Question

A small metal bar whose initial temperature was 20 degrees Celsius is dropped into a large container of boiling water. How long will it take the bar to reach 90 degrees Celsius if it is known that its temperature increases 2 degrees C in 1 second. How long will it ake the bar to reach 98 C?

Answer 1

Below is the answer. I hope it help.
T ( t ) = C e k t + T m where Tm is the temperature of the surroundings 
T ( t ) = C e k t + T m
T ( 0 ) = 20
T ( 1 ) = T ( 0 ) + 2 = 22
C + T m = 20 C+Tm=20 
C e k + T m = 22