Answer to Question #261341 in Molecular Physics | Thermodynamics for Mwalimu

Question

An exterior wall of a house may be approximated by a 0.1 m layer of

common brick (k = 0.7 W/m°C) followed by a 0.04 m layer of gypsum plaster (k = 0.48 W/m°C).

What thickness of loosely packed rock wool insulation (k = 0.065 W/m°C) should be added to

reduce the heat loss or (gain) through the wall by 80 per cent ?

(AMIE Summer, 1997)

Answer 1

$Q_1=\frac A{\frac{L_A}{k_A}+\frac{L_B}{k_B}}=\frac A{\frac{0.1}{0.7}+\frac{0.04}{0.48}},$

$Q_2=\frac A{\frac{L_A}{k_A}+\frac{L_B}{k_B}+\frac{L_C}{k_C}}=\frac A{\frac{0.1}{0.7}+\frac{0.04}{0.48}+\frac x{0.065}},$

$Q_2=(1-0.8)Q_1=0.2Q_1,$ $\implies$

$x=58.8~mm.$