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# Explanation of Insulation R-Value

The second laws of thermodynamics states that heat spontaneously flows from bodies at higher temperature to bodies at lower temperature. Thus, it is an inevitable outcome of all systems left to their own devices to eventually reach thermal equilibrium. The purpose of insulation is to reduce the speed at which equilibrium is reached. Insulation reduces the rate at which heat is conducted between two bodies. The “quality” of insulation is often rated using a ratio called R-value which is defined as the ratio of the temperature difference between the bodies between which the insulation is placed over the rate of heat flow across the insulation per unit area. More compactly,

``R = ΔT/[(dQ/dt)/A]``

where `T` is temperature, `Q` is heat, `t` is time, and `A` is surface area. The SI units for `R` are `K m2 s/J` or `K m2/W` however, most insulations sold in the US use the convoluted units of `oF ft2 h/BTU`.

The larger an insulations R-value, the better it is at slowing the flow of heat.

More insight into the meaning of R-value can be had by considering a different but equivalent definition. R-value is also the ratio of an insulations thickness over the thermal conductivity of the material from which it is made. More compactly,

``R = L/k``

where `L` is thickness and the thermal conductivity `k` has SI units of `W/(K m)` and Imperial units of `BTU/(hr ft oF)`.

In this form, it can be seen that the thicker the insulation, the higher its R-value and the better it is at slowing the flow of heat. Two different insulations may have different R-values even if they are made out of the same material if they have different thicknesses. For this reason, R-value, like weight, is an extrinsic property of insulation. On the other hand, insulation’s thermal conductivity is an intrinsic property of the material from which it is made.

Since R-value depends only on thickness and thermal conductivity, it is additive if two or more pieces of insulation are combined. For example, if one were to sandwich two pieces of foam insulation with R-values of 5 and 8, respectively, the combination would have an R-value of 13.