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Natural Science - Year II

Unit 48: Helmholtz and Entropy

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History Weblecture for Unit 48


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History Lecture for Unit 48: Helmholtz and Entropy

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The Nature of Energy II

Helmholtz: the conservation of "force"

Hermann von Helmholtz was a German physician who worked not on engines, but on the muscle actions of animals. He recognized that the quantity of what he called force (which we now identify as "energy") was conserved in animal actions: that the energy of motion an animal can sustain is limited by the energy available in its food. He expanded his researches to determine the energy equivalence of different substances, and the energy consumption of many processes, even calculating the energy available to the sun, and its approximate lifetime, which he figured at 25 million years (modern estimates based on the principles of nuclear reactions put the sun's probably remaining lifetime at around 5 billion years). Helmholtz' work is important because it was the first mathematical statement of the conservation of energy in general terms.

Read Helmholtz's Lecture given at Karlsruhe in 1862-1863 On the Conservation of Force. You may read the entire article if you wish, for our purposes, you need only read through section 26, before figure 92.

  • What does Helmholtz mean by natural phenomena and mental phenomena? What is the key difference he sees between them?
  • What does Helmholtz mean by the "quantity of force"? Do we use the term "force" in modern science the same way?
  • Helmholtz compares the operation of machines to the activities of the human body. Why do you think she makes this analogy?
  • What does Helmholtz mean by the "amount of work" it takes to perform a task?
  • in the example of the grandfather clock, Helmholtz says the raised weight possessors in "moving force". What would we call this today?
  • How does Helmholtz explain the apparent discrepancy between the amount of "quantity of force" required to raise a weight using a single pulley and that required to raise the same weight using four connected pulleys?

William Thomson

The son of a Glasgow mathematics professor, William Thomson (later Lord Kelvin) was something of a prodigal, entering the University of Glasgow at 11 and becoming a professor at 19 after finishing his education at the University of Paris. He was fascinated by the work of Carnot, Clapeyron, Joule, and Helmholtz, and he realized that both conservation of energy and dissipation of energy were necessary to explain how engines operate.

Read about William Thomson, Lord Kelvin at St. Andrews' Mathematics site.

  • What is the Joule-Thomson effect?
  • Why didn't Thomson accept Maxwell's explanation of electromagnetic theory?

In particular, Thomson was able to show that dissipation of energy continues, and that useful energy, energy we can direct and use to do mechanical work, decreases over time. In effect, this dissipation gives time a direction: it becomes "time's arrow".

Thompson was able to theorize from Carnot's "ideal" engine that a perfect engine would work if the temperature of the heat sink could drop to -273.15 °C. This temperature is the lowest possible temperature at which matter can exist. We know call it "absolute zero". In modern chemistry and physics, temperatures are often measured from this point in "Kelvin" (not degrees). A temperature of 273.15K corresponds to a temperature of 0 °C. A change of 1K in temperature is the same amount of change as 1 °C; we just count from a different zero point. Negative Kelvin temperatures are not possible.

Ludwig Boltzmann and Entropy

The final piece of the thermodynamics puzzle was put in place by the Scottish physicist James Clerk Maxwell and Ludwig Boltzmann. Maxwell (whom we'll meet again when we discuss the nature of electromagnetic radiation) developed a theory of probability and showed that the absolute temperature (temperature calculated from absolute zero) of a sample substance depends on the average kinetic energy of the molecules in the substance. In other words, temperature is not a measure of the total amount of heat in something, but of the average amount of energy of motion of the molecules.

Maxwell also pointed out that increasing entropy is not necessarily an absolute law. He postulated a situation in which two gasses are kept at different temperatures and separated by a controlled gate. If the gate operator (later known as Maxwell's demon) only lets the fastest molecules of the cold gas escape into the hotter gas, entropy will decrease.

In Austria, Ludwig Boltzmann took this idea further, and demonstrated that entropy is really a tendency for the universe to move toward more disordered states, but not an absolute law. In situations where energy is available from an outside source, a system can actually reverse entropy by creating greater order over time. This is indeed the case with living organisms, which rearrange simple molecules into complex organic systems, using excess energy from the sun.

The net result of thermodynamics was a challenge to the materialist, determinist concept of the universe based on Newtonian mechanics. No longer could physicists maintain that one could predict the future of a system by extrapolation from its present state: thermodynamics assumed that nature might chose one of several possible states.

Read about Ludwig Boltzmann at St. Andrews' Mathematics site.

  • What is statistical mechanics?
  • Why were Boltzmann's conclusions controversial?

Study/Discussion Questions:

Further Study/On Your Own