Question

question 13
how much more energy flux does a star that is 2 times hotter than the sun output? (recall the stefan - boltzmann law).
2
8
4
16
32

Explanation:

Step1: Recall Stefan - Boltzmann Law

The energy flux $F$ of a black - body is given by $F=\sigma T^{4}$, where $\sigma$ is the Stefan - Boltzmann constant and $T$ is the temperature.

Step2: Let the Sun's temperature be $T_{1}$ and the star's temperature be $T_{2}$

Given $T_{2} = 2T_{1}$. The energy flux of the Sun $F_{1}=\sigma T_{1}^{4}$, and the energy flux of the star $F_{2}=\sigma T_{2}^{4}=\sigma(2T_{1})^{4}$.

Step3: Calculate the ratio $\frac{F_{2}}{F_{1}}$

$\frac{F_{2}}{F_{1}}=\frac{\sigma(2T_{1})^{4}}{\sigma T_{1}^{4}}=\frac{16T_{1}^{4}}{T_{1}^{4}} = 16$.

Answer:

D. 16