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I have an exam tomorrow on the evolution of stars. Revision is going OK, but I've come across this equation. Some quick help would be very appreciated!!

P = αT^{4}

I'll give you some context:

I'm solving a question that states a star in Virial equilibrium is contracting quasi-statically (slowly). What effect would this have on the temperature of a very large star. (can assume gas pressure is a negligible fraction of the total pressure and temperature is uniform).

I've started the question with:

Ω = -3 ∫ P/ρ dm

Cancelled density ρ, by subbing dm = 4πr^{2}ρ

Then the solution I have shows a substitution for pressure P as above:

P = αT^{4}

Using this we can solve the problem by showing temperature T ∝ 1/R

I'm sure the equation is a correct one. I was just wondering if anyone knew a little more on it? When can/can't I use this substitution.

Thanks

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# Quick help with equation P = a * T^4

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