Common 'Energies'

- Internal Energy: U + Q + W

Checks the gain/loss from any change in the system's internal state. - Helmholtz Energy: A = U - TS

Thermodynamic potential, measure of useful work. Obtainable from a closed thermodynamic system at constant T & V. - Gibbs Energy: G = U + PV - TS = A + PV

Thermodynamic potential giving the maximum amount of reversible work doable by a system at constant temperature and pressure.

Strictly speaking, all of these should probably factor in the particle number and chemical potential, .

Ensembles:

- Canonical Ensemble:

T=const, sytem in contact with thermal bath, energy flows between but is in thermal equilibrium; particles are stuck but heat flows.

(138) (139) - Microcanonical Ensemble:

Isolated system - statistical ensemble representing possible states of equal energy, multiplicity

- Grand Canonical Ensemble:

System in contact with a heat bath and particle bath. Particles and energy can be swapped, with an equilibrium T.(140) G. partition function: (141)

Equipartition Theorem

At temperature T, the average energy of a quadratic degree of freedom

At temperature T, the average energy of a quadratic degree of freedom

(142) | |

etc | (143) |

Entropy, Fluctuations, Heat Capacity

(144) | |

(145) | |

(146) | |

(147) | |

(148) | |

(149) | |

(150) |

Blackbody Radiation

(151) | |

(152) | |

From here on, | |

(153) | |

(154) | |

(155) |

With a 2 added somewhere along the way to properly count polarization modes.

Fugacity, q-potential, average particle number:

(156) | |

(157) | |

(158) |