FYKOS Year 31 Series 5 Problem 4 — thermal losses · FYKOS 31 #31.5.4

Physics · thermodynamics

Problem

At what temperature does the indoor environment of the flat in a block of flats stabilise? Consider that our flat is adjacent to other apartments (except its shorter walls), in which the temperature 22 \C22 \mathrm{\C} is maintained. The shorter walls adjoin the surroundings where the temperature is −5 \C - 5 \mathrm{\C}. The inside dimensions of the flat are height h=2,5 m h = 2{,}5 \mathrm{m}, width a=6 m a = 6 \mathrm{m} and length b=10 m b = 10 \mathrm{m} . The coefficient of the specific thermal conductivity of the walls is λ=0,75 W⋅K−1⋅m−1 \lambda = 0{,}75 \mathrm{W\cdot K^{-1}\cdot m^{-1}} . The thickness of the outer walls and the ceilings are D_out=20 cm D\_{out} = 20 \mathrm{cm}, and the thickness of the inner walls are D_in=10 cm D\_{in} = 10  \mathrm{cm}. How will the result be changed if we add polystyrene insulation to the building? The thickness of the polystyrene is d=5 cm d = 5 \mathrm{cm}, and its specific heat conductivity is λ′=0,04 W⋅K−1⋅m−1 \lambda '= 0{,}04 \mathrm{W\cdot K^{-1}\cdot m^{-1}} .

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