculated by measuring how much heat has entered a closed system (δQ) divided by the common temperature (T) at the point where the heat transfer took place.

The second equation is a way to express the second law of thermodynamics in terms of entropy. The formula says that the entropy of an isolated natural system will always tend to stay the same or increase – in other words, the energy

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