Thermodynamics

Annotations:

• No dissipation Quasi-static process (i.e. only equilibrium states)

1. Reversible Work

   Annotations:

   • Need infinitely many processes, each resulting in an infinitesimally small work.
2. Reversible heat

   Annotations:

   • Need infinitely many reservoirs at infinitesimally different temperature.

Annotations:

• Convert heat into work

1. Cycles: all state variables restored
   1. Brayton Cycle (Jet engine)
2. Two reservoir engines

   Annotations:

   • Theoretical concepts with a hot and a cold reservoir.
   1. Refrigerator: heat engine run in reverse

      Annotations:

      • Heat Q_C comes in from cold reservoir. Work is done on the system. Heat Q_H flows out to hot reservoir.
      1. Heat pump: refrigerator used to heat up (same principle as refrigerator)
         1. Coefficient of performance: w_P = Q_H/W_F
      2. Coefficient of performance: w_F = Q_C/W_F
   2. Heat engines
      1. Efficiency: eta = W_E/Q_in = 1 - Q_out/Q_in
   3. Remember: all efficiency coefficients take form: (what you take out)/(what you put in)

Annotations:

• Kelvin, Clausius and Mathematical statements.

1. Thermodynamic trick for irreversible processes

   Annotations:

   • Choose reversible process between same state variables and calculate change in entropy along that.
   1. e.g. Isothermal reversible expansion VS Adiabatic free expansion
2. Carnot cycle
   1. Carnot's Theorem
      1. Part 1: no machine can be more efficient than Carnot's machine
      2. Part 2: every Carnot engine operating bw same T's has the same efficiency eta = 1 - T_C/T_H
      3. Can define absolute thermodynamic temperature

1. Can use heat flow in the reservoir for thermodynamic trick
2. Entropy of the unverse
   1. Increases in irreversible processes
      1. Energy is degraded in irreversible processes
         1. Entropy defines the arrow of time
         2. Equilibrium is a state of maximum entropy
         3. Exergy/Availability always decreases
   2. Stays constant in reversible processes

1. Operational definitions of observables
2. Clausius' Inequality
3. Fundamental equation of Thermodynamics: dU = TdS - PdV
4. Thermodynamic potentials

   Annotations:

   • Use fund. equation to sub U
   1. Enthalpy: H = U + PV

      Annotations:

      • Can be interpreted as "heat content" of system in  CONSTANT P, REVERSIBLE process.
      1. Joule -Thomson process: Isoenthalpic
      2. dH > 0: endothermic dH < 0 exothermic
   2. Helmoltz Free Energy: F = U - TS
      1. -dF = maximum work that can be extracted in isothermal process
      2. Useful for link to Statistical Physics
   3. Gibbs function: G = U + PV - TS
      1. Useful specific Gibbs function: divide by mass M = N*m_p
   4. Maxwell's relations
   5. Energy equation: apoply when PV is proportional to T as in ideal gases

1. Phase changes
   1. Clausius-Clapeyron equation
   2. Order of phase transition given by first discontinuous derivative of g w.r. to T or P
2. Photon gas
3. Surface tension