# How Can I Measure Thermal Diffusivity of Ice and Water Using Brass Plates?

• Tsportmat
In summary, the poster is looking for help with an experiment to measure the thermal diffusivity of ice and water using 3 brass plates and thermocouples. They are struggling to understand the equation d2T/dx2 and how to obtain the thermal diffusivity from their measurements. The response suggests using Fourier's law of heat conduction and explains how to calculate the thermal diffusivity using the temperature difference between the plates and the distance between them. It also provides the derived equation for the thermal diffusivity and wishes the poster luck in their experiment.
Tsportmat

## Homework Statement

Evening everybody. I am attempting to devise an experiment in order to measure the thermal diffusivity of ice and water.

Imagine 3 brass plates, with water held between them, in approximately a 1mm gap (dx) by surface tension.
The 3 plates have thermocouples between them in order to tell the difference in temperature between them. The part I am miffed about is how to obtain the diffusivity from this measurement.

I have been given this equation to link them, but I am struggling to find where it came from and the significance if the d2T/dx2

d2T/dx2=T1-2T2/dx2+T3

dQ/dT=-D dH/dx

## The Attempt at a Solution

This is not really appropriate, as the above is an experiment plan which I have devised, I just need the final link! I apologise for not using the exact format, but any ideas or leads for me to follow up would be greatly appreciated, I've come to a dead end.

Thank you for sharing your experiment plan with us. It sounds like an interesting project! In order to obtain the thermal diffusivity from your measurements, you will need to use Fourier's law of heat conduction, which states that the rate of heat transfer through a material is proportional to the temperature gradient and the thermal conductivity of the material. This can be written as:

dQ/dt = -kA dT/dx

where dQ/dt is the rate of heat transfer, k is the thermal conductivity, A is the cross-sectional area, and dT/dx is the temperature gradient.

In your experiment, you can use the temperature difference between the three plates (T1, T2, T3) and the distance between the plates (dx) to calculate the temperature gradient (dT/dx). You can also measure the rate of heat transfer (dQ/dt) using the thermocouples.

Now, to obtain the thermal diffusivity (D), you will need to use the equation you mentioned:

d2T/dx2 = T1 - 2T2/dx2 + T3

This equation is derived from Fourier's law by assuming that the temperature gradient is constant between the plates. By substituting this equation into Fourier's law, we can solve for the thermal diffusivity:

dQ/dt = -kA (T1 - 2T2/dx2 + T3)

D = kA/(T1 - 2T2/dx2 + T3)

I hope this helps you in your experiment. Best of luck!

## 1. What is thermal diffusivity?

Thermal diffusivity is a measure of how quickly heat travels through a material. It is a ratio of the material's thermal conductivity and its heat capacity.

## 2. How is thermal diffusivity measured?

Thermal diffusivity can be measured using various techniques, such as the laser flash method, the transient plane source method, or the hot disk method. These methods involve heating a sample and measuring the temperature change over time to calculate the thermal diffusivity.

## 3. What factors affect thermal diffusivity?

Thermal diffusivity is affected by the material's density, heat capacity, and thermal conductivity. It also depends on the temperature and pressure conditions.

## 4. Why is measuring thermal diffusivity important?

Measuring thermal diffusivity is important in various industries, such as materials science, engineering, and geophysics. It helps in understanding heat transfer processes, designing efficient heat exchange systems, and predicting the behavior of materials under high temperatures.

## 5. What are some applications of thermal diffusivity?

Thermal diffusivity is used in many applications, including thermal barrier coatings, electronic packaging, thermal management of buildings, and geothermal energy production. It is also used in research and development of new materials with improved thermal properties.

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