Day 1: Review, variables and equations of state

  1. What is thermodynamics?
  2. What are state variables? Class discussion, list examples, write definition, need for experiments and numbers.
  3. Intensive versus extensive. Implies thermodynamic limit. Systems have to be large, but can be measured by outsider. Extensive variables are boundary conditions for solving the Schroedinger equation!
  4. Entropy and temperature. Class: list thermometers. Reference temperatures. Definitions of temperature, entropy. Entropy of the universe?
  5. Thermodynamic processes. Reversible versus steady state.
  6. Equations of state. Examples: ideal gas, Curie law. How to improve? Virial expansion, van der Waals, Curie-Weiss.
Problems in class
  • Diagnostic: df=xy^3dx+3(x^2/2+5)y^2 dy, find f(x,y).
  • vanderWaals: calculate difference in work done at constant T between ideal and vdW gas from infinity to V. Which problems do you have to deal with? Large V limit, smaller V for low T, what does it mean?
  • Non-linear P vs E. How to write? Meaning of terms? Isotropic material?
  • Bulk modulus, B = - V (dp/dV)|T,N. Solids: (dB/dp)|T,N independent of p. What is the equation of state? Murnaghan.

Many basic words were recognized, so this was basically a review to get thoughts organized. In the in class problem the integral ∫dV/V occured, with limit infinity, and everybody kind of ignored that problem.

Day 2 Review, work, heat, and energy

  1. Discuss diagnostic 1. Use path method or Corinne method. Do not double count.
  2. First law. Heat is a transfer of energy.
  3. Heat and work. Relation to state variables. Reversible versus irreversible. What is irreversible?
  4. Exact differentials. State functions. Test for exactness.
  5. Cycles: Carnot. In pV and TS.
Problems in class
  • Diagnostic: dx/dy|z=3yx, dx/dz|y=3/2y^2+sin(z), find dz/dy|x.
  • Finish pdV from last time (handout). Large V expansion?
  • Carnot engine for ideal gas: pV=NRT, U=3/2NRT. Find W,Q.
  • Stirling engine (handout).
  • Steam engine, Rankin (handout).

Next time review more about heat engines and cycles.

Day 3 Review, response functions

  1. Discussion of diagnostic 2. Notation dx/dy|z. Chain and inverse rule.
  2. Review: state variables, equations of state, first law.
  3. Functions of many variables.
  4. Change of variables.
  5. Measurements relate small changes.
  6. Standard examples of response functions, standard pVTSμN system.
  7. Chain rules.
  8. Maxwell relations and first law.
  9. Not all response functions are independent: Cp/CV=KT/KS.
Problems in class
  • Diagnostic: what is a Lagrange multiplier?
  • Relate CV and Cp.
  • Find dS/dp|VN in terms of adiabatic thermal expansion. Implications?
  • How to generate others: dS =dU/T +pdV/T-μdN/T

Note that Wassermans's book defines kappa as inverse compressibilities, the same as wikipedia, but different from most text books.Class knew the basic ideas behind Maxwell, but review was useful. Connecting the partials to measurements is not obvious to them. Relating partial derivatives like Cp and CV is not obvious, and my first explanation in terms of fuctions f(T,V,N) and g(T,p,N) was very confusing.

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