Final answer:
The ratio of heat transfer rates through two walls with different thermal conductivities and thicknesses can be found using the given ratios. Applying these ratios to Fourier's law of heat conduction, the rate of heat transfer through wall A is double that of wall B, giving us a ratio of qA/qB = 2.0.
Step-by-step explanation:
The question relates to determining the ratio of heat transfer rates through two walls, A and B, which involves understanding the principles of thermal conduction. According to Fourier's law of heat conduction, the rate of heat transfer Q/t through a material is proportional to the thermal conductivity k, area A, and temperature difference across the material (T2 - T1), and inversely proportional to the thickness d of the material.
To compare the heat transfer rates for wall A (qA) and wall B (qB), we can use the ratios provided:
- Thermal conductivity ratio: kA/kB = 4
- Wall thickness ratio: LA/LB = 2
Since the area and temperature difference are the same for both walls, these factors cancel out when taking the ratio of heat transfer rates. We apply the ratios to the formula, giving us:
qA/qB = (kA * A * (T2 - T1))/(LA) / (kB * A * (T2 - T1))/(LB)
Solving the ratios, we have:
qA/qB = (4 * LB)/(2 * LA) = (4 * LB)/(2 * LB) = 4/2 = 2
Therefore, the ratio of heat transfer rates qA/qB is 2.0, meaning option B is the correct answer.