(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?

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# Homework Help: Spherical cloud of molecular nitrogen problem

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