Results 1 to 2 of 2

Math Help - Application of first order differential equation-tomorrow test

  1. #1
    Junior Member
    Joined
    Sep 2008
    From
    Australia
    Posts
    72

    Application of first order differential equation-tomorrow test

    I have a problem of this type of question.
    An object thrown into a large body of water cools at a rate proportional to the difference between its temperature and the water temperature. Suppose know that the the water is at a temperature of 27 degrees Celsius. After 4 minutes the object's temperature is 67 degrees, and after 9 minutes the object's temperature is 47 degrees Celsius. What was the temperature of the object when it was thrown into the water?


    Differential equation is dQ/dt = -k(Q-Qs)


    Q is the temperature of an object
    Qs is the water temperature.

    Not like other question, i can find K (constant) but in this question K ( constant ) i even cant find it out.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    I think you can set up two equations to find k. And I'm assuming the water is kept at a constant temperature.

     \int^{67}_{Q_{0}} \frac {dQ}{Q-27} = -k \int^{4}_{0}dt

     \int^{47}_{Q_{0}} \frac {dQ}{Q-27} = -k \int^{9}_{0}dt
    Last edited by Random Variable; May 29th 2009 at 09:46 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Application of a Differential Equation
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: October 23rd 2011, 11:54 PM
  2. Application of first order differential equation-tomorrow test
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: May 29th 2009, 10:19 AM
  3. Application of 1st order differential equations 2
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: May 19th 2009, 04:52 AM
  4. Replies: 1
    Last Post: March 1st 2008, 12:20 AM
  5. Replies: 27
    Last Post: February 10th 2008, 06:49 PM

Search Tags


/mathhelpforum @mathhelpforum