# Newton's law of cooling

At 4:30 PM on Monday, a Virginia criminalist was called to the scene of a homicide. She noted that the body temperature of the deceased was 85.5 deg. while the air temperature was 78 deg. Thirty minutes later, the deceased's body temperature was 82 deg. Assuming the air temperature stayed constant, what is the estimated time of death of the body? (Assume a normal body temperature of 98.6 deg)

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#### Solution Preview

So we first have to recognize that this is Newton's Law of Cooling with the air temperature of 78 degrees. This will give us the differential equation

du

-- = k(u-78)

dt

This is the information we have:

If we say 4:30 is time t = 0 then we know that

u(0) = 85.5 and ...

#### Solution Summary

This shows how to use decrease in temperature to estimate time of death.

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