Newton\'s Law of Cooling states that the rate of cooling of an object is proport
ID: 3287271 • Letter: N
Question
Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose that a roast turkey is taken from an oven when its temperature has reached 195 degree F and is placed on a table in a room where the temperature is 60 degree F. If u(t) is the temperature of the turkey after t minutes, then Newton's Law of Cooling implies that du/dt = k (u - 60 degree F). This could be solved as a separable differential equation. Another method is to make the change of variable y = u - 60 degree F. If the temperature of the turkey is 165 degree F after half an hour, what is the temperature after 40 min?Explanation / Answer
It's T(t) = s+ (T-s)e^(-kt) where T = temperature at any instant A = temperature of surroundings (ambient temperature) S = initial temperature (I used S for starting) t= elapsed time and k is a constant determined by the conditions.we have k=8.37*10^-3........thus we have.........temperature at 40 min will be T(t)=195-(195-60)e^-kt... thus k=0.05 so we have T at 40min = 60+135e^-k40=156.56 F