# Urgent: Newtons Law of Cooling

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• September 27th 2007, 08:25 AM
Ideasman
Urgent: Newtons Law of Cooling
A medical examiner reviewed a homicide and found that the temp. of the body was 82 degrees F. Make up additional, although plausible, data that is necessary to determine an approximate time of death of the dead person using Newton’s Law of Cooling.
• September 27th 2007, 09:22 AM
CaptainBlack
Quote:

Originally Posted by Ideasman
A medical examiner reviewed a homicide and found that the temp. of the body was 82 degrees F. Make up additional, although plausible, data that is necessary to determine an approximate time of death of the dead person using Newton’s Law of Cooling.

You need to assume the ambient temprature say 70F, and the original body
temprature say 98.6F. You will also have to assume a cooling rate constant,
$k$ so:

$
\frac{dT}{dt}=k(T-T_{amb})
$

Then solve this to find the time taken for the temp to fall to 82F

TonL
• September 27th 2007, 09:27 AM
topsquark
Quote:

Originally Posted by Ideasman
A medical examiner reviewed a homicide and found that the temp. of the body was 82 degrees F. Make up additional, although plausible, data that is necessary to determine an approximate time of death of the dead person using Newton’s Law of Cooling.

Here is Newton's Law of Cooling:
$\frac{dT}{dt} = -k(T - T_{env})$

The solution is
$T(t) = (T_0 - T_{env})e^{-kt} + T_{env}$
where $T_0 = T(0)$, $T_{env}$ is the environment temperature, and k is a constant.

What do you think $T_0$, the initial temperature of the body, should be? What should $T_{env}$ be? Finally, (and this is the tough one) what do you think k should be? (You might try to look this one up on the internet.)

-Dan