Results 1 to 10 of 10

Math Help - Newton's law of cooling, who died first? Extremely hard

  1. #1
    Junior Member
    Joined
    Mar 2013
    From
    Australia
    Posts
    52

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,163
    Thanks
    761

    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).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2013
    From
    Australia
    Posts
    52

    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}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,163
    Thanks
    761

    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.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Mar 2013
    From
    Australia
    Posts
    52

    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
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,163
    Thanks
    761

    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.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Mar 2013
    From
    Australia
    Posts
    52

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

    I assumed that body temperature was 37 degrees initially.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    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.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Mar 2013
    From
    Australia
    Posts
    52

    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.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

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

    Here is the link:

    Code:
    http://math help boards.com/questions-other-sites-52/no-ones-question-yahoo-answers-regarding-newtons-law-cooling-6127.html
    The name of the site is censored out here at MHF, so copy the above into your browser, and then remove the spaces.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. extremely hard partial derivative question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 20th 2013, 08:29 AM
  2. Replies: 1
    Last Post: April 18th 2012, 02:46 AM
  3. Extremely Hard Max/Min Problem
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 7th 2011, 01:43 PM
  4. Extremely hard calculus question.
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 23rd 2010, 12:51 PM
  5. Extremely hard minimization problem
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 7th 2008, 03:33 AM

Search Tags


/mathhelpforum @mathhelpforum