Newton\'s law of cooling states that the temperature of an object changes at a r
ID: 1887469 • 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 195 degree Fahrenheit when freshly poured, and 1.5 minutes later has cooled to 178 degree s in a room at 62 degree s, determine when the coffee reaches a temperature of 128 degree s. The coffee will reach a temperature of 128 degree s in minutes.Explanation / Answer
from Newton's law of cooling
dT/dt = - k(T-62)
=> dT/(T-62) = -kdt
on integrating
T = 62 + ce-kt
given that at t= 0, T = 195 => c = 133
and at t= 1.5 , T = 178 => k = 0.0912
so for T = 128 the time will be
t = 7.638 min
when putting this in the answer box approximate this according to the given rules.