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Sometimes we can develop equations and solve practical problems by knowing nothing more than the dimensions of the key parameters in the problem. For example, consider the heat loss through a window in a building. A certain manufacturer advertises a double-pane window with an R value of 2. The same company produces a triplepane window with an R value of 3. In either case the window dimensions are 3 ft by 5 ft. On a given winter day, the temperature difference between the inside and outside of the building is 45 o F. The propane burner is 80 percent efficient. Propane has approximately 90, Btu of available energy per gallon. In that same h period, how much money would a homeowner save per window by installing triplepane rather than double-pane windows? A typical winter has the equivalent of about heating days at a temperature difference of 45 o F. Ignoring interest and inflation, how many years will it take the homeowner to make up the additional cost of the triple-pane windows from heating bill savings? Write the relation for the in terms of , , , and such that the units are in. Here, the time period is , temperature difference is , the area is , and the factor is.

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