Question

I don't know where to start on this one.

A thermometer is taken from an inside room to the outside, where the air temperature is ten degrees Fahrenheit. After one minute the thermometer reads 40 degrees Fahrenheit, and after two minutes it reads twenty-five degrees Fahrenheit. What is the initial temperature of the inside room?

Answer 1

Start with Newton's Law of cooling. Using your numbers, with To the initial temperature,

T(t) = 10 + (To-10)e^(-kt)

Now you have

T(1) = 10 + (To-10)e^-k = 40
T(2) = 10 + (To-10)e^-2k = 25

(To-10)e^-k = 30
(To-10)e^-2k = 15

(To-10)^2 e^-2k = 900
(To-10) e^-2k = 25
Now divide and the e^-2k stuff goes away, leaving
(To-10) = 900/25 = 36
To = 46