Question

You are building a new house, you can buy cheap ceiling insulation (R =11 ft2-°F-hr/Btu) or more expensive insulation (R=25 ft2-°F-hr/Btu). If the winter outside average temperature is 45°F for 4 months in HSV, and 3 months of summer (85°F). Assume that you keep the house at 70°F. • What is difference in electricity costs if electricity cost are 8 cents/kW hr? (Ahouse = 40 x30 ft) • If the difference in cost is $1,200 at time of installation, what would you recommend?

Answer 1

If insulation with R = 11 ft2-°F-hr /BTU

∆Q = 1/11 *(70-45)*(40*30)*4*30*24 BTU + 1/11 *(85-70)*3*24*(40*30) BTU = 7972363.636 BTU

If insulation with R = 25 ft2-°F-hr/ BTU

∆Q = 1/25 * (70-45)*(40*30)*4*30*24 + 1/25 *(85-70)*3*24*(40*30) = 3507840 BTU

Thus difference in electricity consumption = (7972363.636-3507840) BTU = 4464523.636 BTU

1 BTU = 0.000293071 kWh

Thus difference in electricity cost = 4464523.636*0.000293071*8/100 = $104.674

If the difference in cost is $1200 at time of installation then the benefit of electricity cost saving would require nearly 12 years to break even. However the life span of insulation is much more. Hence expensive insulation would prove cheaper in long run and the same shall be recommended.