Newton S Law Of Cooling States That The Temperature Of An Object Changes At A Rate Proportional To The Difference Betwee 1 (56.43 KiB) Viewed 68 times
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. Let k> 0 be the constant of proportionality. Assume the coffee has a temperature of 205 degrees Fahrenheit when freshly poured, and 3 minutes later has cooled to 194 degrees in a room at 70 degrees. (a) Write an initial value problem for the temperature T of the coffee, in Fahrenheit, at time t in minutes. Your answer will contain the uknown constant k: d=0 T(0) (b) Solve the initial value problem in part (a). Your answer will contain the unknown constant k. T(t) (c) Determine the value of the constant k k (d) Determine when the coffee reaches a temperature of 144 degrees. minutes.
A thermometer is taken from a room where the temperature is 25°C to the outdoors, where the temperature is -11°C. After one minute the thermometer reads 7°C. (a) What will the reading on the thermometer be after 4 more minutes? (b) When will the thermometer read -10°C? minutes after it was taken to the outdoors.
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