Newton\'s law of cooling states that the temperature of an object changes at a r
ID: 1949213 • Letter: N
Question
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 (185) degrees Fahrenheit when freshly poured, and (2.5) minutes later has cooled to (172) degrees in a room at (64) degrees, determine when the coffee reaches a temperature of (127) degrees.The coffee will reach a temperature of (127) degrees in minutes.
Explanation / Answer
T =- k(detlaT)/t (185-172) = k(172-64)*60/2.5 k = 0.005 185-127 = .005(127-64)*60/t t =6.3min