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239.


Problem 25.57 (RHK)


An idealised representation of the air temperature as a function of distance from a single-pane window on a calm, winter day is as shown in the figure. The window dimensions are . (a) We have to calculate the rate at which heat is flowing out through the window. (b) We have to estimate the difference in temperature between the inner and outer glass surfaces. We can use that the temperature drop across the glass is very small.



Solution:           Click For PDF Version

We note data from the diagram. The heat flow across the glass will be the same as the heat flow across air corridor of thickness 8 cm, when the temperature across the corridor is

The thermal conductivity of air,

Area of the glass window,

From the heat conduction formula, we calculate the heat flow from the inside to the outside across the glass window. It will be

We will next estimate the temperature difference between the inner and the outer surface of the glass-pane by using the result that 1.75 W of heat energy is flowing through it.

The thermal conductivity of glass is

Let be the temperature difference.

We use the relation