# Two different thermal conductivity constants

• a_lawson_2k
In summary, the question asks for the temperature of the blackened end of a solid cylindrical copper rod, which is 0.2m long and has one end maintained at 20K while the other is exposed to thermal radiation from surrounding walls at 500K. The rod is insulated, meaning no energy is lost or gained except at the ends. Using the equation H = dQ/dt = kA(T_h-T_c)/L, where H is the heat flux, dQ/dt is the rate of change of heat, k is the thermal conductivity constant, A is the cross-sectional area of the rod, T_h is the temperature of the hot end, T_c is the temperature of the cold end, and L is
a_lawson_2k

## Homework Statement

Solid cylindrical copper rod 0.2m long has one end maintained at temperature 20K, other end blackened and exposed to thermal radiation from surrounding walls at 500K. As the rod is insulated, no energy is lost or gained except at the ends of the rod. When equilibrium is reached, what is the temperature of the blackened end? hint: at 20K, copper's thermal conductivity constant is 1670 W/(mK), so the blackened end will only be slightly over 20K

## Homework Equations

$$H=\frac{dQ}{dt}=kA\frac{T_h-T_c}{L}$$

## The Attempt at a Solution

Thus far, I'm not sure how to approach it given the presence of two different thermal conductivity constants; the one specified in the book is 385, but the other specified is only for one specific circumstance...

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I don't see how to do that, as I was not given a constant of emissivity. All I have is an equation which, frankly, I'm not sure how to apply here. The only example in the book with two heat currents was one with two rods between each heat/cooling source...how would you set it up?

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## 1. What is thermal conductivity and why does it have two different constants?

Thermal conductivity is the measure of a material's ability to conduct heat. The two different constants, also known as thermal conductivities, refer to the different directions of heat transfer in a material. These directions are known as the longitudinal (along the length of the material) and transverse (across the width of the material) directions.

## 2. How are the two thermal conductivity constants different from each other?

The longitudinal thermal conductivity is typically higher than the transverse thermal conductivity. This is because heat is more easily transferred in the direction of the material's fibers or particles, compared to across them.

## 3. Why is it important to know both thermal conductivity constants?

Knowing both constants is important for accurately predicting the heat transfer in a material. For example, in a building insulation material, the longitudinal thermal conductivity would be more important to consider as heat primarily travels in that direction. However, in a material used for electronic devices, both constants may be important to consider as heat can transfer in multiple directions.

## 4. Can the two thermal conductivity constants change?

Yes, the thermal conductivity constants can change based on various factors such as temperature, pressure, and the composition of the material. For example, some materials may have a higher longitudinal thermal conductivity at higher temperatures, while others may have a higher transverse thermal conductivity at lower pressures.

## 5. How are the two thermal conductivity constants measured?

The two thermal conductivity constants can be measured using different techniques such as the guarded hot plate method, the hot wire method, or the laser flash method. These methods involve applying a known heat source to one surface of the material and measuring the temperature difference across the material in both the longitudinal and transverse directions.

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