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Case: At 9:00 PM a coroner arrived at a hotel room of a murder victim
Case: At 9:00 PM a coroner arrived at a hotel room of a murder victim. The temp. of the room was 70 degrees F. It was assumed that the victim had a body temp. of 98.6 degrees F (AT THE TIME OF DEATH)(not at 9:00PM). The coroner took the victim's temp. at 9:15 PM at which it was 83.6 degrees F and again at 10:00 PM at which it was 80.3 degrees F.
A. At what time did the victim die? I solved that question to be at 7:15 PM (165 min before 10:00PM)
B. If the assumption of the victim's body temp. at the time of death was found to be incorrect due to a major outbreak of influenza at the hotel during the victim's stay and the usual fever a flu case will run is 103 degrees F. What is the time of death then? I solved it to be 6:37 PM(203 min before 10:00PM).
C. If the victim had no influenza at the time of death, but the room temp was really 75 degrees F what was the time of death then? answer was 7:47PM(133 min before 10:00PM)
D. Assuming the victim was murdered 3 minutes of the time the murderer got off the elevator(which had video surveillance) what five minute sequence should have been reviewed in each scenarios a, b, and, c?
Expert Solution
Please see the attached file.
Theory
Newton's Law of Cooling describes the cooling of a warmer object to the cooler temperature of the environment. Specifically we write this law as,
T (t) = Te + (T0 − Te ) e - kt (1)
where T (t) is the temperature of the object at time t, Te is the constant temperature of the environment, T0 is the initial temperature of the object, and k is a constant that depends on the material properties of the object.
Solution
1. In this case: Te = 70 oF
First find k
From 9:15 to 10:00 (45 minutes) the body temperature changed from 83.6 to 80.3. Thus:
80.3 = 70 + (83.6 - 70)e-45k
Hence we can find the time of death using the temperature at 10PM
80.3 = 70 + (98.6 - 70)e-0.006176t
80.3 = 70 + 28.6e-0.006176t
Thus the time of death is 165 minutes before 10PM or at ~7:15PM
2. I think it is better at this stage to re-arrange equation 1:
or
Now T0 = 103 oF
Find new time taking 10PM as the reference point:
-1.16
t = 188 (min)
Thus if the victim got influenza, the time of death was 188 min before 10PM, which was at ~6:52PM
3. T0 = 98.6 oF
Te = 75 oF
Have to calculate new k:
80.3 = 70 + (83.6 - 70)e-45k
New time of death can then be found using the temperature at 10PM
-1.49
t = 138 (min)
So the time of death was 138 min before 10PM in this case, which was at ~7:42PM
4. Assuming the victim was murdered 3 minutes of the time the murderer got off the elevator (which had video surveillance) what five minute sequence should have been reviewed in each scenarios a, b, and ,c?
Case a:
Check video surveillance at ~7:14 PM until around 7:19 PM. It would be better to check the whole period of camera surveillance to see the overall situation.
Case b:
Check video surveillance at ~6:51 PM until around 6:56 PM.
Case c:
Check video surveillance at ~7:41 PM until around 7:46 PM.
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