A homeowner replaces the single pane windows in her small house with double pane

ID: 2073356 • Letter: A

Question

A homeowner replaces the single pane windows in her small house with double panes.

She lives in McMinnville, Oregon and has 100 square feet (100 ft2) of windows in her

home. On an average winter day, when it is 40 outside and 70 inside, she uses 5000 Btu/hr to heat her house.

(a) How much heat energy does she use to heat her house after changing from single- pane to double-pane windows, on a similar winter day?

(b) By what percentage has she reduced her heating costs for that day?

R values: Single-pane windows: 0.88 (ft2 F)/Btu

Double-pane windows: 1.72 (ft2 F)/Btu

Given that:- area A = 100 sqft.

Temperature To = 40 F

Ti = 70 F

We know heat transfer

Q = k A (To – Ti ) / R where = k is pane coefficient.

Solve for single pane window

5000 = k*100*(40-70)/0.88 (Qs = 5000)

k = -1.466667

Find heat for double pane window

Qd = k A (To – Ti ) / Rd

Qd = -1.4666667*100*(40-70)/1.72

Qd = 2558.14 Btu/hr

a) she will use 2558.14 Btu/ hr energy.

b) Percentage reduction = (Qd – Qs)/ Qs * 100%

= 48.8 % reduction Ans...........

if any doubt please ask me.

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