Proving a thermal conductivity/resistance formula.

In summary, the figure shows a block with two materials of different thickness and thermal conductivities, with temperatures Thigh and Tlow on the outer surfaces. The thermal resistance equation R = l/λ can be used to find the temperature Tx at the interface of the block, given by Tx = R1Thigh + R2Tlow/R1 + R2. Two separate equations for heat flow through each block can be used, with common unknowns, similar to two electrical resistors in series between two voltages.
  • #1
thatguythere
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Homework Statement


The figure below shows a block that consists of two materials with different thicknesses l 1 and l 2 and different thermal conductivities λ1 and λ2. The temperatures of the outer surfaces of the block are Thigh and Tlow, as shown in the figure. Each face of the block has a cross-sectional area A. Using the thermal resistance equation R = l/λ,show that the temperature Tx at the interface of the block is given by:
Tx = R1Thigh + R2Tlow/R1 + R2


Homework Equations


R=l/λ


The Attempt at a Solution


I'm not even sure where to begin. A nudge in the right direction would be greatly appreciated.
 

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  • #2
You will need a separate equation for the heat flow through each block. (I assume you have an equation relating heat flow, temperature difference etc.) Invent unknowns as necessary. Some unknowns will be common to the two equations.
 
  • #3
Think about two electrical resistors in series between a voltage of Vhigh and Vlow. Get the voltage at the junction of the two resistors.
 

1. What is thermal conductivity and why is it important?

Thermal conductivity is the measure of a material's ability to conduct heat. It is an important property to understand in order to optimize the efficiency of thermal systems and to select appropriate materials for specific applications.

2. How is thermal conductivity measured?

Thermal conductivity is typically measured using a device called a thermal conductivity meter, which measures the rate at which heat passes through a material. This can also be calculated using the formula: thermal conductivity = (heat flow * thickness) / (area * temperature difference).

3. What is the difference between thermal conductivity and thermal resistance?

Thermal conductivity is a measure of a material's ability to conduct heat, while thermal resistance is a measure of how much a material resists the flow of heat. They are inversely related, meaning that materials with high thermal conductivity have low thermal resistance and vice versa.

4. How can a thermal conductivity/resistance formula be proven?

A thermal conductivity/resistance formula can be proven through experimental data and mathematical calculations. This involves conducting experiments to measure the thermal conductivity of different materials, and then using these values in the formula to determine if it accurately predicts the results.

5. What factors can affect thermal conductivity and resistance?

Several factors can affect thermal conductivity and resistance, including the material's composition, density, and temperature. Other factors such as moisture content, porosity, and surface roughness can also impact these properties. Additionally, the presence of air gaps or other insulation materials can affect thermal conductivity and resistance.

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