A solid concrete wall has dimensions 4.0 m × 2.4 m and is 30 cm thick.The thermal conductivity of the concrete is 1.3 W/m ∙ K,and it separates a basement from the ground outside.The inner surface of the wall is at 18°C,and the outside surface is at 6°C.How much heat flows through the wall every hour?
A)1.8 MJ
B)1.8 kJ
C)500 J
D)5.0 MJ
E)5.0 kJ

Question

Quizplus · Accepted Answer

The heat flow through the wall can be calculated using the formula $Q = \frac{kA(T_{hot} - T_{cold})t}{d}$, where $Q$ is the heat flow, $k$ is the thermal conductivity, $A$ is the area of the wall, $T_{hot} - T_{cold}$ is the temperature difference across the wall, $t$ is the time, and $d$ is the thickness of the wall.Given:- $k = 1.3 \, \text{W/m} \cdot \text{K}$- $A = 4.0 \, \text{m} \times 2.4 \, \text{m} = 9.6 \, \text{m}^2$- $T_{hot} - T_{cold} = 18^\circ\text{C} - 6^\circ\text{C} = 12 \, \text{K}$- $t = 1 \, \text{hour} = 3600 \, \text{s}$- $d = 30 \, \text{cm} = 0.3 \, \text{m}$Substituting these values into the formula gives:$$Q = \frac{1.3 \times 9.6 \times 12 \times 3600}{0.3} = 1,814,400 \, \text{J} = 1.8 \, \text{MJ}$$Therefore, the correct answer is 1.8 MJ.

A Solid Concrete Wall Has Dimensions 4