Question

Consider two walls, A and B, with the same surface areas and the same temperature drops across their thicknesses. The ratio of their thermal conductivities is kA/kB=4 and the ratio of the wall thickness is LA/LB=2. The ratio of heat transfer rates through the walls qA/qB is:

A. 2.0
B. 0.5
C. 1.0
D. 4.0
E. 8.0

Answer 1

The ratio of heat transfer rates through Wall A to Wall B is 8.0 when given that the ratio of thermal conductivities is 4 and the ratio of wall thickness is 2, making option E correct.

Step-by-step explanation:

To determine the ratio of heat transfer rates through two walls, Wall A and Wall B, we can use the formula for heat conduction, Q/t = kA(T₂ - T₁)/d. Given that the ratio of their thermal conductivities is kA/kB = 4 and the ratio of wall thickness is LA/LB = 2, we can substitute these values into the formula to find the ratio of heat transfer rates qA/qB. Since the surface areas and temperature drops across the walls are the same, they cancel out in the ratio, and we find that qA/qB = (kA/LA)/(kB/LB) = (4k/k)/(L/2L) = (4/1)/(1/2) = 4 * 2 = 8. Therefore, the ratio of heat transfer rates through the walls is 8.0, which makes option E the correct answer.