One star has a temperature of 30,000 K and another star has a temperature of 6,000 K. Compared to the cooler star, how much more energy per second will the hotter star radiate from each square meter of its surface
A)5 times
B)25 times
C)$8.1 × 10^{17}$ times
D)625 times
E)$1.3 × 10^{15}$ times

Question

Quizplus · Accepted Answer

The energy radiated per second per square meter from a star's surface is given by the Stefan-Boltzmann law, which states $E = \sigma T^4$, where $E$ is the energy radiated per unit area, $\sigma$ is the Stefan-Boltzmann constant, and $T$ is the temperature in Kelvin. Comparing the two stars, the ratio of their energy outputs is $(30000/6000)^4 = (5)^4 = 625$. Thus, the hotter star radiates 625 times more energy per second per square meter than the cooler star.

One Star Has a Temperature of 30,000 K and Another 8.1×10178.1 × 10^{17}8.1×1017

One Star Has a Temperature of 30,000 K and Another $8.1 × 10^{17}$