Newton's Law of Cooling
The police discover the body of a murder victim. Critical to solving the crime is determining when the murder was committed. The coroner arrives at the murder scene at 12:00pm. She immediately takes the temperature of the body and finds it to be 94.6 degrees F. She then takes the temperature 1 hour later and finds it to be 93.4 degrees F. The temperature of the room is 70 degrees F. When was the murder committed?
College Algebra Application - MathMate, Friday, May 6, 2011 at 12:32pm
Let t=0 at time of death.
We have two temperatures, 94.6 at t=t1, and 93.4 at t=t1+1.
Also, normal body temperature is 98.6, so T1=98.6.
T0=ambient temperature = 70.
Substitute in given formula:
We try to solve for t1 and k.
Subtract (2) from (1):
Rearrange (1) and (2)
Divide (2a) by (1a)
take natural log on both sides,
Substitute k in (1a):
take natural log on both sides
-0.05t1 = -0.15066
So the victim was dead 3 hours before the coroner arrived, or at 9 a.m.