Thermodynamics and Statistical Mechanics: Intermediate Flashcards
How to count degrees of freedom
The number of degrees of freedom is the number of quadratic terms in the hamiltonian
n choose m definition
Stirling’s formula for asymptotic values of ln(n!)
Work done by a reversible process
Entropy change for a reversible process
Isentropic processes
An isentropic process is one with no net change in entropy. It is equivalent to a process which is reversible and adiabatic. An example is compressing a gas in a cylinder.
Free expansion
When a gas suddenly expands from a smaller region to a larger region. The temperature of an ideal gas does not change during free expansion.
Fundamental thermodynamic identity
Definition of temperature
Relation between derivatives of P and T
Definition of heat capacity at constant X (X = V or P)
Formula used for calculation of heat capacity at constant volume
Relation between ideal gas heat capacities
Specific heat (c)
Maximum efficiency for a heat engine
Work done on a PV diagram
In a PV diagram, the work done is just the area of the interior of the shape.
Fermi-Dirac distribution
Bose-Einstein distribution
What is the mu in the Fermi-Dirac and Bose-Eintsein formulas?
It is the chemical potential, which is, roughly speaking, the energy associated with adding or removing a particle from the system.
Grand canonical ensemble
Like the canonical ensemble, but instead of fixing the number particles, you fix the chemical potential.
Degeneracy factors in quantum statistical mechanics
For discrete states, we have g(Ei), which gives the number of states with the ith energy. If the energy levels are roungly continuous, we instead use the density of states.
Number of particles total in the discrete energy case
Number of particles total in the continuous energy case
Heat capacity of an ideal relativistic gas
Debye law (for low temperatures)
Heat flow law
