Question

Using Newton’s cooling model, what will the temperature of a cup of hot tea be 2 hours after it is poured if its initial temperature is 200°F, the surrounding temperature is 70°F, and the value for k is 0.6?

A.130
B.109.16
C.109.76
D.71.35
E.60

Answer 1

Newton's Law of cooling is a differential equation that is simplified by using limits in temperature and time. The simplified equation is:

ln(T-Ts) = ln(T0-Ts) - kt

where
T is the final temperature
T0 is the initial temperature
Ts is the temperature of the surroundings
t is the time
k is a constant

Substituting the values:
ln(T-70) = ln(200-70) - (0.6)(2)
T = 109.16°F

The answer is B.