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Chapter 11: Problem 22

The temperature drop through a two-layered furnace wall is \(900^{\circ} \mathrm{C}\). Each layer is of equal area of cross-section. Which of the following actions will result in lowering the temperature \(\theta\) of the interface? (A) By increasing the thermal conductivity of outer layer (B) By increasing the thermal conductivity of inner layer (C) By increasing thickness of outer layer (D) By increasing thickness of inner layer

Short Answer

Expert verified
The methods to lower the temperature of the interface are (C) By increasing the thickness of the outer layer and (D) By increasing the thickness of the inner layer.

Step by step solution

01

Understanding thermal conductivity and its influence

Thermal conductivity is a property of a material that indicates its ability to conduct heat. In this context, if the thermal conductivity of a layer is increased, it will facilitate heat conduction, thus raising the temperature of the interface.
02

Understanding effect of thickness on heat transfer

The thickness of a layer determines how much material the heat must traverse to get to the next layer. The greater the thickness, the more the layer resists heat transfer. Hence, increasing the thickness of a layer would actually lower the temperature at the interface because less heat managed to cross this layer.
03

Evaluating the multiple choice options

Now we can evaluate the given options: (A) Increasing the thermal conductivity of the outer layer would increase the heat transfer through this layer, thus increasing the temperature at the interface between the layers, not lowering it. (B) If the thermal conductivity of the inner layer is increased, it will also conduct more heat towards the interface, hence increasing the temperature there, not lowering it. (C) Increasing thickness of the outer layer increases the resistance to heat transfer hence lowering the temperature at the interface. (D) Adding to the thickness of the inner layer also increases the resistance to heat transfer but from the interface side, hence lowering the temperature at the interface.

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