2nd Week: Properties of Astrophysical Plasmas

[[Image:Main tycho remnant full.jpg|right|right|thumb|300px|The remnant of "Tycho's Supernova Plasma is a state of matter in which the atoms and molecules are so hot, that they have ionized into negatively charged electrons and positively charged ions. The plasma found in the universe, whose physical properties are studied in astrophysics is known as astrophysical plasma. To study the properties of astrophysical plasma the equation of state of matter is very important. Here, we will bring some basic tools from thermodynamics and derive the equation of state for non-relativistic and relativistic plasma.

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.