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Thermodynamics

1 Reversibility

Annotations:

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

1.1 Reversible Work

Annotations:

- Need infinitely many processes, each resulting in an infinitesimally small work.

1.2 Reversible heat

Annotations:

- Need infinitely many reservoirs at infinitesimally different temperature.

2 Engines

Annotations:

- Convert heat into work

2.1 Cycles: all state variables restored

2.1.1 Brayton Cycle (Jet engine)

2.2 Two reservoir engines

Annotations:

- Theoretical concepts with a hot and a cold reservoir.

2.2.1 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.

2.2.1.1 Heat pump: refrigerator used to heat
up (same principle as refrigerator)

2.2.1.1.1 Coefficient of performance: w_P = Q_H/W_F

2.2.1.2 Coefficient of performance: w_F = Q_C/W_F

2.2.2 Heat engines

2.2.2.1 Efficiency: eta = W_E/Q_in = 1 - Q_out/Q_in

2.2.3 Remember: all efficiency coefficients take
form: (what you take out)/(what you put in)

3 2nd Law

Annotations:

- Kelvin, Clausius and Mathematical statements.

3.1 Thermodynamic trick for irreversible processes

Annotations:

- Choose reversible process between same state variables and calculate change in entropy along that.

3.1.1 e.g. Isothermal reversible expansion
VS Adiabatic free expansion

3.2 Carnot cycle

3.2.1 Carnot's Theorem

3.2.1.1 Part 1: no machine can be more
efficient than Carnot's machine

3.2.1.2 Part 2: every Carnot engine operating bw same T's
has the same efficiency eta = 1 - T_C/T_H

3.2.1.3 Can define absolute
thermodynamic temperature

4 Entropy

4.1 Can use heat flow in the reservoir
for thermodynamic trick

4.2 Entropy of the unverse

4.2.1 Increases in irreversible processes

4.2.1.1 Energy is degraded in
irreversible processes

4.2.1.1.1 Entropy defines the arrow of time

4.2.1.1.2 Equilibrium is a state of maximum entropy

4.2.1.1.3 Exergy/Availability always decreases

4.2.2 Stays constant in reversible processes

5 Classical thermodynamics

5.1 Operational definitions of observables

5.2 Clausius' Inequality

5.3 Fundamental equation of
Thermodynamics: dU = TdS - PdV

5.4 Thermodynamic potentials

Annotations:

- Use fund. equation to sub U

5.4.1 Enthalpy: H = U + PV

Annotations:

- Can be interpreted as "heat content" of system in CONSTANT P, REVERSIBLE process.

5.4.1.1 Joule -Thomson process: Isoenthalpic

5.4.1.2 dH > 0: endothermic
dH < 0 exothermic

5.4.2 Helmoltz Free Energy: F = U - TS

5.4.2.1 -dF = maximum work that can be
extracted in isothermal process

5.4.2.2 Useful for link to Statistical Physics

5.4.3 Gibbs function: G = U + PV - TS

5.4.3.1 Useful specific Gibbs function:
divide by mass M = N*m_p

5.4.4 Maxwell's relations

5.4.5 Energy equation: apoply when PV is
proportional to T as in ideal gases

6 Applications

6.1 Phase changes

6.1.1 Clausius-Clapeyron equation

6.1.2 Order of phase transition given by first
discontinuous derivative of g w.r. to T or P

6.2 Photon gas

6.3 Surface tension

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

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