ANS:C - k_A < 0.5k_B

To analyze this scenario, let's consider the heat conduction through the composite wall. The rate of heat conduction through each plate can be expressed using Fourier's law of heat conduction: Q=Lk⋅A⋅ΔT​ Where:

• Q is the rate of heat transfer,
• k is the thermal conductivity of the material,
• A is the cross-sectional area through which heat flows,
• ΔT is the temperature difference across the plate, and
• L is the thickness of the plate.

For plates A and B in series, the total rate of heat transfer must be the same through both plates at steady state. Given that plate B has twice the thickness of plate A, we can express the total rate of heat transfer as: Qtotal​=QA​+QB​ Since QA​ and QB​ are both equal to⋅ΔLk⋅A⋅ΔT​ (using the same temperature difference ΔT across both plates), we have: total=⋅Δ⋅Δ2Qtotal​=LkA​⋅A⋅ΔT​+2LkB​⋅A⋅ΔT​ total=2+2⋅⋅ΔQtotal​=22kA​+kB​​⋅A⋅ΔT Now, let's consider the conditions for the temperature difference across plate A to be greater than that across plate B:

1. If CPA​>CPB​: This condition involves specific heat capacities and does not directly affect the temperature difference across the plates. Therefore, it is not the correct answer.
2. If kA​<0.5kB​: If the thermal conductivity of plate A (kA​) is less than half of the thermal conductivity of plate B (kB​), then the temperature difference across plate A will be greater than that across plate B. This is because plate A offers more resistance to heat flow due to its lower thermal conductivity.
3. If kA​>2kB​: This condition means that the thermal conductivity of plate A (kA​) is more than twice the thermal conductivity of plate B (kB​). In this case, plate A will offer less resistance to heat flow compared to plate B, potentially resulting in a smaller temperature difference across plate A.

Therefore, the correct condition for the temperature difference across plate A to be greater than that across plate B is if kA​<0.5kB​.