- #1

girlinphysics

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Given [tex]\frac{dT}{dr}\propto\frac{\kappa\rho{L}}{r^2T^3}[/tex] and [tex]\frac{dL}{dr}\propto{r^2}{\rho}\epsilon[/tex] show that [tex]L\propto {M^{5.4}}[/tex] and [tex]R\propto {M^{0.2}}[/tex] if [tex]\kappa\propto\rho{T^{-3.5}}[/tex] and [tex]\epsilon\propto\rho{T^{5}}[/tex].

Using the equation [tex]\frac{dT}{dr}\propto\frac{\kappa\rho{L}}{r^2T^3}[/tex] and substituting the value for [tex]\kappa[/tex] and also [tex]\rho\propto{\frac{M}{R^3}}[/tex] I got the answer [tex]L\propto {M^{5.5}R^{-0.5}}[/tex]

Then using [tex]\frac{dL}{dr}\propto{r^2}{\rho}\epsilon[/tex] and substituting [tex]\epsilon\propto\rho{T^{5}}[/tex] as well as [tex]\rho\propto{\frac{M}{R^3}}[/tex] and the result from above I got [tex]M^{2.5}\propto{R}[/tex]

Obviously I have done something wrong. I'm a little slow in tex but if you would like my full working in order to help me just let me know.