Question

A loaf of bread is removed from an oven at 350° F and cooled in a room whose temperature is 70° F. If the bread cools to 210° F in 20 minutes, how much longer will it take the bread to cool to 185° F.

Answer 1

Answer:

The bread will take 216.40 minutes to cool to 185°F

Explanation: Newton law of cooling

states that the rate of cooling of an object is inversely proportional to the difference of temperatures between the object and its surroundings i.e. dTdt=−kT, where t is the time taken and T is the difference of the temperatures between the object and its surroundings.

This gives us T as a function of t and is given by T(t)=ce−kt.

T(0)= Ce^-kt

C=35₩F- 185F= 165F

T(20) = 165×e^-20k=(350-70)

T(20)= e^-20k =280/165

-20k= ln(280/165)

-20k= ln(1.697)

-20k= 0.5289

K= 0.5289/20

K= 0.0264

If it cools at 185F in t minutes

165e^-0.0264×t=0.5

e^-0.0264t= 0.5/165

-0.0264t= on 3.03×10^-3

-0.0264t= -5.7129

t= 5.7129/0.0264

t=216.40minutes