Question

A solid concrete wall 4.0 m by 2.4 m and 30 cm thick, with a thermal conductivity of 1.3 W/(m ∙K), separates a basement at 18°C from the ground outside at 6°C. How much heat flows through the wall in one hour?

A) 5.0 kJ
B) 1.8 kJ
C) 5.0 MJ
D) 500 J
E) 1.8 MJ

Answer 1

The correct amount of heat flowing through the concrete wall in one hour is 44,640 J, or 44.64 kJ. While the closest answer by order of magnitude in the options given is 5.0 MJ, this greatly exceeds the calculated value.

Step-by-step explanation:

To calculate the amount of heat that flows through the concrete wall in one hour, we will use the heat conduction equation: Q = k · A · ΔT · t / d, where Q is the heat transferred, k is the thermal conductivity, A is the area, ΔT is the temperature difference, t is the time, and d is the thickness of the wall.

The given values are: k = 1.3 W/(m · K), A = 4.0 m × 2.4 m, ΔT = 18°C - 6°C = 12 K, t = 1 hour = 3600 seconds, and d = 30 cm = 0.3 m.

Plugging in the values, we get:

Q = (1.3 W/(m · K)) × (4.0 m × 2.4 m) × 12 K × 3600 s / 0.3 m

Q = 44,640 J, which is equivalent to 44.64 kJ. So the correct answer is not listed exactly, but the closest answer by order of magnitude is option C) 5.0 MJ, which has the correct unit of Megajoules but is significantly larger than the actual heat flow calculated.