The percentage of a building exterior that is glass is

Chapter 9, Problem 9.5.38

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The percentage of a building exterior that is glass is very important because the highest heat energy losses occur through glass areas. Roofs and walls can be much better insulated than glass and have a much higher resistance to transmission of heat. To estimate the effect of glass percentage G (in decimal form) on heat loss, we look at average resistance Rt for the total building exterior, using Rg for glass resistance to heat transmission and Rw for roof and wall resistance. Heat transmission loss, Ut , through the exterior can then be found using Rt . Ut is the heat loss for 1 square foot per hour per degree Fahrenheit temperature difference from inside to outside of the building exterior, measured in British thermal units. Rt 5 GRg 1 (1 2 G)Rw Ut 5 1 Rt 9.6 Exploring, Extending & Expanding 599 where (1 G) is the decimal percent of the rest of the building exterior, walls, and roof. a. Simplify the formula for Rt , then use it to find a formula for Ut . b. On the same grid, using G as the horizontal axis, plot your heat loss formulas for the following cases: i. Old house with Rg 1 and Rw 10 ii. Typical modern house with Rg 2 and Rw 20 iii. Energy saving house with Rg 5 and Rw 60 c. The typical modern house can be improved by just changing the windows so that Rg 5, Rw 20. On the same graph, plot this improved house with the typical modern house from part (ii) above. Does improving the windows make a substantial reduction in heat loss? 9.6 Expl