Exam Information

Topics for Exam 1

Definition of terms: First law, isothermal, adiabatic, open and closed systems, homogeneous, heterogeneous, etc.

Calculation of virial coefficients from the equation of state.

Application of the gas laws (ideal and van der Waals) to estimate pressures.

Determination of heat, work, Delta H, Delta U, T_{final}/T_{initial}, P_{final}/P_{initial} for various processes (see homework) such as isothermal, adiabatic, constant pressure expansions of ideal gases.

Derivations. Techniques so far are limited to the cyclic rule and to the substitution and simplification of existing formulas.

Topics for Exam 2

Big picture things: Meaning of G(T,P) and A(T,V). Statement of the 1st, 2nd and 3rd laws of Thermodynamics.

Calculation of Delta U, Delta H, Delta S and Delta G for isothermal, adiabatic, isobaric processes for the system and the environment.

Proofs of thermodynamic identities (40 pts, four proofs)

Derivation of properties given G(T,P) or A(T,V) or H(S,P) or U(S,V). If H(S,P) was known, what properties could be derived from it?

Topics for the final exam

Statement of the four laws of thermodynamics (using equations with definitions of each term in the equation). Meaning of the functions each law introduces. Meaning of U (kinetic and potential energy), H (related to heats in constant pressure transformations), A (relevant to processes at constant T and V), G (relevant to processes at constant T and P, i.e., earth).
Why and when do G(T,P) and A(T,V) determine the position of equilibrium?
Once equilibrium is achieved,
- T and P are uniform in all phases, and the chemical potential of each species is the same in each phase. Different molecules will have different chemical potentials however.
Virial expansions and power series: systematic deviations from ideal behavior.
Why state functions were introduced. Because of the odd way the 1'st law introduced energy conservation, i.e., through q and w, both highly path dependent.
Expansion and compression of ideal gases and the calculation of thermodynamic properties. Compare isothermal vs. adiabatic vs. constant pressure processes. Which expansion leaves the gas cooler and why. Calculation of properties around a thermodynamic cycle.
Derivation of the equations for dH, dA, dG from the combined 1'st and 2'nd laws as given by dU
- dU = TdS - PdV + mu dn
  and the related equations for d(H/P), d(G/T), d(A/V), d(U/V), etc.
When is TdS = dq_{by}; when is PdV = dw_{by} . Difference between reversible and irreversible quantities.
Results that come from the derivatives:
- Delta A = - P Delta V (at fixed T); Delta G = V Delta P at fixed T, etc.
  so that one can determine changes in the state functions from the finite differences in system properties.
Units of energies, entropies, heat capacities, etc.

Phase transitions and phase diagrams:

1. The difference between 1'st and 2'nd order phase transitions, examples, and the properties that change at the transition.

2. How to read a phase diagram (gas-liquid, liquid mixtures, liquid-solid) and the application of the phase rule (F = 2+c-p).

3. Variation of chemical potential with T and P and its relationship to the colligative properties.

4. Henry's and Raoult's laws for vapor pressures.

5. Chemical equilibrium: variation of K_eq with T, and G with mole fraction.

6. Regular solutions as a way to introduce non-ideality and phase separation into the analysis of liquid mixtures.

7. Pressure-composition and temperature-composition phase diagrams for liquid mixtures.

Answer Keys for Past Examinations

Exam 1	Exam 2	Final

2009	2009	2009
2010	2010	2010
2011	2011	2011