(a) Would a hot solid cube cool more rapidly if it were left intact or cut in ha
ID: 2017620 • Letter: #
Question
(a) Would a hot solid cube cool more rapidly if it were left intact or cut in half?
-if it were cut in half
-if it were left intact
Explain your answer in terms of one or more of the three heat transfer processes.
(b) Using reasoning similar to that used in answering part (a), decide which cools faster, one pound of wide and flat lasagna noodles or one pound of spaghetti noodles. Assume that both kinds of noodles are made from the same pasta and start out with the same temperature.
-one pound of spaghetti noodles
-both type of noodles cool at the same rate
-one pound of wide and flat lasagna noodles
explain
Explanation / Answer
a. A hot solid cube will cool more rapidly if it is cut in half, rather than if it is left intact. Since the cube is warmer than its environment, it will lose heat primarily through radiation. Convection currents will also remove some heat from the surface of the cube. When the cube has been cut in half, the surface area of the solid has been increased. If the length of one edge of the original cube is L, then cutting the cube in half increases the surface area from 6L^2 to 8L^2
b. One pound of spaghetti noodles has a larger effective surface area than one pound of lasagna noodles. Imagine cutting many spaghetti noodles from one large lasagna noodle, in a way similar to what was done to the cube in part (a). Since the effective surface area of the spaghetti noodles is greater than that of the lasagna, heat will be radiated from the surface of the spaghetti noodles more effectively than heat will be radiated from the surface of the lasagna noodles. Therefore, the spaghetti noodles will cool more rapidly from the same initial temperature than the lasagna noodles.
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