Question

Problem 8.14 A house is heated with electricity at a cost of $0.10 per kWh. The building has 20 m² of double-glazed windows with an Rsı value of 0.4. A mechanism is constructed that covers the windows with 10 cm of polystyrene foam at night (i.e., for 12 hours per day) during six months of the year. If the outside temperature is constant at 0°C and the inside temperature is kept at 20°C, calculate the annual savings from this approach.

Answer 1

- Given A house is healed ceith Elleebrécity at a cost obo $ 0.10 per khin. . The building has a double-glazed windows of 20m2 It has the Rst vailece of one A mechanism is constriected that comers the windows cecith locm of polystyrene foam all night outside temperature is constant at 0°c inside temperature is kept at 20°c = 30+273.15 = 293115 K outside temperature To = 0+243. = 273k - 6 Without the cover To = 200 1 Rs: 1 6 - 0 C ③ With coveer, it can be written as Rsil Real -0.441 ?| FOC the Rsi vaclece for the polystyrene be written as {rside = 0.03 per mm the insulation thickness of this toons Teslyp = 0.03 x 100 = 3 foam can of locom 100m

Without cover the heat transfer saule can be writtene Đ, 5 A x Or des RS - 0.4 ccheere A = Area = 20m? AT = change in temperalure DY = Inside tempercaliere cocelside temp. = Tirto = 293.15 – 273 DY = 20.15k Now the heat transfer seate becomes Oni 20 x 20.15 403 0.4 Oh = 100715 W the totoul RsI when the coveer is place RSI), = 0.61 + (RSI) p=0.5+ 3 - 315 mkle the heat tram far reate or becomes Ory= A xDT {Ret] , = 20 x 20:15 - 3.5 og = 115.141 403 3.5

The heat loss rate i{ the diffevence between a On and one 00 = Oricorn = 1006.5 -115.14 Do = 892.35 the total loss saved in 6 months period is - given by the or=0 x 6month = 892-35 x 365 x 24 o = 3908-5 kalb total cost saved i = 0.10 x 3908.5 . Total cost saved is 7:$3911 Ven