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by dropping it (known as gravitational potential energy), so a hot thing has energy that can be released, at least in part, by putting it next to a cold thing. To heat something up, you simply have to transfer energy to it by doing work on it, as Joule found by using a falling weight, and it doesn’t matter how that work is done. It can be a falling weight, a shining light or an electric current, but as long as you do the same amount of work, the temperature increase will be the same. This was all quantified, as a result of Joule’s work, into the First Law of Thermodynamics, which is a statement of the fact that energy cannot be created or destroyed; it can only be changed from one form into another. Rudolf Clausius made the first explicit statement of the law, and laid down the foundations of the science of thermodynamics, in his landmark 1850 publication ‘On the mechanical theory of heat’.

Newcomen’s engine, created in 1712, was the first commercially successful steam engine and laid the foundations for the work of other inventors, such as James Watt, which would power forward the industrial revolution in Britain. the Newcomen atmospheric engine was used to pump water out of coal mines, using a pivoted arm (top) to transfer power between the piston and the rod. the piston was driven down by the pressure of a partial vacuum in the cylinder, which drew the rod upwards. as steam in the cylinder condensed, the piston was forced up, and the rod down.

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The first law can be written down mathematically as

which in words says that the increase in the internal energy of something (ΔU) is equal to the heat flow into it (Q) minus the work performed by it (W). If you performed work on it, the W would have a plus sign, and if you took heat out of it, the Q would have a minus sign.

Fifteen years after writing down the first law of thermodynamics, and far more importantly for our understanding of the arrow of time, Clausius introduced a new concept known as entropy, which lies at the heart of the Second Law of Thermodynamics. Clausius’s statement of the second law does not at first sight sound as if it has profound implications for the future of our universe. He simply stated that ‘No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature’. This simple proposition occupies such a profound position in modern science that Arthur Eddington said of the second law:

‘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.’

The concept of entropy enters when the second law is written down in quantitative form. The change in entropy of a system, such as a tank of water, is simply the amount of heat added to it at a fixed temperature. In symbols,

where ΔS is the change in the entropy as a result of adding a small amount of heat, ΔQ, at a fixed temperature T. It may still be unclear what this has to do with the Universe, but here is the profound point discovered by Clausius. In any physical process at all, you find that entropy either stays the same or increases. It never decreases. Here is the thermodynamic arrow of time. Clausius had discovered a physical quantity that can be measured and quantified which only ever increases in practice, and never decreases even in theory, no matter how cleverly you design your experiment or piece of machinery. This is extremely useful information if you are designing a steam engine, because it puts a fundamental limit on the efficiency. It also prevents the construction of the so-called ‘perpetual motion machines’ so beloved of crackpot inventors to this day. You could say