Question

Colonel Mustard was found murdered with a wooden-handled knife in the billiard room. Police arrived at 11:00 pm. The temperature of the body at that time was 30 degrees C. After an hour the body had cooled to 28 degrees C.The temperature of the room in which the body was found was 22 degrees C. Estimate the time at which the murder occurred. Assume a healthy human has an internal body temperature of 37 degrees C.


Answer 1

lmfao clue

Answer 2

If we can assume that the room is large enough that its temperature won't increase appreciably as the body cools, then this will be a little easier.

Answer 3

How do I set up the question?

Answer 4

This can be a little tricky because the temperature change is likely non-linear.

Answer 5

Are you a thermo guy or watching too much CSI?

Answer 6

If you use linear interpolation, then you can use the points (11am, 30º) and (12pm, 28º) and draw a straight line between them.
But if you're trying to extrapolate from that back to 37º then I don't think that will be very accurate.
Thermo principles say that the minimum temperature the body can reach is 22º because that is the temperature of the room (state of equilibrium). Again, this is assuming that we can ignore the temperature increase of the air in the room as the body cools.
Minimum simplifying assumption would be that the curve approaches 22º asymptotically making this an inverse variation situation.

Answer 7

Since the problem is only asking for an estimation, I don't think you need to be very exact here.
Besides, we don't know the mass or surface area of the body, the velocity of air currents in the room, the volume of air in the room. Too many unknowns to give a more precise answer.
Try linear extrapolation first, then maybe fit an inverse variation model and see if either give a sensible answer. . .

Answer 8

I love this solution!!

Any chance a straight linear model will work? Perhaps knowing what class it is for will help "fit" the solution to the problem.

But... I also plan to use this next time I play Clue! Well done @CliffSedge!!!

Answer 9

thanks man.

Answer 10

I may need to use differential equations here though. What your saying makes sense, but it doesn't give me an exact answer. Very approx.

Answer 11

Yeah, well the problem says to 'estimate' so don't worry about being too exact.
Look up "differential equations heat equation" and maybe also "Newton's law of cooling" for guidance.

@jakev8 I actually think a linear model would be terrible, but it will give a quick first approximation.