Thermometry

The capacity of a substance to conduct or transfer heat is called thermal conductivity. It is represented by the character ‘k’, or the sign “λ.” It is also defined as the amount of heat that can be transferred per unit time per unit area through the plate of a given material of unit thickness, with the faces of the plate differing by one unit of temperature. The inverse of this metric is thermal resistivity. 

Heat sinks employ high thermal conductivity materials, whereas thermal insulators use low thermal conductivity materials. Through the course of this article, we will study the influence of temperature on the Fourier law of thermal conductivity. We will also look at different methods for calculating thermal conductivity. 

Thermal conductivity can be measured through four dimensions which are temperature, mass, length and time. Watts per meter-Kelvin or in some cases Wm-1K-1, is the SI unit for thermal conductivity. It is commonly represented as power/(length * temperature). For each Kelvin of temperature difference, these units provide us with the rate of heat conduction through a material of unit thickness.

Fourier’s Law

Fourier derived a law in 1822 to showcase the connection between temperature gradients considered towards the direction of flow of energy with rate of conduction in a material. Fourier stated that heat flux caused by thermal conduction in a material is proportional to the magnitude of the temperature and in sign opposite to itself. Fourier’s law is commonly known as the law of heat conduction. 

The following equation states this law’s differential version:

q = -k.△T

△T is used to symbolise the temperature gradient, k is the thermal conductivity, and q is the thermal flux or heat flow. Thus, Fourier’s Law defines thermal conductivity and serves as the foundation for numerous techniques of calculating its value. When paired with the concept of conservation of energy, Fourier’s Law of said conduction process, lays the basis for the study of various conduction issues. 

Measuring Thermal Conductivity

The thermal conductivities of materials can be measured using a variety of ways. These methods are majorly derived from experiments. These approaches to measuring thermal conductivity are roughly categorised into two types: steady-state and transient procedures.

Steady-state procedures

These methods employ measurements in which the temperature of the tested substance stays constant over time. One notable limitation of this approach is that it needs a well-engineered set-up to carry out the study. Also, as the temperature is constant, these techniques just require fundamental analysis. Searle’s bar technique and Lee’s disc method are two steady-state approaches for determining the thermal conductivity of a material that exhibits superior conductivity.  

Transient procedures

The readings are noted throughout the phase in which heat is supplied during his processes. One key benefit of such systems is that measures are rapidly implemented. One disadvantage of transitory systems is their inability to quantitatively analyse the measurements data. There are various ways for determining the thermal conductivity of materials, each with its own set of advantages and disadvantages. A point to note here is that the thermal characteristics of solids are more easily investigated experimentally than others.

Effect of temperature on Thermal Conductivity

Metals: According to the Wiedemann-Franz equation, heat conductivity is always proportional to the multiplied product of temperature as well as electrical conductivity. The presence of free electrons in a metal influences its heat conductivity. A pure metal’s electrical conductivity decreases as the temperature rises. At temperatures ranging from 2K to 10K, some pure metals exhibit peak heat conductivity value. Metal alloys’ electrical conductivity does not greatly vary as temperature rises, meaning their heat conduction also increases. As a result, the thermal conductivity of pure metal changes to a certain extent as the temperature rises. When temperatures dip below 0 degrees Celsius, thermal conductivity plummets significantly.

Nonmetals: Nonmetal thermal conductivities are mostly related to lattice vibrations. During experiments when we try to induce lattice vibrations we notice that the results are extremely different in the ßcase of non-metals as that in metals. When the temperature is reduced below the Debye temperature, the heat conductivity and heat capacity of non-metals fall. The mean accessible route for phonons never varies significantly as temperature rises, meaning the thermal conductivity stays stable and never changes as significantly as the temperature rises.

Conclusion

Thermal conductivity is an essential component of the material-material connection. Understanding it allows us to get the maximum performance out of the materials we use in our daily lives. Thermal conductivity testing and measurement are essential components of this attempt. As we saw in the preceding sections, thermal conductivity testing methods may be characterised as either steady-state or transient. This article also helped us comprehend the ideas of Fourier Law and the effects of temperature on a material’s thermal conductivity.