3 identical containers, A, B, and C. A contains one liter of 90 degrees Celsius water, B contains one liter of 10 degree Celsius water, and container C is empty. All three containers are very well insulated and loses little heat.
You also have a container D which fits easily into any of the containers A, B, and C. Container D has perfect thermally conducting walls.
You are forbidden to mix the hot water with the cold. Can you heat with the aid of container D and the hot water so that the final temperature of the cold water will be higher than the final temperature of the hot water?
You also have a container D which fits easily into any of the containers A, B, and C. Container D has perfect thermally conducting walls.
You are forbidden to mix the hot water with the cold. Can you heat with the aid of container D and the hot water so that the final temperature of the cold water will be higher than the final temperature of the hot water?
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put half of the cold water in to D. put D in to the hot water.
Wait for both containers to equalise. this should be at approximately 63.3°C.
Put the warm water from D into C.
Put half the remaining cold water into D and put D in to the 63.3°C water in A.
wait for the two containers to equalise, this should now be at approx. 45.6°C.
Put the warm water from D into C. this mixed water should now be 54.5°C
Voila the "cold water" from B is now at 54.5°C, the "hot water" from A is now 45.6°C
This entire method simply uses the fact that the heat will be equally distributed between all the water currently in contact with each other.
Wait for both containers to equalise. this should be at approximately 63.3°C.
Put the warm water from D into C.
Put half the remaining cold water into D and put D in to the 63.3°C water in A.
wait for the two containers to equalise, this should now be at approx. 45.6°C.
Put the warm water from D into C. this mixed water should now be 54.5°C
Voila the "cold water" from B is now at 54.5°C, the "hot water" from A is now 45.6°C
This entire method simply uses the fact that the heat will be equally distributed between all the water currently in contact with each other.
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I assume "container C is empty" actually means container C contains air at ambient temperature.
Use D to repeatedly transfer heat until A, B, and D are all at the same temperature (50°).
Then use D to transfer heat from A to C.
Heating the air in C will be slow and will not reduce the temperature of A by much, but it will end up a little cooler than B.
Use D to repeatedly transfer heat until A, B, and D are all at the same temperature (50°).
Then use D to transfer heat from A to C.
Heating the air in C will be slow and will not reduce the temperature of A by much, but it will end up a little cooler than B.