What is theratio of the luminosity per aquare meter coming from a part of the Sun that is 5800 K versus a sunspot where the temperature is 5000 K?
To find the ratio of the luminosity per square meter coming from a part of the Sun with a temperature of 5800 K compared to a sunspot with a temperature of 5000 K, we can use the Stefan-Boltzmann Law.
The Stefan-Boltzmann Law states that the total power radiated by a blackbody is proportional to the fourth power of its temperature. Mathematically, it is expressed as:
Luminosity ∝ Temperature^4
Since we are interested in the ratio of the two luminosities, we can set up the following equation:
(Luminosity of 5800 K)/(Luminosity of 5000 K) = (Temperature of 5800 K)^4 / (Temperature of 5000 K)^4
Let's calculate the values:
Luminosity ratio = (5800^4) / (5000^4)
Using a calculator or programming language, we can find the luminosity ratio:
Luminosity ratio ≈ 1.7122
Therefore, the ratio of the luminosity per square meter coming from a part of the Sun that is 5800 K to a sunspot where the temperature is 5000 K is approximately 1.7122.