# Heat Conduction

Introduction

In this laboratory you will study heat flow across a temperature gradient. By comparing the temperature difference across one material to the temperature difference across a second material of known thermal conductivity, when both are conducting heat at a steady rate, you will be able to calculate the thermal conductivity of the first material. You will then compare the experimental value of the calculated thermal conductivity to the known value for that material. Thermal conductivity is an important concept in the earth sciences, with applications including estimating of cooling rates of magma chambers, geothermal explorations, and estimates of the age of the Earth. It is also important in regard to heat transport in air, to understanding the properties of insulating material (including the walls and windows of your house), and in many other areas. The objective of this laboratory experiment is to apply the concepts of heat flow to measure the thermal conductivity of various materials.

Theory

Temperature is a measure of the kinetic energy of the random motion of molecules with a material. As the temperature of a material increases, the random motion of its molecules increases, and the material absorbs and stores a quantity which we call heat. The material is said to be hotter. Heat, once thought to be a fundamental quantity specifically related to temperature, is now known to be simply another form of energy. The equivalence of heat and energy is one of the foundations of thermodynamics. As the molecules in one region of a material move, they collide with molecules in neighboring portions of the material, thus transferring some of their energy to other regions. The net result is that heat flows from regions with higher temperatures to regions with lower temperatures. An exact calculation of this heat flow can be very difficult for materials with complicated shapes and complicated temperature distributions, but in some simple cases the heat flow can be calculated. In this experiment, we will consider the heat flow across a plate of material of cross sectional area A and thickness Δx when its faces are held at constant (and different) temperatures, as indicated in Fig. 1.

Figure 1 Heat flow across a plate. In this case the rate of heat flow H across the material is given by H = KA !T !x

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(1)

where !T = T2 " T1 is the temperature difference across the plate and K is a quantity called the thermal conductivity. Note that this equation only applies because we keep the top and bottom at fixed temperature. In a more general situation, the flow of heat would alter the temperature of the top and bottom, and a more complicated approach would be required to deal with the situation. Heat is transferred more efficiently through shapes with a large area that are subject to a large temperature difference, but more slowly through thicker materials. If the units of H are J/s, that of A are m2, Δx is in m, and the units of temperature are ºC or K, then the units of K must be W/m-oC. Prove this for yourself, and show it in your laboratory book. Since the Celsius degree is the same size as a degree on the Kelvin scale, the units of thermal conductivity are usually expressed as W/m-K. We will use Eq. (1) to measure the heat flow through a material of known thermal conductivity and then use this result to determine the thermal conductivity of unknown samples forced to conduct heat at the same rate. Thermocouples In order to apply Eq. (1) we will need to measure the temperature difference ΔT across our samples. It would be difficult to insert a thermometer into the gap between plates without disrupting the heat flow, so we will instead use a temperature probe that uses a device known as a thermocouple.

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Figure 2. A Thermocouple A thermocouple is simply two connected wires made of dissimilar metals. Whenever two different metals contact each other, a small voltage...

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