A room features a window of dimensions 1.0 m 2.0 m equipped with two glasspanes. Each glasspane has a thickness of 1 mm and they are separated by an air gap of 1 mm . Determine the rate of heat flow through the closed window if the temperature inside the room is 32^ C while the outside temperature is 40^ C . The thermal conductivity of the window glass is 1.0 J s ⁻¹ m ⁻¹ ^ C⁻¹ and that of air is 0.025 J s ⁻¹ m ⁻¹ ^ C

Step-by-step solution

Area of the window, A = 1.0 2.0 = 2.0 m ^2 Thickness of each glass pane, d_g = 1 mm = 10⁻³ m Thickness of the air gap, d_a = 1 mm = 10⁻³ m Temperature difference, T = 40^ C - 32^ C = 8^ C The system consists of two glass panes and one air gap connected in series. The equivalent thermal resistance is given by: R_ eq = R_ g1 + R_a + R_ g2 = d_g K_g A + d_a K_a A + d_g K_g A R_ eq = 2d_g K_g A + d_a K_a A Substituting the given values: R_ eq = 2 10⁻³ 1.0 2.0 + 10⁻³ 0.025 2.0 R_ eq = 10⁻³ + 10⁻³ 0.05 = 10⁻³ + 20 10⁻³ =