One tool that a coroner uses to estimate the time of death for someone who has d
ID: 110866 • Letter: O
Question
One tool that a coroner uses to estimate the time of death for someone who has died while exposed to the environment is Newton's Law of Cooling. This law provides the relationship between the rate of change of the temperature of an object (i.e., the loss of heat) when exposed to the environment. Let's set up the equation: T(t) = T_e + T_0e^kt t = time T(t) = temperature at time of death T_e = Temperature of the environment (in degree F) T_0 = Starting temperature of the object (i.e., normal body temperature) k = -0.011 per minute Imagine a woman was walking her dog on a really cold day, and while far from her house, she had a heart attach and died. The dog ran away and got help, but took a long time to do so. When the police discovered the body later that day at 8PM, her body temperature had dropped from 98.6 degree F to 36 degree F. The environmental air temperature was 6 degree F. What time did she die from the heart attack? Show all of your work!Explanation / Answer
At the time of death, 8PM, temperature was 36F 36=6+(98.6 x e0.011 t ) 30/98.6 = e0.011t log 0.304 = 0.011 t -0.516 = 0.011 t t= - 0.516/0.011 = - 46.97 minutes = 46 minutes 58.2 seconds Calculating backwards from 8PM, the time of death is 07:14:58.2 PM
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