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lquinnl
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Homework Statement
The monochromatic flux emitted from unit surface area of a black body is given by
[tex] F_{\lambda}(T) = \frac{2h\pi c^{2}}{\lambda^{5}} \frac{1}{exp(hc/\lambda KT)-1} Wm^{-2}m^{-1} [/tex]
If the distance to star X is 620 parsecs, calculate:
(a) the radius of star X, in Solar radii; [3]
(b) the bolometric luminosity of star X, in units of Solar luminosity. [1]
Homework Equations
OK so I know if we integrate the given equation between 0 and infintiy we get the bolometric flux for F(T). When we perform this integration we end up with the stefan Boltzmann equation:
[tex]F(T) = \sigma T^{4} Wm^{-2}[/tex]
this enables me to calulate the bolometric surface flux, great.
Now i want the radius of star X. I am aware that
[tex]F^{bol} = (\frac{R}{d})^{2}\sigma T^{4}[/tex]
where R is the stellar radius and d the distance to the star.
My problem comes here. I can't calculate the flux from the stefan Boltzmann equation and use it in this last equation because I will always have the distance to the star equal to the radius, which cannot be correct.
Any help would be greatly appreciated