Question #90278
Estimate the radius of a star in thermal equilibrium of mass 10^30 kg and average internal temperature 10^7 K. It is given that
kB =1.38 x 10^-23 JK^-1, mH - 1.67 x 10^-27 kg and G=6.7 x 10^-11 m³ kg^-1s^-2.
1
Expert's answer
2019-06-04T12:18:47-0400

A cloud wtith radius R, mass M, and temperature T will collapse to form a star if the total energy of the cloud is <0, i.e, if the (absolute value) of the potential energy exceeds the thermal energy of the cloud:



PEgrav=KEcloud(1)PE_{grav}=KE_{cloud} (1)

We can rewriter (1) as


35GM2R=N32kT(2)\frac {3}{5} \frac {GM^2}{R}=N \frac {3}{2} kT (2)

where N is total number of particles in cloud


The total number of particles in cloud is can written as



N=MmH(3)N=\frac {M}{m_H} (3)

Solving for R gives:


R=158πkTGmH2nH(4)R=\sqrt {\frac {15}{8\pi} \frac {kT}{G m_H^2 n_H}} (4)

Using (4) we get:

R=7×108 m


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