Question

Energy conservation is important for houses. To what fraction is the heat transfer rate reduced by replacing a glass window 3 ft wide and 5 ft high with a smaller window 2 ft wide by 3 ft high? As a typical case, assume the outside temperature in the winter is 25°F and the inside temperature is 75°F. For this example assume U = 5.5 Btu/(hr)(ft2)(°F)

Answer 1

Step-by-step explanation:

Given

Initial Area
`A_1` of glass window is
`3* 5 ft^2`

Area of second window
`A_2=2* 3 ft^2`

And Heat transfer is given by

`Q=(kAdT)/(dx)`

where k=thermal conductivity

dT=Temperature difference

dx=Thickness

Assuming k,\Delta T and thickness remains same

`Q_1=(k* 15dT)/(dx)` ----1

`Q_2=(k* 6dT)/(dx)`----2

dividing 1 & 2

`(Q_1)/(Q_2)=(15)/(6)=(5)/(2)=2.5`

Thus
`(Q_1-Q_2)/(Q_1)=-0.6`

Thus heat is reduced by 60 %