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?

Question

Quizplus · Accepted Answer

According to the Stefan-Boltzmann law, the amount of energy radiated per second per unit area is proportional to the fourth power of the absolute temperature. Therefore, the ratio of the energies radiated is:
$$\frac{(T_1/T_2)^4}{1} = \left(\frac{30,000}{6,000}\right)^4 = 625$$
Hence, the hotter star will radiate 625 times more energy per second per unit area than the cooler star. According to the Stefan-Boltzmann law, the energy radiated per second per unit area (also called the radiative flux) is proportional to the fourth power of the temperature. Therefore, if one star has a temperature that is 5 times hotter than another star, its radiative flux will be 5^4 = 625 times greater. In this case, the hotter star (30,000 K) is 5 times hotter than the cooler star (6,000 K), so its radiative flux will be 5^4 = 625 times greater. Therefore, the hotter star will radiate 625 times more energy per second from each square meter of its surface compared to the cooler star. The answer is D.

One Star Has a Temperature of 30,000 K and Another