A room features a window equipped with a single 1.0 m 2.0 m glass of thickness 2 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 .

Step-by-step solution

The rate of heat flow through a material is given by Fourier's law of heat conduction: H = K A T d Given: Area of the glass, A = 1.0 m 2.0 m = 2.0 m ^2 Thickness of the glass, d = 2 mm = 2 10⁻³ m Temperature difference, T = 40^ C - 32^ C = 8^ C Thermal conductivity, K = 1.0 J s ⁻¹ m ⁻¹ ^ C ⁻¹ Substituting the values into the formula: H = 1.0 2.0 8 2 10⁻³ H = 16 2 10⁻³ H = 8000 J s ⁻¹