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R-value insulation problem

  1. Nov 23, 2009 #1
    1. The problem statement, all variables and given/known data
    The ceiling of a single-family dwelling in a cold climate should have an R-value of 25. To give such insulation, how thick would a layer have to be if it were made of each of the following materials?

    (a) polyurethane foam (thermal conductivity k = 0.024 W/m · K)



    2. Relevant equations
    R = L/k

    L = length(thickness)
    k = thermal conductivity



    3. The attempt at a solution

    Rk = L
    25(.024) = .6m

    My homework is telling me that I'm wrong and I have no idea why. This seems like a pretty simple and straight forward question. Can anyone help point out where I'm going wrong? Please!
     
  2. jcsd
  3. Nov 23, 2009 #2

    diazona

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    Re: R-values

    For starters, something must be wrong with that equation because the units don't work out. If R is a dimensionless number, then L and k would have the same units. But they clearly don't. So what's missing? Either there's some part of the formula you haven't written, or one of those numbers (R, L, or k, and I'm guessing R) has different units than you've stated.
     
  4. Nov 23, 2009 #3

    Delphi51

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    Re: R-values

    Could it be a confusion of units? Apparently the USA has an R value in ft²·°F·h/Btu rather than the SI units used in the rest of the world. Nice article on it at http://en.wikipedia.org/wiki/R-value_(insulation)
     
  5. Nov 29, 2009 #4
    Re: R-values

    Ah yes the units is the problem. However, now I'm having trouble converting it..here is what I did and it didn't produce the correct answer:

    .024[W/(m)(K)] x [(.3048m)^2]/1ft^2 x [(1.8K)/1 F] x (1 Btu/1055 J) x [(3600s)/1hr]

    where F = fahrenheit
     
  6. Nov 30, 2009 #5

    Delphi51

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    Re: R-values

    According to the wikipedia article
    Can you use this to convert the given R = 25? Is that 25 in metric or US units?
     
  7. Nov 30, 2009 #6

    ideasrule

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    Re: R-values

    Why (0.3048m)^2/1ft^2 and not 0.3048m/1ft?
     
  8. Nov 30, 2009 #7
    Re: R-values

    because R is given as 25 [(ft^2 * F * hr)/ (Btu)]
     
  9. Nov 30, 2009 #8
    Re: R-values

    and yes, I think that I can you use that conversion. Thanks!
     
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