Thermal energy density of the milky way

[acdurbin953]

Homework Statement

Interstellar medium is composed of atomic hydrogen at 100 K and number density 2E-7 m^-3. Compute the average thermal energy density of the milky way disk. Then find the average magnetic energy density given the magnetic field strength of 3E-10 T.

Homework Equations

E=3/2 kT, maybe? Trying to recall some stuff from thermal physics.

The Attempt at a Solution

Embarrassingly, I had no idea where to begin with this problem, and have no idea if I'm on the right track.
So far I have solved for E, and was going to multiply my value by the number density to find the thermal energy density. There's nothing in our book or notes about how to solve a problem like this (no idea why), so I feel totally lost.
I have no idea how to solve fore the magnetic energy density. Any hints about where to start would be very, very helpful.

 

[TSny]

Your method of finding the thermal energy density looks good.

Did you try a web search for magnetic field energy density?

 

[acdurbin953]

I did, and found magnetic field energy density is B²/8π? Never seen that one before, but is that correct for this situation?

 

[TSny]

You want the version of this equation for the SI system of units (or, MKS system).

http://scienceworld.wolfram.com/physics/MagneticFieldEnergyDensity.html