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 = 0.12/hr and Δt = 0.5 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∘C over the 5-hr period.
(b) Further investigation reveals that the room temperature had actually dropped linearly from 20 to 10∘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.