Question 35.1: What is the Jeans density of a cloud composed of hydrogen at......

Concepts in Thermal Physics [1054960]

What is the Jeans density of a cloud composed of hydrogen atoms and with total mass $M_{\odot}$ at 10 K?

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Using eqn 35.10,

$ρ_{J} = \frac{3}{4πM^{2} } \left[\frac{3k_{B} T }{2Gm} \right]^{3},$ (35.10)

$ρ_{J} = \frac{3}{4πM^{2}_{\odot } }\left[ \frac{3k_{B} \times 10 }{2Gm_{H} }\right]^{3} \approx 5\times 10^{-17} kg m^{−3} ,$ (35.11)

which corresponds to about $3\times 10^{10}$ particles per cubic metre.

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