MolecularEntropy

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previous index next Entropy and the Kinetic Theory: the Molecular Picture Michael Fowler 7/15/08 Searching for a Molecular Description of Entropy Clausius introduced entropy as a new thermodynamic variable to measure the “degree of irreversibility” of a process. He believed that his two laws of thermodynamics (conservation of energy and that entropy never decreases) were profound and exact scientific truths, on a par with Newton’s laws of dynamics. Clausius had also made contributions to kinetic theory, publishing work as early as 1857, although unlike Maxwell he did not adopt a statistical point of view—he took all the molecules to have the same speed. (Actually, this work inspired Maxwell’s first investigations of kinetic theory and his discovery of the velocity distribution.) Clausius was the first to attempt a semiquantitative analysis of the effects of molecular collisions (see later). Obviously, if the kinetic theory is correct, if heat is motion of molecules, the fundamental laws of thermodynamics must be expressible somehow in terms of these molecular motions. In fact, the first law of thermodynamics is easy to understand in this way: heat is just kinetic energy of molecules, and total energy is always conserved, but now instead of having a separate category for heat energy, we can put the molecular kinetic energy together with macroscopic kinetic energy, it’s all ½ mv 2 with the appropriate masses. ( Note : What about potential energy? For the ideal gas, potential energy terms between molecules are negligible, by definition of ideal gas. Actually, potential energy terms are important for dense gases, and are dominant during phase changes, such as when water boils. The extra energy needed to turn water into steam at the same temperature is called the latent heat . It is simply the energy required to pull the water molecules from each other working against their attraction—in other words, for them to climb the potential energy hill as they move apart. The term “latent heat”— still standard usage— is actually a remnant of the caloric theory: it was thought that this extra heat was caloric fluid that coated the steam molecules to keep them away from each other!) But how do we formulate entropy in terms of this molecular mechanical model? Boltzmann, at age 22, in 1866, wrote an article “On the Mechanical Meaning of the Second Law of Thermodynamics” in which he claimed to do just that, but his proof only really worked for systems that kept returning to the same configuration, severely limiting its relevance to the real world. Nevertheless, being young and self confident, he thought he’d solved the problem. In 1870, Clausius, unaware of Boltzmann’s work, did what amounted to the same thing. They both claimed to have found a function of the molecular parameters that increased or stayed the same with each collision of particles and which could be identified with the macroscopic entropy.
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This note was uploaded on 12/07/2011 for the course PHYSICS 152 taught by Professor Michaelfowler during the Fall '07 term at UVA.

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