Newton's Law of Cooling (Calculating Time of Death)

In summary, the problem involves determining the time of death of a victim whose body was found at a certain temperature in a freezer, using a given formula. After plugging in the numbers and solving for t, the time of death was determined to be 35.55 hours ago. However, upon further confirmation, the actual time of death was found to be 1:45 am on Wednesday.
  • #1
JacksonSolo
8
0

Homework Statement



The problem states that you discovered the body at 1pm Thursday in a freezer where the temperature was 10F. Temperature of the corpse at discovery was 40F. I have to find how many hours ago the victim died.

Homework Equations



You are given the formula T = Ta + (98.6 - Ta)(0.97)^t where Ta is air temperature.

The Attempt at a Solution



So I plugged the numbers in: 40 = 10 + (98.6-10)(0.97)^t but I have no idea how to solve for t. Any help?
 
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  • #2
Move the constants to one side and take logs on both sides you should get:

[tex] t log(0.97) = log \frac{30}{88.6} [/tex]

Evaluate that for t.
 
  • #3
Ok so I get the log of 30/88.6 and divide that by the log of 0.97 to get t, which equals 35.55 hours. Did I do that right?
 
  • #4
Im just looking for confirmation i solved the problem right.
 
  • #5
It appears correct to me. But the answer is actually... 1:45 am on Wednesday?
 
Last edited:
  • #6
Ok thanks. Yes, true ;)
 

FAQ: Newton's Law of Cooling (Calculating Time of Death)

What is Newton's Law of Cooling?

Newton's Law of Cooling is a mathematical formula that describes the rate at which the temperature of an object changes when it is in contact with a surrounding medium with a different temperature.

How is Newton's Law of Cooling used in calculating time of death?

In forensic science, Newton's Law of Cooling can be applied to determine the approximate time of death of a deceased individual by measuring the body temperature and comparing it to the ambient temperature.

What factors affect the accuracy of using Newton's Law of Cooling to calculate time of death?

The accuracy of using Newton's Law of Cooling to calculate time of death can be affected by factors such as the initial body temperature, the ambient temperature, the type of clothing the individual was wearing, and the location of the body.

Are there any limitations to using Newton's Law of Cooling in calculating time of death?

Yes, there are limitations to using Newton's Law of Cooling in calculating time of death. It assumes that the body is in a closed environment and that there is no external heat source or cooling mechanism acting on the body.

Can Newton's Law of Cooling be used in all cases to determine time of death?

No, Newton's Law of Cooling should be used in conjunction with other methods and evidence to determine time of death. It is not always accurate and can only provide an estimated time of death within a certain range.

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