Question

how much more energy flux does a star that is 3 times hotter than the sun output? (recall the stefan - boltzmann law).
243
81
9
6
3

Explanation:

Step1: Recall Stefan - Boltzmann Law

The Stefan - Boltzmann law for energy flux is $F=\sigma T^{4}$, where $F$ is the energy flux, $\sigma$ is the Stefan - Boltzmann constant, and $T$ is the temperature.

Step2: Let the Sun's temperature be $T_{1}$ and its energy flux be $F_{1}=\sigma T_{1}^{4}$. The star's temperature $T_{2} = 3T_{1}$, and its energy flux $F_{2}=\sigma T_{2}^{4}=\sigma(3T_{1})^{4}$.

Step3: Calculate the ratio of the star's energy flux to the Sun's energy flux

$\frac{F_{2}}{F_{1}}=\frac{\sigma(3T_{1})^{4}}{\sigma T_{1}^{4}}=\frac{81\sigma T_{1}^{4}}{\sigma T_{1}^{4}} = 81$.

Answer:

B. 81