Problem P. 4476. (November 2012)
P. 4476. Kate invited her friends to her birthday party. She wanted to endear herself to her friends by making them some icecream. She mixed the icecream powder with water at 4 o'clock in the afternoon, her friends were invited to come to 6 o'clock, and she was a bit worrying whether the icecream will be ready or not. In order not to worry so much, she measured how fast the initially 25 ^{o}C icecream mixture cools down in the freezer. She observed that after 10 minutes the temperature of the icecream was 21 ^{o}C. Was she able to serve the icecream to her friends in the party if the party lasted until 10 at night, and the icecream must cool down to at least 6 ^{o}C? (Suppose that the heat extraction of the freezer is uniform, and the thermal properties of the liquid icecream and the icecream are the same as those of the water and ice.)
(4 pont)
Deadline expired on December 10, 2012.
Sorry, the solution is available only in Hungarian. Google translation
Megoldásvázlat. Kb. 4,5 óra alatt, tehát fél 9re kész lesz a fagylalt. (A fagylaltlé fagyáspontig történő lehűtéséhez 1 óra, a megfagyasztásához 3,5 óra szükséges, a további hűtés ideje nem számottevő.)
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