How Thick Should Polyurethane Foam Be for Optimal Insulation?

[G-reg]

Homework Statement

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)

Homework Equations

R = L/k

L = length(thickness)
k = thermal conductivity

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!

 

[diazona]

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.

 

[Delphi51]

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)

 

[G-reg]

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

 

[Delphi51]

According to the wikipedia article

The conversion between SI and US units of R-value is 1 h·ft²·°F/Btu = 0.176110 K·m²/W, or 1 K·m²/W = 5.678263 h·ft²·°F/Btu.[3]

Can you use this to convert the given R = 25? Is that 25 in metric or US units?

 

[ideasrule]

Why (0.3048m)^2/1ft^2 and not 0.3048m/1ft?

 

[G-reg]

because R is given as 25 [(ft^2 * F * hr)/ (Btu)]

 

[G-reg]

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