* Luminosity and Temperature are Intertwined: A star's luminosity depends on both its temperature and size. A larger, cooler star can have the same luminosity as a smaller, hotter star.
* The Stefan-Boltzmann Law: This law states that the luminosity of a star is proportional to its surface area and the fourth power of its temperature. Mathematically:
```
L = 4πR²σT⁴
```
where:
* L is luminosity
* R is radius
* σ is the Stefan-Boltzmann constant
* T is temperature
To find the temperature, we would need additional information, such as the star's radius.
Here's how we can reason about the temperature:
* General Relationship: Higher luminosity generally implies higher temperature. However, this is not a simple linear relationship.
* Estimating Temperature: Without knowing the radius, we can make a rough estimate. Since luminosity is proportional to the fourth power of temperature, a star with 100 times the luminosity of the Sun would have a temperature roughly 2.15 times higher than the Sun's surface temperature (~5800 K). This is a very rough estimate, as it assumes the stars have the same radius.
In conclusion: We need more information (like the star's radius) to calculate the precise temperature of a star with 100 times the Sun's luminosity.
