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

Answer:

Explanation:

Given

Initial Area $A_1$ of glass window is $3\times 5 ft^2$

Area of second window $A_2=2\times 3 ft^2$

And Heat transfer is given by

$Q=\frac{kAdT}{dx}$

where k=thermal conductivity

dT=Temperature difference

dx=Thickness

Assuming k,\Delta T and thickness remains same

$Q_1=\frac{k\times 15dT}{dx}$ ----1

$Q_2=\frac{k\times 6dT}{dx}$----2

dividing 1 & 2

$\frac{Q_1}{Q_2}=\frac{15}{6}=\frac{5}{2}=2.5$

Thus $\frac{Q_1-Q_2}{Q_1}=-0.6$

Thus heat is reduced by 60 %