Results 1 to 3 of 3

Math Help - Mathematical mdelling with diffrential equations

  1. #1
    Junior Member
    Joined
    Dec 2010
    Posts
    26

    Post Mathematical mdelling with diffrential equations

    A cold water has a temperature of 10 'c. It stands in the room of the temperature 30 'c. After 10 min the temperature of the water rises to 15 'c. The temperature y 'c,
    rises at a rate that is proportional to the difference of 30-y.

    a) Setup a diffrential equation that describes this situation.
    b)What will be the temperature of water after 20 min.
    c)How fast does the temperature rise when it is 20 'c.

    I would be grateful if somebody could help me.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by hejmh View Post
    A cold water has a temperature of 10 'c. It stands in the room of the temperature 30 'c. After 10 min the temperature of the water rises to 15 'c. The temperature y 'c,
    rises at a rate that is proportional to the difference of 30-y.

    a) Setup a diffrential equation that describes this situation.
    b)What will be the temperature of water after 20 min.
    c)How fast does the temperature rise when it is 20 'c.

    I would be grateful if somebody could help me.
    You could start with (a) the last sentence of the problem statement before it "The temperature 'y' in degrees centigrade,
    rises at a rate that is proportional to the difference of '30-y' " is what you need to rewrite as a differential equation.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    South Africa
    Posts
    1,630
    Thanks
    6
    I would use Newton's Law of Cooling on this one.

    \frac{dT}{dt} = k(30 - T)

    Seperate, integrate by parts.

    Then solve for the constant using the known temperature T = 10 when t = 0

    Solve for the constant of proportionality, k by solving the equation when T = 15 when t = 10
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Diffrential equations help
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: January 27th 2010, 09:19 AM
  2. Diffrential Equations..
    Posted in the Calculus Forum
    Replies: 8
    Last Post: May 2nd 2009, 05:29 PM
  3. diffrential equations
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 20th 2009, 10:27 AM
  4. Diffrential equations!
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: December 10th 2008, 07:50 AM
  5. Diffrential equations...can't seem to get answer =(.
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: November 13th 2008, 01:47 PM

Search Tags


/mathhelpforum @mathhelpforum