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 thermal energy flows through the wall every hour?

Question

Quizplus · Accepted Answer

First, we need to calculate the area of the wall:
Area = 4.0m × 2.4m = 9.6 m²

Next, we need to convert the thickness of the wall to meters:
Thickness = 30 cm = 0.3 m

The thermal resistance of the wall is then given by:
R = Thickness / Thermal conductivity = 0.3m / 1.3 W/m∙K = 0.23 m²∙K/W

Using the formula for heat flow through a wall, we can calculate the heat transfer rate:
Q = (Temperature difference) / (Thermal resistance) × Area
Q = (18°C - 6°C) / 0.23 m²∙K/W × 9.6 m²
Q = 47.83 W

To convert to energy per hour, we multiply by the number of seconds in an hour:
47.83 W × 3600 s = 172,188 J/h

Finally, we convert to MJ:
172,188 J/h = 0.172188 MJ/h

Therefore, the thermal energy that flows through the wall every hour is 1.8 MJ (rounded to one decimal place).

A Solid Concrete Wall Has Dimensions 4