Question

A 2.0 m2 Thermopane window is constructed, using two layers of glass that are each 4.0 mm thick, separated by an air space of width ∆x. The temperature difference is 20◦C from the inside of the house to the outside air, and the rate of heat flow through the window is P = 640W. Determine the thickness of the air space. (Thermal conductivity for glass is 0.84 J/s·m·◦C and for air 0.023 4 J/s·m·◦C.) a. 0.38 mm b. 0.77 mm c. 1.22 mm d. 3.49 mm

Answer 1

The thickness of the air space in the Thermopane window is 0.77 mm.

Step-by-step explanation:

To determine the thickness of the air space in the Thermopane window, we can use the formula for heat conduction through a composite material. The rate of heat conduction through the window can be calculated using the formula P = (k1 * A * (T1 - T2))/L1 + (k2 * A * (T1 - T2))/L2 + (k3 * A * (T1 - T2))/L3, where P is the rate of heat flow, k1 and k2 are the thermal conductivities of the glass layers, L1 and L2 are the thicknesses of the glass layers, k3 is the thermal conductivity of air, L3 is the thickness of the air space, A is the area of the window, T1 is the inside temperature, and T2 is the outside temperature.

In this case, we have P = 640W, A = 2.0 m², k1 = k2 = 0.84 J/s·m·◦C, L1 = L2 = 4.0 mm = 0.004 m, k3 = 0.0234 J/s·m·◦C, T1 - T2 = 20◦C. Solving for L3, we find that the thickness of the air space is 0.77 mm.