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## Homework Statement

Answer the following questions. Pleas show all of your work and your line of thinking and state your assumptions.

There are several phases of the ISM. Consider the following three phases with different typical number densities ## n ## and temperatures ## T ##.

- The cold neutral medium (CNM) with ## n \simeq 10 cm^{-3} ## and ##T \simeq 100 K##;
- The warm ionized medium (WIM) with ## n \simeq 0.1 cm^{-3} ## and ##T \simeq 10^4 K##;
- The hot ionized medium (HIM) with ## n \simeq 10^{-3} cm^{-3} ## and ##T \simeq 10^6 K##;

(b) If the gas in a galaxy were equally distributed between the phases so that 1/3 of the mass were in each of the three phases above, what would be the relative volumes filled by the three phases?

(c) For the Milky Way, half of the mass is thought to be in the warm phase, and it also resides in half of the volume of the galaxy. What are the relative volumes and masses of the other two phases?

## Homework Equations

Ideal gas law

##PV = NRT##

##n = \frac{N}{V}##

##V_{total} = V_{CNM} + V_{WIM} + V_{HIM} ##

## The Attempt at a Solution

Part (a) was very simple to do. I found the pressure in each to be ## 8314 \frac{J}{cm^3 \cdot mol} ##. For whatever reason, I cannot figure out part b, and I feel that c will easily follow. I've tried assuming the mass of the Milky Way, dividing it into thirds, and then using the molar mass of each phase of the ISM to find the relative volume of each phase. The problem is, the entire mass of the Milky Way is not in gaseous form for one, and another thing is that the CNM is mostly neutral hydrogen and the WIM is mostly singly ionized hydrogen. I can easily calculate the number of atoms of each necessary to make up their respective 1/3 of the mass of the galaxy, but the rest of the mass coming from the HIM is made up of everything else, so I can't calculate the number of particles in the HIM to find the amount of volume it occupies.