Question

the radiation emitted by a star A per second is 10000 times than that of the sun. if the surface temperature of the sun and the star A are 6000K and 2000K respectively the ratio of the radii of the star A and the sun is

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{According}\mathrm{to}\mathrm{stefan}\text{'}\mathrm{s}\mathrm{law},\mathrm{Q}=\mathrm{\sigma eAT}\left({\mathrm{T}}_{\mathrm{A}}^4-{\mathrm{T}}_{\mathrm{S}}^4\right)......\left(1\right) \\ \mathrm{But}\frac{{\mathrm{Q}}_{\mathrm{A}}}{{\mathrm{Q}}_{\mathrm{S}}}=10000 \\ \frac{{\mathrm{Q}}_{\mathrm{A}}}{{\mathrm{Q}}_{\mathrm{S}}}=\frac{\left({\mathrm{\sigma T}}_{\mathrm{A}}^4\right)\left(4{\mathrm{\pi r}}_{\mathrm{A}}^2\right)}{\left({\mathrm{\sigma T}}_{\mathrm{S}}^4\right)\left(4{\mathrm{\pi r}}_{\mathrm{S}}^2\right)} \\ 10000=\frac{{\left(2000\right)}^4\times {\mathrm{r}}_{\mathrm{A}}^2}{{\left(6000\right)}^4\times {\mathrm{r}}_{\mathrm{S}}^2} \\ 10000=\frac{16\times {10}^{12}\times {\mathrm{r}}_{\mathrm{A}}^2}{1296\times {10}^{12}\times {\mathrm{r}}_{\mathrm{S}}^2} \\ \frac{810000}{1}=\frac{{\mathrm{r}}_{\mathrm{A}}^2}{{\mathrm{r}}_{\mathrm{S}}^2} \\ \frac{{\mathrm{r}}_{\mathrm{A}}}{{\mathrm{r}}_{\mathrm{S}}}=\frac{900}{1} \end{gathered}$$