Chapter 1, Problem 19P

You are working as a crime-scene investigator and must predict the temperature of a homicide victim over a 5-hr period. You know that the room where the victim was found was at 10°C when the body was discovered.

(a) Use Newton's law of cooling (Prob. 1.14) and Euler's method to compute the victim's body temperature for the 5-hr period using values of $k=\text{ 0}\text{.12/hr and }\Delta t=\text{0}\text{.5 hr}$. Assume that the victim's body temperature at the time of death was 37°C, and that the room temperature was at a constant value of $10°\text{C}$ over the 5-hr period.

(b) Further investigation reveals that the room temperature had actually dropped linearly from 20 to $10°\text{C}$ over the 5-hr period. Repeat the same calculation as in(a) but incorporate this new information.

(c) Compare the results from(a) and (b) by plotting them on the same graph.