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Entropy

Entropy - previous index next A New Thermodynamic Variable...

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previous index next A New Thermodynamic Variable: Entropy Michael Fowler 7/10/08 Introduction The word entropy is sometimes used in everyday life as a synonym for chaos, for example: the entropy in my room increases as the semeste r goes on. But it’s also been used to describe the approach to an imagined final state of the universe when everything reaches the same temperature: the entropy is supposed to increase to a maximum, then nothing will ever happen again. This was called th e Heat Death of the Universe, and may still be what’s believed, except that now everything will also be flying further and further apart. So what, exactly, is entropy, where did this word come from? In fact, it was coined by Rudolph Clausius in 1865, a few years after he stated the laws of thermodynamics introduced in the last lecture. His aim was to express both laws in a quantitative fashion . Of course, the first law the conservation of total energy including heat energy is easy to express quantitatively: one only needs to find the equivalence factor between heat units and energy units, calories to joules, since all the other types of energy (kinetic, potential, electrical, etc.) are already in joules, add it all up to get the total and that will remain constant. (When Clausius did this work, the unit wasn’t called a Joule, and the different types of energy had other names, but those are merely notational developments.) The second law, that heat only flows from a warmer body to a colder one, does have quantitative consequences: the efficiency of any reversible engine has to equal that of the Carnot cycle, and any nonreversible engine has less efficiency. But how is the “amount of irreversibility” to be measured? Does it correspond to some thermodynamic parameter? The answer turns out to be yes : there is a parameter Clausius labeled entropy that doesn’t change in a reversible process, but always increases in an irreversible one. Heat Changes along Different Paths from a to c are Different! To get a clue about what stays the same in a reversible cycle, let’s review the Carnot cycle once more. We know, of course, one thing that doesn’t change: the internal energy of the gas is the same at the end of the cycle as it was at the beginning, but that’s ju st the first law. Carnot himself thought that something else besides total energy was conserved: the heat, or caloric fluid, as he called it. But we know better: in a Carnot cycle, the heat leaving the gas on the return cycle is less than that entering earlier, by just the amount of work performed. In other words, the total amount of “heat” in the gas is not conserved, so talking about how much heat there is in the gas is meaningless. To make this explicit , instead of cycling, let’s track the gas from o ne point in the ( P , V ) plane to another, and begin by connecting the two points with the first half of a Carnot cycle, from a to c :

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