Question

The brick wall (of thermal conductivity 0.77 W/m ·◦ C) of a building has dimensions of 4.3 m by 5 m and is 19 cm thick.How much heat flows through the wall in a 7.7 h period when the average inside and outside temperatures are, respectively, 29◦C and 4◦C?Answer in units of MJ.

Answer 1

Given:

The thermal conductivity of the wall, k=0.77 W/(m·°C)

The dimensions of the wall, 4.3 m by 5 m

Thus the area of the wall, A=4.3×5=21.5 m²

The thickness of the wall, d=19 cm=0.19 m

The time period, t=7.7 h=7.7×3600=27720 s

The temperature inside the building, T₁=29 °C

The temperature outside the building, T₂=4 °C

To find:

The amount of the heat that flows through the wall in 7.7 h

Explanation:

The amount of the heat lost through the wall is given by,

$Q=\frac{ktA(T_1-T_2)}{d}$

On substituting the known values,

$\begin{gathered} Q=\frac{0.77\times27720\operatorname{\times}21.5\operatorname{\times}(29-4)}{0.19} \\ =60.38\times10^6 \\ =60.38\text{ MJ} \end{gathered}$

Final answer:

The heat that flows through the wall in the given time period is 60.38 MJ