How Can Low Temperature Systems Be Used to Measure Thermal Properties?

[enyce]

This is my solid state physics report questions but I think it's related to thermodynamics or something. I have never taken a course in that respect and I have no clue . Please tell me what books or websites I can look for the answer. THX!
1. Lattice heat capacity Debye T3 law is valid only at low temperature. How to decrease and measure the sample temperature from 300 K down to 1-2 K?
(Hint: check the low pressure He4 phase diagram)
2. Describe as much as you can on the principle of any low temperature heat
transport system to measure the temperature variation of thermal conductivity κ(T) down to 1-2 K?
(Hint) ju = - κ∇T with κ = (L/A)(ΔW/ΔT) for a long rod sample with uniform cross section A and L = Δx between temperature difference ΔT, where K ≡ ΔW/ΔT is thethermal conductance

 

[Jhero]

Hello,

Thank you for your questions. It is great to see your interest in solid state physics and thermodynamics. I would recommend the following books and websites for further reading on these topics:

1. "Introduction to Solid State Physics" by Charles Kittel - This is a classic textbook that covers the basics of solid state physics, including lattice vibrations and heat capacity.

2. "Thermodynamics" by Enrico Fermi - This book provides a thorough introduction to thermodynamics and its applications in various fields, including solid state physics.

3. "Low Temperature Physics" by John M. Goodkind - This book specifically focuses on the principles and techniques used in low temperature physics, including methods for measuring temperature and thermal conductivity.

In addition to these resources, I would also recommend checking out online lecture notes and tutorials from universities such as MIT, Stanford, and Caltech. These can provide a more in-depth understanding of the concepts and equations involved in your questions.

Now, let's address your specific questions:

1. To decrease the sample temperature from 300 K down to 1-2 K, you can use a cryogenic system such as a dilution refrigerator or a He3/He4 dilution refrigerator. These systems use liquid helium as a coolant to achieve very low temperatures. The low pressure He4 phase diagram can help you understand the behavior of liquid helium at different temperatures and pressures.

2. The principle of a low temperature heat transport system is to use a temperature gradient to measure the thermal conductivity of a material. This is achieved by applying a temperature difference ΔT across a long rod sample with uniform cross section A and length L. The thermal conductivity κ is then given by the equation κ = (L/A)(ΔW/ΔT), where ΔW is the heat flow and ΔT is the temperature difference. By measuring the heat flow and temperature difference, you can determine the thermal conductivity at different temperatures down to 1-2 K.

I hope this helps to answer your questions and guide you in your research. Best of luck with your report!