Results 1 to 9 of 9

Math Help - Newton's law of cooling/warming

  1. #1
    Junior Member
    Joined
    Apr 2009
    Posts
    33

    Newton's law of cooling/warming

    A thermometer reading 4˚C is brought into a room where the temperature reading is 30˚C. If the thermometer reads 10˚C after 2 minutes, determine the temperature reading 5 minutes after the thermometer is first brought into the room.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Apr 2009
    Posts
    33
    22.46c?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by mikegar813 View Post
    22.46c?
    If you show the work leading to your answer it will be easier to check things.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Apr 2009
    Posts
    33
    30+(4-30)e^(-k2)
    k=-.5ln (10/13)
    30+(-26)e^((-3)-.5ln (10/13))=12.46
    2 minutes = 10C
    3 minutes = 12.46C
    10+12.46= 22.46C

    is this correct?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by mikegar813 View Post
    30+(4-30)e^(-k2)
    k=-.5ln (10/13)
    30+(-26)e^((-3)-.5ln (10/13))=12.46
    2 minutes = 10C
    3 minutes = 12.46C
    10+12.46= 22.46C

    is this correct?
    I have no idea what this all means. Where have you used Newton's law of cooling/warming to set up the differential equation? Where is your working for solving that differential equation?

    Please show ALL the work leading to your answer if you want your answer reviewed.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Apr 2009
    Posts
    33
    H= temperature of the object at time t
    H sub s= the constant surrounding temperature
    t= time
    H sub 0= the temperature at t=0
    H-H sub s=(H sub 0-H sub s)e^(-kt)

    I found this formula in my book.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,596
    Thanks
    1421
    So you didn't actually use "Newton' law of cooling", you used a formula derived from that.

    Okay, here H_0= 4, H_s= 30 and your formula becomes H= (4- 30)e^{kt}. You want to find H when t= 5 but you still don't know what "k" is. You can find that by using the fact that H= 10 when t= 2: 10= (4- 30)e^{2k}. Then you can find H when t= 5 by using that same k and t= 5.

    Warning: This is NOT linear! H(5) is NOT equal to H(2)+ H(3)! Do NOT find H(3), just use the formula with t= 5, not 3.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Apr 2009
    Posts
    33
    so 'k' would not change even though the 't' time does?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by mikegar813 View Post
    so 'k' would not change even though the 't' time does?
    k is a constant. It does not change.

    Were you expected to use Newton's Law of Cooling to solve this question? If yes, then the fact that k is a constant should be clear and you shouldn't be taking shortcuts by applying formulas you don't understand. If not, then the title of your post is misleading and a lot of time might have been wasted answering this question in a way that would ultimately have made no sense to you.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Newton's law of cooling.
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 11th 2010, 07:01 PM
  2. Newton's Law of Cooling/Warming
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: September 14th 2009, 12:05 AM
  3. Newton's Law of Cooling
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: August 8th 2009, 10:43 AM
  4. Newton's Law of cooling?? HELP!!
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 22nd 2009, 08:53 AM
  5. Newton's Law of Cooling
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: February 3rd 2009, 03:58 PM

Search Tags


/mathhelpforum @mathhelpforum