A thermometer is taken from a room where the temperature is

A thermometer is taken from a room where the temperature is 19oC to the outdoors, where the temperature is 5oC. After one minute the thermometer reads 9oC.

(a) What will the reading on the thermometer be after 2 more minutes? ,

(b) When will the thermometer read 4oC? minutes after it was taken to the outdoors.

Solution

By Newton\'s Law of cooling
T(t) = S +(To-S)*e(-kt) where To = initial temperature at t = 0

after one minute the thermometer reads 9oC.

then T(t) = 9oC, S = 5oC and To = 19oC

then 9 = -5 + (19+5)*e^(-k)
14 = 24e^-k
ln(7/12) = -k
k = 0.539
T(t) = -5+24e^(-0.539t)
(a) T(3) = -5+24e^(-0.539*3)
T(5) = 15.41 C
(b) -4 = -5+24e^(-0.539t)
1/24 =e^(-0.539t)
ln(1/24) = -0.539t
t = 5.88 minutes