Question Help Consider a house in Blacksburg, Virginia. The typical annual space

Question

Question Help Consider a house in Blacksburg, Virginia. The typical annual space-heating load for this size of a house is 100 x 106 Btu. That is, with no insulation in the attic, we lose about 100 × 106 Btu per year. With insulation in the attic the amount of heat lost each year will be reduced. The value of energy savings that results from adding insulation and reducing heat loss is dependent on what type of residential heating furnace is installed. Assume that an electrical resistance furnace is installed by the builder, and its efficiency is near 100%. The cost of electricity is $0.16 per kWh. The cost of several insulation altematives and associated space-heating loads for this house are given in the following table. Which amount of attic insulation is most economical? The life of the insulation is estimated to be 25 years R11 2,400 739 × 106 R19 3,700 70 x 10 Amount of Insulation R30 5,200 R38 6,600 66 x 10 Investment cost ($) Annual heating load (Btu/year) 67.1x106 Recall that 1 Btu = 0.293 Wh and calculate the cost of electricity per million Btu Fill in the table below. (Round to the nearest cent.) R11 R19 R30 R38 Investment cost (S) Cost of heat loss per year (S) Cost of heat loss over 25 years ($) Total life cycle costs ($) To minimize total life-cycle costs, select insulation

Explanation / Answer

Annual heat loss without insulation = 100 x 106 Btu = 2.93 x 107kWh

To calculate cost of heat loss per year,

= heat loss x cost per unit

For R11 , annual heating load = 73.9 x 106 Btu = 21.65 x 106 kWh

Cost of heat loss = (100-73.9) x 106 Btu x (0.293 kWh/Btu) x (0.16 $/ kWh) = 1.22 x 106 $ /year

Cost of heat loss over 25 years = 1.22 x 25 x 106 $ = 30.5 x 106 $

Total life cycle cost = cost of heat loss over 25 years + investment cost = 30.5 x 106$ + 2400$ = 30. x 106 $

From above table it is clear the total life cycle cost is minimum for R11. Hence, most economical.

R11 R19 R30 R38 Investment cost 2400 3700 5200 6600 Cost of heat loss/year ($) 1.22 x 106 1.41 x 106 1.54 x 106 1.59 x 106 cost of heat loss over 25 years ($) 30.5 x 106 35.16 x 106 38.55 x 106 39.84 x 106 Total life cycle cost ($) 30.502 x 106 35.163 x 106 38.564 x 106 39.865 x 106

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.