Suppose you have three identical Dewar flasks labeled A, B, and C. (A Thermos is a Dewar flask.) You also have an empty container labeled D, which has thermally perfect conducting walls and which fits inside a Dewar flask.
Pour 1 liter of 80°C water into flask A and 1 liter of 20°C water into flask B. Now, using all four containers, is it possible to use the hot water to heat the cold water so that the final temperature of the cold water is higher than the final temperature of the hot water? How? (You can’t actually mix the hot water with the cold.)
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Pour half the cold water into D and put D into the hot flask (A). The final temperature in both A and D will be about 60°C. Empty D into C and the repeat the procedure, pouring the remaining half of the cold water in B into D and immersing it in the hot water. Now the final temperature of the water in A and D will be about 47°C. Empty D again into C; the final temperature of the mixture there will be about 53°C. So in two operations we’ve warmed the cold water to 53°C and cooled the hot water to 47°C.
From Christopher Jargodzki’s books Science Brain-Twisters (1976) and Mad About Physics (2002).
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