How to convert cc to bar?

Question

In astronomy/astrophysics, medium density is often given in cc, particles per cubic centimeter. Also, the temperature of the medium is usually given, in Kelvins.

For some materials the melting point differs significantly even at very low pressures; water melts at $10\mu{bar}$ in about 230K while at $1\mu{bar}$ its melting point is close to 1K. And the pressure is given in common pressure units - bar, Pascals etc.

So, if I want to know the melting points of various materials in space (and various areas of it), using common phase-temperature-presure diagrams (possibly extrapolating a little), I need to find the 'ambient pressure' of the inter[planetary|stellar|galactic] medium in units the graph is in, usually bar.

How can I calculate the gas pressure given particles per cubic centimeter, and its temperature in Kelvin?

Answer 1

How can I calculate the gas pressure given particles per cubic centimeter, and its temperature in Kelvin?

as pointed out in comment by KyleKanos

$$pV=Nk_\mathrm BT$$

where $p$ is pressure, $V$ is volume (in $\mathrm{m^3}$), $N$ is the number of particles, $k_\mathrm B$ is Botzmann's constant and $T$ is temperature in Kelvin.

If you rearrange it

$$p= \frac NVk_\mathrm BT$$

so you can use this to convert to particles per volume to pressure, but note that volume units in the equation are $\mathrm{m^3}$ so you need to convert from $\mathrm{cm^3}$ (multiply by $10^6$).