Results 1 to 3 of 3

Math Help - Temperature in a Room

  1. #1
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9

    Temperature in a Room

    Say I have a rectangular room (so its volume is easy to find) and an air conditioner that cools this room. I know the initial state of the room without the air conditioner and cool this room eventually to the same temperature as the air conditioner. I turn off the air conditioner. How much time does it take for the room to heat up to its initial state?

    My idea: Maybe we can use Newton's Law of Cooling (or Heating) here somehow? But I think the volume has something to do with the solution to this problem.
    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 ThePerfectHacker View Post
    Say I have a rectangular room (so its volume is easy to find) and an air conditioner that cools this room. I know the initial state of the room without the air conditioner and cool this room eventually to the same temperature as the air conditioner. I turn off the air conditioner. How much time does it take for the room to heat up to its initial state?

    My idea: Maybe we can use Newton's Law of Cooling (or Heating) here somehow? But I think the volume has something to do with the solution to this problem.
    You would normaly assume that the rate of change of temprature with the
    air conditioner turned off is:

    <br />
\frac{dT_{room}}{dt}=k(T_{ambient}-T_{room})<br />

    and (oversimplifying) that when the airconditioner is on that:

    <br />
\frac{dT_{room}}{dt}=k(T_{ambient}-T_{room})-K<br />

    The essential assumption is that the air conditioner removes heat at a constant rate,
    while heat flows into the room at a rate proportional to the temprature difference.

    The problem is that the thermal capacity and heat loss constant for a room
    are difficult things to calculate. There are tools to do so but I doubt you
    will want to look for them.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,939
    Thanks
    338
    Awards
    1
    Quote Originally Posted by ThePerfectHacker View Post
    Say I have a rectangular room (so its volume is easy to find) and an air conditioner that cools this room. I know the initial state of the room without the air conditioner and cool this room eventually to the same temperature as the air conditioner. I turn off the air conditioner. How much time does it take for the room to heat up to its initial state?

    My idea: Maybe we can use Newton's Law of Cooling (or Heating) here somehow? But I think the volume has something to do with the solution to this problem.
    And a spherical room would be much simpler to work with.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Room assignments
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: July 31st 2010, 09:36 AM
  2. A room is 25 ft
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 31st 2010, 09:35 AM
  3. In a certain class room
    Posted in the Statistics Forum
    Replies: 7
    Last Post: December 29th 2009, 08:29 PM
  4. Room Assignments
    Posted in the Statistics Forum
    Replies: 1
    Last Post: January 29th 2007, 12:26 PM

Search Tags


/mathhelpforum @mathhelpforum