(adsbygoogle = window.adsbygoogle || []).push({}); How big would a spherical cloud of molecular nitrogen at a uniformed pressure of 1 atm (1x10^5 Pascal) and a temperature of 300 K have to be for it to collapse under the mutual gravitational attraction of its molecules? i.e., What is the critical radius for Jean's collapse of a nitrogen cloud initially at this temperature and pressure? Compare your answer with the radius of the Earth and comment. Repeat for a cloud of molecular hydrogen at a pressure of 1 matm and 300 K and compare this with the radius of the Sun.

jean's criterion is

[tex] \frac{GM^2}{R_{C}} \geq \frac{3}{2} NkT [/tex] where N is the number of molecules

[tex] R_{C} \geq \frac{2}{3} \frac{GM^2}{NkT} [/tex]

now over to PV = NkT [/tex]

im assuming this gas will form a sphere... so the volume is 4/3 pi r^3

[tex] \frac{GM^2}{R_{C}} \geq \frac{3}{2}PV = 2 \pi P R_{C}^3 [/tex]

[tex] R_{C}^4 \leq \frac{GM^2}{2 \pi P} [/tex] (1)

the probem is the MAss of this cloud

PV = n RT where n is the number of moles

[tex] PV = \frac{MRT}{M_{m}} [/tex] where Mm is the molar mass

substituting this into 1

[tex]R_{C}^4 \leq \frac{8GM_{m}^2}{9RT} \pi R_{C}^6 [/tex]

so

[tex] R_{C}^2 \leq \frac{9RT}{8GM_{m} \pi} [/tex]

is this fine?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Spherical cloud of molecular nitrogen problem

**Physics Forums | Science Articles, Homework Help, Discussion**