insulation

Single pane windows are terrible insulators.   So much so, that covering up my windows with clear plastic wrap cut my electric bill from $50 in january to $25 in february.   The plastic wrap blocks convection.   The windows are the weakest link by far -- there's no point in improving wall insulation when you lose 90% of the heat through the windows anyway.   You can approximate the relative amount of energy loss through a surface by measuring its interior surface temperature.  For example, the wall surface is only 1 degree below room temperature, while the window surface is 40-50 degrees below room temperature, which basically proves that the windows are hemorrhaging energy.   The relationship between convective heat transfer and temperature difference is probably between linear and quadratic in this case, because larger temperature differences cause faster flows of air over the surface.  (bouyancy would be linear but drag would be roughly quadratic so I'd expect the speed of the air flow to increase as the square root of delta T)   Black body radiation is neglegible compared to convection at these temperatures.  So in this example the windows must have *at least* 50 times the conductivity of the walls, but the figure is probably more like 300 times.

 100% of my electricity consumption goes to heat the apartment, because all electricity consumed by electrical appliances or the heater is converted into heat, by the law of conservation of energy (ignoring the negligible amount of EM that might be produced by these devices and escape the apartment).    So as long as it's really cold outside, my electric consumption is determined by only two things:

1. The conductivity of the apartment.

2. The temperature difference that I want to maintain between the apartment and the outside. 

Asking which of these is more important is like asking whether the length or the width contributes more to the area of a rectangle.      Improving the wall insulation without doing something about the windows would be like putting a fifth lock on the front door while leaving the back door wide open.

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