Lecture notes
Department of Architecture, Cornell University

ARCH 2614/5614 Building Technology I: Materials and Methods

Jonathan Ochshorn

Permeance Example Disclaimer

Predicting condensation within a wall is complicated; the following example is quite simplistic, as is doesn't account for all sorts of phenomena, including the ability of wet areas to dry out, or the movement of air within the wall itself, which can transport vapor in unexpected ways, or the complex hygrothermal behavior of specific materials. Nevertheless, it may provide some insight into why condensation — when it does occur — does occur.

Typical water vapor permeance values (perms*, unless otherwise noted)

concrete	3.2 perm-in.**
brick, 4" thick	0.8
concrete block, 8" thick	2.4
glazed tile masonry, 4" thick	0.12
plaster on metal lath, 3/4" thick	15
plaster on wood lath, 3/4" thick	11
gypsum board, unpainted	50
gypsum board, latex paint	2-3
plywood with exterior glue	0.7
polyethylene, 6 mil	0.06
air, still	120 perm-in.**
RCPS insulation (EPS)	2.0-5.8 perm-in.**
RCPS insulation (XPS)	1.2 perm-in.**
aluminum foil	0.001

* Note that perm values for materials listed with a given thickness may be adjusted to account for a different thickness by dividing the given perm value by the ratio of new to given thickness. So, for example, the perm value of an 8" thick brick wall would be 0.8 / (8 / 4) = 0.8 / 2 = 0.4, where 0.8 is the perm value listed for a 4"-thick wall.

** To find the perm value where units are "perm-in.," divide the tabulated value by the material's actual thickness in inches.

For materials not listed above, search online for perm values.

Example of temperature/permeance gradient diagram

Determine whether condensation might occur inside the wall shown above, consisting of (from outside to inside):

A = 12" brick
B = 3" air space
C = 2" EPS insulation board
D = 1/2" gypsum board, painted

For this example, assume steady-state temperature and water vapor conditions. The inside temperature is 70 degrees F; the outside temperature is 40 degrees F; the inside dew point is 55 degrees F, and the outside dew point is 35 degrees F. Note that the inside dew point temperature is higher than the outside dew point temperature only when the humidity has been mechanically adjusted indoors (or when humidity has been added inadvertently through various processes associated with human occupation: cooking, bathing, etc.)

Construct a section through the wall with a temperature scale superimposed. Then compute the gradients of temperature and dew point as follows:

For the temperature gradient through the wall, find all the R values for the constituent materials and compute their relative contribution to the total R-value (I have omitted the contribution of air films on the wall surfaces):

material	R-value	fraction of total R-value	change in temperature*
12" brick	2.4	2.4 / 13.85 = 0.173	0.173 x 30 = 5.2
3" air space	3.0	0.217	6.5
2" EPS	8.0	0.578	17.3
1/2" gypsum board	0.45	0.032	1.0
totals	13.85	1.00	30

* the number of degrees change in temperature within a particular material is found by multiplying the fraction of total R-value by the difference between the indoor and outdoor temperature, in this case equal to 70 - 40 = 30 degrees.

The temperature gradient (shown in black in the diagram below) can now be plotted, based on the change in temperature within each material.

For the dew point gradient through the wall, find all the perm-values (see table above) for the constituent materials and compute their relative contribution to the total "inverse" permeance":

material	perm-value	inverse perm-value	fraction of total inverse perm-values	change in dew point temperature**
12" brick	0.26	1 / 0.26 = 3.85	3.85 / 4.875 = 0.790	0.790 x 20 = 15.80
3" air space	40	0.025	0.005	0.10
2" EPS	2.0	0.5	0.1025	2.05
1/2" gypsum board	2.0	0.5	0.1025	2.05
totals		4.875	1.00	20

** the number of degrees change in dew point temperature within a particular material is found by multiplying the fraction of total inverse perm-values by the difference between the indoor and outdoor dew point temperature, in this case equal to 55 – 35 = 20 degrees.

The dew point temperature gradient (shown in green in the diagram below) can now be plotted, based on the change in dew point temperature within each material.

In the diagram above, A, B, C, and D refer to the brick, air space, insulation, and gypsum board respectively. The temperature (degrees Fahrenheit) is plotted along the vertical axis. Note that a red line has also been plotted based on the addition of a polyethylene vapor retarder just inside the gypsum board, assuming a perm value of 0.06, and no effect on the temperature (calculations for the red line are not shown). One can see that condensation may occur inside the wall, where the green line is higher than the black line. However, no condensation will occur when a vapor retarder is added, as the red line is always below the black line.