What temperature increase is necessary to increase the power radiated from an object by a factor of 6?

Question

What temperature increase is necessary to increase the power radiated from an object by a factor of 6?
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Quizplus · Accepted Answer

The power radiated by an object is proportional to the fourth power of its temperature (Stefan-Boltzmann law: P∝T^4). Therefore, we can use the following equation to solve for the necessary temperature increase (ΔT) to increase the power radiated by a factor of 6:

(ΔT/T)^4 = 6

Taking the fourth root of both sides and rearranging, we get:

ΔT/T = (6)^(1/4) = 1.565

So, the necessary temperature increase is about 57% (or 0.57T). Therefore, the correct answer is D. Choice A is incorrect because a 6 K increase would only result in a 6^4 = 1,296-fold increase in power, which is much greater than a factor of 6. Choices B, C, and E are incorrect because they either do not represent the correct temperature increase, or they are not a reasonable or accurate estimation of the necessary increase.

What Temperature Increase Is Necessary to Increase the Power Radiated