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Thermodynamic Geometry

Thermodynamic Geometry. Peter Salamon Udine Advanced School October 2005. Finite Time Thermodynamics. 3 (at least) Big Questions Maximum power Minimum dissipation Thermodynamic waiting time Number of fluctuations 1 (at least) Big Failing No contact with experiment. Min  S u. Max

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Thermodynamic Geometry

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  1. Thermodynamic Geometry Peter Salamon Udine Advanced School October 2005

  2. Finite Time Thermodynamics • 3 (at least) Big Questions • Maximum power • Minimum dissipation • Thermodynamic waiting time • Number of fluctuations • 1 (at least) Big Failing • No contact with experiment

  3. Min Su Max Power Given that something should happen, How much we care about wasting fuel In between lies: Economics, Biology, ??

  4. Economics -- • marginal propensity to consume power. • Industrialist vs. Environmentalist • Should the marginal propensity to consume power be the same across a well equilibrated market? Other input to production

  5. Biology Examples -- • Is there a lion chasing me? • What degree of flagellar stirring should I do to get the most food (O2). Degree of multicellularity as a function of Peclet number. (Ray Goldstein, U. of Ariz.)

  6. Finite Time Thermodynamics • 3 (at least) Big Questions • Maximum power • Minimum dissipation • Thermodynamic waiting time • 1 (at least) Big Failing • No contact with experiment Endoreversible Geometry Untried One sad story in second lecture

  7. Minimum Dissipation • Measured by lost exergy or by entropy produced. • Gouy-Stodola

  8. Basic physical problem: • How much entropy must be produced to bring a system along a given sequence of states? • Example: Heat a cup of coffee.

  9. Coffee Cup Motel

  10. … Tn T0 T1 Entropy production is a small equilibration

  11. Exercise

  12. What does distance measure? • Velocity -- shock tube • dL2 = dissipation in a small equilibration • Fluctuation

  13. "Thermodynamics is the only physical theory of universal content which, within the framework of the applicability of its basic concepts, I am convinced will never be overthrown." — Albert Einstein Thermodynamics is almost mathematics.

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