Thermodynamics

Equalibrium

• Properties (measurements) do not change over obeservation time
• e.g.

0th Law

• AB, BC AB
• As the consequence: We can define as Temperature. And is Equation of state

1st Law

1. Adiabatic wall: no heat exchange diathermic wall: can heat exchange isolated system

2. State1State2: "Inner Energy":

   State1State2: "Heat": or

3. Quasi-static process: is the generalize force (Intensive quantity), and is the generalized displacement (Extensive quantity)

4. Heat capacity:

   1. Const. V:
   2. Const. P:

   : Enthalpy

e.g. Ideal Gas: Jouler's Expension:

Heat Engine

2nd Law

1. Kevin: No process is possible whose sole effect is complete conversion of heat to work Clausius: No process is possible whose sole effect is transfer of heat from colder to hotter body
2. Carrot Engine:
   • Cycle, reversible
   • Operates between two heat baths at temperatue and
   • Carrot Thereom: Carrot is the best
3. Clausius Inequality
   • Carrot:
   • Other cycles: (: temperature of heat bath)

Entropy

1. Reversible: potential: entropy Infinitesimal:
2. Inreversible: Infinitesimal:
3. Adiabatic process: ,

   • e.g.1. Jouler's Expension:

   • e.g.2. ![[1.Thermodynamics 2023-10-30 18.35.49.excalidraw]] Consider a const volumn process: >Choose a reversible process to calculate

   • : natural variable S, V.

Systems of variable particles

• Can happen: open system; phase transition
• : Extensivity,
  1. Thermodynamic limit: fixed.
  2. Short-ranged interaction
  3. Consequence of extentivity: : 1st order homogeneous function. : scale factor. Differential and Gibbs-Duhem relation:

Thermodynamic potentials

1. , we are at liberty to choose other variables.
2. Enthalpy:
3. Helmholtz Free Energy:
4. Gibbs Free Energy:
5. Grand potential: (Gibbs-Duhem relation)

Towards Equal

1. fixed,
2. fixed,
3. fixed,

Maxwell's Relation

Relate quantities to experimentally measurable quantities. - e.g. Heat Capacity - Response Function 1. Extensivity: 2. Conpressibility:

Phase Equalibrium

• Partition into uniform subsystem. Maximize , subject to constraint: $$

  $$

• Lagrange Multiphier:

• Stability condition: is maximiazed. e.g.

  Choose as independed variables: :