Evaluate the improvement in heat loss afforded by a double p

Evaluate the improvement in heat loss afforded by a double pane glass window with dead air space between the panes, versus a single pane glass window (see figure below). The situation indicated in the figure represents a heated home in a northern climate during winter conditions outside. Given the dimensions, k values for glass and air in Appendix A and an indoor temperature (equals inner glass temp) of 20 C and an outdoor (outer glass temp) of -10 C, then calculate: Heat transfer rate (W) for single glass pane (glass is 1/4 inch thick) system, with glass dimensions of 1 m x 1 m; Heat transfer rate (W) for double glass pane system (same glass thickness, air space is 3/8-inch thick) and same glass dimensions; What is the percent improvement (or decrease) of the double pane system over the single pane system?

Solution

a. Heat transfer rate, Q = kAdT/dx
Q for single glass pane (025 inch thich = 0.00635 m thick) = kA((20+10)/0.00635) = kA4724.409449 W
k = 0.19 for plexiglass
Q = 897.6377 W
b. Q = kA(20 - T)/0.00635 = 2k\'A(T - T\')/3*0.00635 = kA(T\' + 10)/0.00635
20 - T = T\' + 10
T\' = 10 - T
also, 2k\'(T - 10 + T) = 3k(20 - T)
k\' for air = 0.0260
so, 0.104T - 0.52 = 11.4 - 0.57T
T = 17.6854 C
Q = 69.2539 W
c. Percent improvemnt = (heat loss prevented)/original heat loss = 92.384 pc