Thermodynamics

Thermodynamics

1. Reversibility

   • No dissipation Quasi-static process (i.e. only equilibrium states)
   • Reversible Work
     • Need infinitely many processes, each resulting in an infinitesimally small work.
   • Reversible heat
     • Need infinitely many reservoirs at infinitesimally different temperature.

2. Engines

   • Convert heat into work
   • Cycles: all state variables restored
     • Brayton Cycle (Jet engine)
   • Two reservoir engines
     • Theoretical concepts with a hot and a cold reservoir.
     • Refrigerator: heat engine run in reverse
       • Heat Q_C comes in from cold reservoir. Work is done on the system. Heat Q_H flows out to hot reservoir.
       • Heat pump: refrigerator used to heat up (same principle as refrigerator)
         • Coefficient of performance: w_P = Q_H/W_F
       • Coefficient of performance: w_F = Q_C/W_F
     • Heat engines
       • Efficiency: eta = W_E/Q_in = 1 - Q_out/Q_in
     • Remember: all efficiency coefficients take form: (what you take out)/(what you put in)

3. 2nd Law

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

4. Entropy

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

5. Classical thermodynamics

   • Operational definitions of observables
   • Clausius' Inequality
   • Fundamental equation of Thermodynamics: dU = TdS - PdV
   • Thermodynamic potentials
     • Use fund. equation to sub U
     • Enthalpy: H = U + PV
       • Can be interpreted as "heat content" of system in  CONSTANT P, REVERSIBLE process.
       • Joule -Thomson process: Isoenthalpic
       • dH > 0: endothermic dH < 0 exothermic
     • Helmoltz Free Energy: F = U - TS
       • -dF = maximum work that can be extracted in isothermal process
       • Useful for link to Statistical Physics
     • Gibbs function: G = U + PV - TS
       • Useful specific Gibbs function: divide by mass M = N*m_p
     • Maxwell's relations
     • Energy equation: apoply when PV is proportional to T as in ideal gases

6. Applications

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

7. 3rd Law: S=0 at T=0 => Impossible to reach T=0 in finite number of steps