2nd Week: Properties of Astrophysical Plasmas

Basic Thermodynamics for Quantum Systems

Particle density:

$n={\frac {N}{V}}=\int _{0}^{\infty }{w(p)f(p)dp}$ where $f(p)$ is the occupation probability and $w(p)$ is the state density per unit volume.

Energy Density:

$u={\frac {U}{V}}=\int _{0}^{\infty }{Ew(p)f(p)dp}$ where E in the energy.

Pressure:

$P={\frac {1}{3}}\int _{0}^{\infty }{pvw(p)f(p)dp}$ where $p$ is momentum and $v$ is velocity.