Newton\'s Law of Cooling states that the rate at which the temperature of a cool
ID: 2889653 • Letter: N
Question
Newton's Law of Cooling states that the rate at which the temperature of a cooling object decreases and the rate at which a warming object increases are proportional to the difference between the temperature of the object, TO, and the temperature of the surrounding medium Ta T(t) = Ta + (To-Tale-kt A cup of water with a temperature of 89 C is placed in a room with a constant temperature 21° (a Assuming that Newton's Law of Cooling applies, find the temperature of the water minutes after it is placed in the room. Write the constant of proportionality as T(t) = Click here to enter or edit your answer 2Explanation / Answer
T(t)=T a+(T o - T a)e -kt
a. T a= 21° ,T O=89°
T(t)= 21+(89-21)e -kt =21+68e -kt
b. T(1)=79°
79=21+68e -k(1)
58=68e -k
58/68=e -k
k=-ln(58/68)=ln(68/58)=ln(34/29)
45=21+68e -t ln(34/29)
24=68e -t ln(34/29)
6/17=e -t ln(34/39)
t=6.55min