Answer :

Final answer:

Given Star A is 10,000 times brighter than Star B, using the relationship of brightness to temperature from the Stefan-Boltzmann law, Star A is 10 times hotter than Star B. The correct answer is option A.

Explanation:

The question asks: Star A is 10,000 times brighter than Star B. How many times hotter is Star A than Star B? To answer this, we need to understand the relationship between a star's brightness (luminosity) and its surface temperature. According to the Stefan-Boltzmann law, the luminosity of a star (how bright it ultimately appears) is proportional to the fourth power of its surface temperature.

The term Delta T (ΔT) is in science, the difference of temperatures between two measuring points. The temperature differs either in time and/or position. We at Merus use it for example, to measure the efficiency of a heat exchanger. Or for checking the performance of a heating system or a cooling system. This means if you double a star's temperature, its brightness increases by a factor of 24 = 16. Therefore, to find out how much hotter Star A is compared to Star B given that Star A is 10,000 times brighter, we need to solve for the temperature ratio: TA^4/TB^4 = 10,000. By taking the fourth root on both sides, we find that TA/TB = 10.

Thus, Star A is 10 times hotter than Star B.

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Rewritten by : Barada