Here’s the problem:(adsbygoogle = window.adsbygoogle || []).push({});

A body was found dead in the refrigerator at 5:30am at 6 am the coroner measured the core temp of the body to be 85 degrees at 6:30 it was measured again, 84 degrees. Assume the body was killed in the refrigerator what time was the person killed?

I figured this part out. I used:

dT/dt = k(T-Tm)

Solving this:

T(t) = (T-Tm)e^kt +Tm

T is the temperature at time t and Tm is the temp around the body, the environmental temperature.

I solved this and got t = 5.3.

We needed to use positive numbers for t so the book assigned 6:00 am to t = 0 and so t= 1 would be 5 am and t = 5.3 would be roughly 12:42am.

Before I go to the next part I understand you can solve this with something called Laplace Transform but I haven’t learned that yet.

That part I think I understand. Now assume that the person wasn’t killed in the refrigerator and let h represent the number of hours in the refrigerator. So at h = 1 the body was moved in to the refrigerator at 5:00am what time was the person killed? And so on with h = 1 then 2 then 3 …

Filling in this chart:

h time body moved time of death.

12 6:00pm

11

10

9

8

7

6

5

4

3

2

1

I think my trouble is this idea of ‘h’

Numbers that need to be known are

Tm in the refrigerator is 50 degrees F

Tm in the diner is 70 degrees F

The person was initially 98.6 degrees

In the beginning I solved for e^k which I got 1.06

So the equations I’m working with is:

In refrigerator

T(t) = (T-50)(1.06)^h + 50 (*)

In the diner:

T(t) = (T-70)(1.06)^t + 70 (**)

I thought I needed to work backwards

If he was in the refrigerator for h= 1 plug this into (*) but I get 83 which doesn’t make sense because he needed to be warmer when he went into the refrigerator to be cooled down to 85. I was looking for that number to be 88 or 87 ish then I could use that as the target temp for (**) to solve for the time to get to 88 or 87 ish.

If you could be any help that would be great. Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Differential Equations Question - Temperature

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**