The Diamond Ring Solution. The processing chip on the computer that controls the navigation equipment on your spacecraft is overheating. Unless you fix the problem, the chip will be damaged and the navigation system will shut down. You open the panel and find that the small copper disk that was supposed to bridge the gap between the smooth top of the chip and the cooling plate is missing, leaving a 2.2 mm gap between them. In this configuration, the heat cannot escape the chip at the required rate. You notice by the thin smudge of thermal grease (a highly thermally conductive material used to promote good thermal contact between surfaces) that the missing copper disk was 2.2 mm thick and had a diameter of 1.0 cm. You know that the chip is designed to run below 75∘C, and the copper cooling plate is held at a constant 5.0 ∘C. (a) What was the rate of heat flow from the chip to the copper plate when the original copper disk was in place and the chip was at its maximum operating temperature? (b) The only material that you have available on board to bridge the gap between the chip and copper plate is lead. If the crosssectional area of the lead piece you plan to wedge into the gap is 1.0 cm 2, what is the rate of heat flow from the chip to the copper plate? Does it match the value calculated in part (a)? (c) While brainstorming for other possible solutions to your problem, you happen to glance down at the engagement ring on your finger: a large, glittering diamond. The top and bottom surfaces are flat and nearly rectangular (L=0.75 cm and W=0.55 cm), and the thickness looks to be about 2.2 mm, just right to bridge the gap. You pry the diamond out of its holder and press it into the gap. What is the rate of heat flow now? Good enough? (a) Number Units (b) Number Units
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