# Newton's law of cooling, who died first? Extremely hard

• August 21st 2013, 03:10 PM
iamapineapple
Newton's law of cooling, who died first? Extremely hard
Two bodies have been found. The wife was found dead inside the heated home where the temperature was maintained at 22 degrees celsius. The husband dragged himself outside, where the outside temperature during the preceding day was 8 to 12 degrees celsius.

The doctor took the temperatures of the body as soon as they arrived:
Wife: 33 degrees celsius
Husband: 26 degrees celsius

Who died first? Develop a model to help decide this question.

I'm really unsure of what to do. If I set up equations for both of the bodies, I still have a variable k, and the varying outside temperature is really confusing me. Help super apprecitaed.
• August 22nd 2013, 02:11 AM
chiro
Re: Newton's law of cooling, who died first? Extremely hard
Hey iamapineapple.

Hint: What is the functional model for the temperature as a function of time for Newtons law of cooling? (If you get this then you can setup your simultaneous equations and solve).
• August 22nd 2013, 01:33 PM
iamapineapple
Re: Newton's law of cooling, who died first? Extremely hard
$\frac{dT}{dt}$ = $-k ( T - T\subscribttext{s})$

and $T = Ae\textsuperscript{-kt} + T\subscribttext{s}$
• August 22nd 2013, 06:03 PM
chiro
Re: Newton's law of cooling, who died first? Extremely hard
Do you have information about the A constants for each equation (ie husband and wife)?

I'm not exactly sure you have enough information to solve this problem. You need information about the constants such that you can solve for t in both equations and since you have three constants per equation, it means you need six pieces of information (A, k, and s). In your question, you are given 4.

You need to either get new information or assume something to get a unique answer.
• August 22nd 2013, 08:03 PM
iamapineapple
Re: Newton's law of cooling, who died first? Extremely hard
This is why the question is so hard! This is all of the information I get
• August 22nd 2013, 08:14 PM
chiro
Re: Newton's law of cooling, who died first? Extremely hard
I think you should ask your teacher/lecturer if there is anything else you can assume.

Just mention the part about not having enough information and I'm sure they will understand.
• August 23rd 2013, 01:13 AM
iamapineapple
Re: Newton's law of cooling, who died first? Extremely hard
I assumed that body temperature was 37 degrees initially.
• August 23rd 2013, 01:18 AM
MarkFL
Re: Newton's law of cooling, who died first? Extremely hard
The assumption I made at the other site is that since both the husband and wife are composed of essentially the same material and are similarly shaped, then it is reasonable to assume the heat transfer coefficient $k$ is the same for both bodies. So then we may compare the quantity $kt$ for both bodies.
• August 24th 2013, 12:00 AM
iamapineapple
Re: Newton's law of cooling, who died first? Extremely hard
Hey again :P

@chiro, Mark's been helping me out here: http:///questions-other-sites-52/no-...html#post27975

It's really good if you'd like to check it out.
• August 24th 2013, 03:13 AM
MarkFL
Re: Newton's law of cooling, who died first? Extremely hard
http://math help boards.com/questions-other-sites-52/no-ones-question-yahoo-answers-regarding-newtons-law-cooling-6127.html