Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 192 °F when freshly poured, and 1 min later has cooled to 182 °F in a room at 70 °F, determine when the coffee reaches a temperature of 144 °F.
Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 192 °F when freshly poured, and 1 min later has cooled to 182 °F in a room at 70 °F, determine when the coffee reaches a temperature of 144 °F.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:Newton's law of cooling states that the temperature of an object
changes at a rate proportional to the difference between its
temperature and that of its surroundings. Suppose that the
temperature of a cup of coffee obeys Newton's law of cooling. If the
coffee has a temperature of 192 °F when freshly poured, and 1 min
later has cooled to 182 °F in a room at 70 °F, determine when the
coffee reaches a temperature of 144 °F.
Note: Enter the exact symbolic expression for the asked time.
The coffee reaches the temperature 144 in
In (37)
61
minutes. ✔
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