Question

A wall in a house contains a single window. The window consists of a single pane of glass whose area is 0.15 m2 and whose thickness is 1.9 mm. Treat the wall as a slab of the insulating material Styrofoam whose area and thickness are 15.00 m2 and 0.110 m, respectively. Heat is lost via conduction through the wall and the window. The temperature difference between the inside and outside is the same for the wall and the window. Of the total heat lost by the wall and the window, what is the percentage lost by the window? (The thermal conductivity for glass window is kG = 0.80 J/(s·m·C°), and the thermal conductivity for Styrofoam is kS = 0.010 J/(s·m·C°).) Percentage lost by window = %

Answer 1

Area of window = A₁ = 0.15 m²

Thickness of window = t₁ = 1.9 mm = 1.9 x 10^-3 m

Area of wall = A₂ = 15 m²

Thickness of wall = t₂ = 0.11 m

Thermal conductivity of glass window = k_G = 0.8 J/(s.m.^oC)

Thermal conductivity of styrofoam = k_S = 0.01 J/(s.m.^oC)

Temperature difference between inside and outside of the wall and window = T

Heat lost by the window = H₁

Heat lost by the wall = H₂

H₁ = 63.157(T) J/s

H₂ = 1.363(T) J/s

Percentage heat lost by window = P

P = 97.88%

Percentage heat lost by the window = 97.88%