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Guys I am living in a 500 sq ft apartment built in the 1950's and it has a south facing wall. I run the 10000 BTU AC almost 24/7 and in the afternoons the wall is very warm if not hot to the touch on the inside. and appears from the windows to be around 9 inches thick with stucco on the outside.

Because of the age and the make of the wall, I believe there is either no or little insulation. Would it be worth the cost to place rigid R type insulation over this sheet rock (drywall) on the inside and drop the temperatures?

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    Note: Code may require foam be covered with drywall for fire-safety reasons. – keshlam Jul 20 '16 at 11:49
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If the apartment is a 8" thick "cinder-block" wall with no insulation, then it's R value is likely around 1.5-2. If it's a concrete wall, it's R-value is around 3.8-4.

In any case, 1" thick polystyrene foam has an R-value of 5, and ½" drywall is about .5, so adding the foam and drywall (combined R-value of 5.5) over your existing drywall will more than double the wall's insulation value (in the case of concrete) and almost quadruple it (in the case of cinder block). All assuming there really is no existing insulation.

I would say the wall will become dramatically cooler.

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