Thread: how many hours elapsed when the body was found...

a dead body was found within a closed room of a house where the temperature was a constant 70 F. at the time of discovery the core temperature of the body was determined to be 85 F. one hour later a second measurement showed that the core temperature of the body was 80 F. assume that the time of death corresponds to t=0 and that the core temp at that time was 98.6 F, how many hours elapsed before the body was found?


ok so my equation that i want to use will be T = Tm + Ce^(kt)
so can i say that t(0)= 98.6 F. if that is true then i can find my C value and have the actual problem set up. but im not sure where to go after this. I know i need to find k and then eventually t...which my book says is 1.6 hours

well any help would be appreciated..thanks in advance

Hi
The temperature of the body is , k being negative
We know that :
- at infinite time T(t) is the temperature of the room, therefore Tm=70
- T(0)=98.6=Tm+C therefore we know the value of C

The temperature of the body at the time it was found is
One hour later

Now you just have to solve

Don't confuse capital T with lowercase t in Newton's Law of Cooling problems! Highly dangerous. Might get a negative citation from the Citation Writing Subgroup of the Committee for the Prevention of Notational Abuse.

I would agree that .

The target variable is the time at which the temperature is 85 degrees, call it for the time of discovery. You know that

and you also know that



With your underlying equation of



you should be able to find what you're looking for. Make sense?

yeah that does make sense, that was the trick that i missed! that was the missing link the Td and then Td+1....

thanks!

You're welcome!