PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
Two identical rectangular windows, each with glass thickness L=4.0mm and area A=0.40m2, are installed in adjacent rooms of a house. At night, the temperature inside both rooms is held fixed at 20∘C.
• Window 1 has ordinary single-pane glass with thermal conductivity k1=1.0W⋅m−1⋅K−1. The outdoor temperature is 0∘C.
• Window 2 has a special low-emissivity (low-"e") coating on the outer surface that lowers the glass emissivity to ε=0.10 while leaving its thermal conductivity unchanged. The same outdoor temperature of 0∘C and no wind are present.
Assume all energy transfer is perpendicular to the window surfaces, convection effects are negligible, and each window quickly reaches a steady state in which its two faces maintain constant but possibly different temperatures. The interior face of each window remains at 20∘C.
(a) For Window 1, determine the steady-state rate at which energy leaves the room through conduction only.
(b) Explain qualitatively how the presence of the low-e coating on Window 2 affects the overall energy-transfer rate, considering both radiation and conduction mechanisms.
(c) Suppose exterior measurements show that the outer surface of Window 2 stabilizes at −4∘C rather than 0∘C. Determine whether the total energy loss rate for Window 2 is larger, smaller, or equal to that found for Window 1 in part (a). Support your conclusion with quantitative reasoning, explicitly identifying any assumptions.