Question

Which of the following two windows would insulate better, and by how many times lower would the rate of thermal conduction through it be compared to the other? Take both to be airtight and ignore radiative losses. Each window has a total size of 1.2 m high by 0.6 m wide, with the outer 2 cm edge of each window being the frame. For simplicity, take the frames to have the same thickness as the pane (of course for a real window, the frame would be slightly thicker, and the pane would extend into the pane to be secured, but let us keep the window a bit simpler for this problem). For the first window, let the frame be solid wood with thermal conductivity of 0.1 W/(m*K), and the pane is solid glass with thermal conductivity of 0.8 W/(m*K). For the second window, let the frame by two thin pieces of steel (each 1/10 of the total thickness), with an air gap in between. The steel has a thermal conductivity of 50 W/(m*K), and air has a thermal conductivity of 0.025 W/(m*K). The pane is made of two thin layers of glass (each 1/3 of the total thickness), with an air gap in between. The glass used is the same type as that used in the first window.

Answer 1

window 1 is similar as

let the first part be K₁ and second be K₂

now K₁ =

substituting the values we get K₁ = 0.726

now same formula but different values for K₂

now K₂ = 0.717

now K _net = K₁/2+K₂/ 2 =0.7218

now window 2

nowwe can see that window 2 is better insulator and by  10.76 times

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-V.K