7.3 Heat loss through the walls of a residential structure is estimated to be 7.

Question

7.3 Heat loss through the walls of a residential structure is estimated to be 7.8 Btu/hr/ft?. The temperature differential between indoors and outdoors is 50° F. How long (years) wl it take the homeowner to recover the $0.75 per square foot cost of adding loose fill fiberglass insulation to the wall cavity at an average heating season temperature differential of 50° F? The wall with additional insulation has a new total R-value of 18.2 h ft F/Btu. A heat pump is used to heat the home at an average cost of S10.00 per 10 Btu. The heating season in five month long.

Explanation / Answer

R-value of the insulation = 18.2 h-ft2/Btu

R = dT/Q

heat transfer by the insulation Q = dT/R

tmeperature diff. = 50 F

with the insulation heat loss per hr.per sq.ft = 50/18.2 = 2.74 Btu/hr/sq.ft

heat loss without the insulator   =7.8 Btu/hr/sq.ft

Energy saved per hr per sq.ft = 7.8-2.74 = 5.06 Btu.

cost of energy /hr/sq.ft = 1.0E-5 *5.06 = 5.06 E-5 $

cost of insulation/sq.ft =0.75$

cost recovery time =0.75/5.06E-5 = 14822 hrs

heating session per yr = 5*30*24 = 3600 hrs

recover period = 14822/3600 = 4.12Yrs

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