# Newtons Law of Cooling: A dead body was found within a closed room of a house where the...

## Question:

Newtons Law of Cooling:

A dead body was found within a closed room of a house where the temperature was a constant 70 degrees Fahrenheit. At a time of discovery, the core temperature of the body was determined to be 85 degrees Fahrenheit. One hour later a second measurement showed that the core temperature of the body was 80 degrees Fahrenheit. Assume that the time of death corresponds to t=0 and the core temperature at that time was 98.6 degrees Fahrenheit. Determine how many hours elapsed before the body was found.

## Newton's Law of Cooling:

Newton discovered a law of cooling in 1701 which states that the rate a body is losing heat is proportional to the difference in the temperatures between the cooler environment and the warmer body. This gives a differential equation for the temperature-difference as a function of time, and it can be solved for a simple exponential decay.

Newton's law is given for the temperature change as a function of time:

{eq}\displaystyle \frac{dT}{dt}= -r(T-T_e) {/eq}

where {eq}T {/eq} is the...

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