A window used to thermally insulate a room from outside consists of two parallel glass sheets each of area 2.6 ~m ^2 and thickness 1 ~cm separated by 5 ~cm thick stagnant air. In the steady state, the room glass interface is at 18^ C and the glass-outdoor interface is at -2 ^ C . If the thermal conductivities of glass and air are respectively 0.8 Wm ⁻¹ ~K ⁻¹ and 0.08 Wm ⁻¹ ~K ⁻¹ , the rate of flow of heat through the

Step-by-step solution

According to the question, room-glass interface and glass-outdoor interface are connected in series combination so, the equivalent thermal resistance, aligned & R_ e q =R₁+R₂+R₃ & R₁= l₁ k₁ A₁ , R₂= l₂ k₂ A₂ , R₃= l₃ k₃ A₃ aligned Where, k₁ and k₃ are thermal conductivity of glass and k₂ is thermal conductivity of air. or R_ e q = l₁ k₁ A₁ + l₂ k₂ A₂ + l₃ k₃ A₃ Given, l₁=l₃=1 ~cm =10⁻² ~m , aligned l₂ & =5 ~cm =5 10⁻² ~m k₁ & =k₃=0.8 Wm ⁻¹ ~K ⁻¹, k₂ & =0.08 Wm ⁻¹ ~K ⁻¹ and A₁=A₂ & =A₃=2.6 ~m ^2 aligned Putting the