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Homework Help: Heat loss problem- thermodynamics

  1. Dec 18, 2009 #1
    1. The problem statement, all variables and given/known data

    We are heating up the cabin log with a furnace that has strength of 4 kW. The surface of the walls of the log cabin is 35 m². What is the temperature in the log cabin, if the outside temperature is -20 °C? The thermal conductivity of wood is 0.4 W/mK; the average wall thickness is 15 cm. How many degrees will be the temperature reduced in the log cabin, if we install windows into walls, through which escapes heat flow of 1800 W, and the surface area of the windows is 10 m²?

    2. Relevant equations

    ΔQ/Δt= K [AΔT/d]

    3. The attempt at a solution

    First part: What is the temperature in the log cabin, if the outside temperature is -20 °C?

    ΔQ/Δt= K [A(T(hot)-T(cold))/d]
    4000 W= 0.4 W/mK [T(hot)-253 K)/ 0.15 m
    T(hot)= 295.86 K= 22.7 C

    Are my calculations correct?

    Now, for the second part, I really don’t know how to approach it. I tried several times but my results didn’t make any sense (either too high or too low temperature). Can someone please help me?
    Thank you!
     
  2. jcsd
  3. Dec 19, 2009 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    Looks good to me.

    It is the same calculation except that you have effectively 1800 W less heat (ie. 2200 W) from the furnace and 10m^2 less wall area for the 2200 W to conduct through.

    AM
     
  4. Dec 19, 2009 #3
    Second part: How many degrees will be the temperature reduced in the log cabin, if we install windows into walls, through which escapes heat flow of 1800 W, and the surface area of the windows is 10m²?

    ΔQ/Δt= K [A(T(hot)-T(cold))/d]
    2200 W= 0.4 W/mK [25 m² (T(hot)-253 K))/ 0.15 m]
    T(hot)= 286 K= 12.9 ºC

    The temperature in the room is reduced for: ΔT= 22.7 ºC - 12.9 ºC= 9.8 ºC

    Are my calculations correct?
    Thank you for helping!
     
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