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Document1-Word PAGE LAYOUT REFERENCES MAILINGS REVIEW VIEW Foxit PDF 1-Normal]1No Spac . .E- Paragraph Heading 1 Heading 2 Font Styles Example 2.7 Consider a 2400 ft? single-story house. The typical annual space heating load for this size of house is 100 x 10 Btu. That is, with no insulation, the house will lose 100 x 10 Btu of heat per year Thus, we want reduce the annual heat loss by installing insulation The energy savings of the insulation are dependent on the heating furnace installed in the house. For this purpose, we will assume the furnace installed will have an efficiency near 100% 2-28. According to the U.S. Department of the Interior, the amount of energy lost because of poorly insulated homes is equivalent to 2 million barrels of oil per day. In 2009, this is more oil than the United States imports from Saudi Arabia each day. If we were to insulate our homes as determined by Example 2-7, we could eliminate our oil dependence on Saudi Arabia. If the cost of electricity increases to $0.15 per kWh and the cost of insulation quadruples, how much insulation should be chosen in Example 2-7? (2.3)

Explanation / Answer

Total heat Insulated = 100*10^6 BTU per year

Insulation Area = 2400 ft2

Therefore Insulation capacity = 100*10^6/2400 = 41667 BTU/ft2/year

To Maintain the heat load inside the house, we have two options

1) Proper insulation to reduce heat loss

2) Compensate heat loss by adding extra energy using electrical heater

Electrical cost = $0.15/KWH

1 KWH = 3412.14 BTU

Therefore, Electrical Cost = $0.15/3412.14 BTU = S 4.39*10^-5 /BTU

Let Initial Insulation cost = $I/ft2

Therefore, Initial Insulation cost = I*2400 ft2 -(1)

In current situation,

Insulation cost = $4*I/ft2

Let's assume 'A' Ft2 area be covered with Insulation and Heat losing via remaining (2400-A) Ft2 be compensated by Electricity.

Then, Current cost = 4*I*A+41667*(2400-A)*4.39*10^-5 -(2)

Because (1) = (2)

2400*I = 4*I*A+41667*(2400-A)*4.39*10^-5

Therefore A = (2400*I-41667*2400*4.39*10^-5)/(4*I-41667*4.39*10^-5) ft2

Since, No information is given to calculate initial Insulation cost, I

Assuming, I = $10/Ft2

Then required Insulation Area, A = 514 ft2

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