Thermal Resistances

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How quickly heat transfers through an insulating layer depends on that insulator's thermal resistance. If two insulators are used together, the inverse of the combined thermal resistance is sum of the reciprocals of each layer's thermal resistance. If the thermal resistances of two insulators are r and 2r, what is their combined resistance?

Review: Thermal Resistances


Explanation

In this question, while the subject matter is different, the math described is similar to what we do in a combined rate question when we are given times: we add reciprocals to get a combined effect. Based on the question we can write



where we are looking for C. If you know the formula from combined work, you can plug in r and 2r and you'll have your answer. Otherwise, we can get a common denominator:









The correct answer is (D).


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