Heat Conduction

Experiment 16 Heat conduction Introduction In this research laboratory you go away canvas modify prey a carrefour a temperature gradient. By comparing the temperature unlikeness across one veridical to the temperature difference across a spot material of known caloric conductivity, when both be conducting commove at a stimulate rate, you will be able to calculate the caloric conductivity of the first material. You will then compargon the auditionational cherish of the metric thermal conductivity to the known jimmy for that material.Thermal conductivity is an important c at a cartridge holderpt in the earth sciences, with applications including estimating of cooling rates of magma chambers, geothermal explorations, and estimates of the geezerhood 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 ho enjoyment), and in many other areas. The objective of this laboratory experiment is to apply the concepts of heat catamenia to m the thermal conductivity of various materials. Theory Temperature is a measure of the kinetic energy of the haphazard motion of molecules with a material.As the temperature of a material increases, the random motion of its molecules increases, and the material lines and stores a quantity which we call heat. The material is said to be hotter. Heat, once thought to be a fundamental quantity specifically link to temperature, is now known to be simply another form of energy. The comparing of heat and energy is one of the foundations of thermodynamics. As the molecules in one division of a material move, they collide with molecules in neighboring portions of the material, thus transferring nearly of their energy to other regions.The net result is that heat flows from regions with higher temperatures to regions with bring low temperatures. An exact calculation of this heat flow can be really difficult for materials with mingled shapes and complicated temperature distributions, but in just about mere(a) cases the heat flow can be calculated. In this experiment, we will remove the heat flow across a domicile of material of cross sectional area A and thickness ? x when its faces are held at constant (and different) temperatures, as indicated in Fig. 1. radiation pattern 1 Heat flow across a dwelling house. In this case the rate of heat flow H across the material is given by H = KA T x ( ) (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 beca delectation we keep the big bring in and bottom at fixed temperature. In a more ecumenical situation, the flow of heat would alter the temperature of the go on 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, ? x is in m, and the units of temperature are ? C or K, then the units of K must(prenominal) be W/m-oC. move up 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 ? T across our samples. It would be difficult to insert a thermometer into the gap mingled with plates without disrupting the heat flow, so we will instead use a temperature try out that uses a spin known as a thermocouple. 2 Figure 2. A Ther mocouple A thermocouple is simply two attached wires made of dissimilar metals. Whenever two different metals extend to each other, a small voltage difference is generated. This voltage difference is dependent on the temperature of the junction.If we measure this voltage difference with an accurate voltmeter, we can look up the temperature of the junction relative to the temperature of the connection to the voltmeter in a thermocouple table. The musical instrument used in this lab does the conversion for you, so can rake the temperature directly. The thermocouple probe is now a very common dev grouch for measuring temperature, particularly in small places. For, example many checkup thermometers are now based on thermocouples rather than the more tralatitious liquid in a glass tube. Experiment ApparatusThe instrument for this experiment are shown in the following figure, which also demonstrates how you will use the equipment. Figure 3. The apparatus for measuring thermal condu ctivity. 3 The apparatus for this experiment consists of a hot plate to supply heat, an ice vat to absorb heat, and plates of various materials through which heat will follow. Temperatures of the plates will be heedful with a glass thermometer. In addition, the diam and thickness of each plate will be measured with vernier calipers. Method Measure the diameter and thickness of each plate provided.Calculate the areas of the plates. Create the following table in your report and fill it in. Table 1. Dimensions of various plates satisfying Masonite aluminum plexiglass Plywood polytetrafluoroethylene Using the glass thermometer, measure the temperature of the room and ice toilet. book your determine. I. Thermal conductivity of Plexiglass Construct a prepare consisting of aluminium, masonite and plexiglass with the slots arranged so that thermocouples can be inserted on each side of the masonite plate. Place the sandwich on the hot plate with the aluminum side down. Place the ic e bath on top of the sandwich.Switch the hot plate controller on and set the Variac to approximately 40% power. The exact value is not important, but if the power is set much higher some of the materials may get too hot. WARNING Use extreme warn around the hot plate and when handling any of the materials that come into contact with it for the remainder of the experiment. The surfaces will become HOT It will take up to 30 minutes for the heat flow to achieve a unshakable state. Monitor the progress by plotting the temperature readings T1 of the thermocouple 1 and T2 of thermocouple 2 as a function of time. Expect a maximum time of 45 minutes.Take readings every 1 to 2 minutes. If you miss a reading, burn it and record the next reading at the appropriate time on your plot. 4 Diameter (cm) Diameter (m) Area (m2) Thickness (cm) Thickness (m) You should ensure that the temperature readings eventually approach constant value. Even if they are still blow after 30 minutes, the small ch anges to the heat flow will bring forth only a small effect on your results. Record lowest values of the temperatures for the aluminum/masonite/plexiglass sandwich. You now have all the information needed to calculate the thermal conductivity of plexiglass.See the analysis section later on in these notes for details about how to do this. Calculate its value. II. Thermal conductivity of Plywood Carefully remove the Plexiglas plate and replace it with the plywood sheet (with slot down). Reinsert thermocouple 2 and place the ice bath back on top of the sandwich. Since a energise state heat flow has already been established in the aluminum and masonite, this new pattern should take only about 20 minutes to achieve a steady state. While you are waiting for the temperature readings to stabilize, you may wish to use the time to calculate the thermal conductivity of Plexiglas.If you do this, keep an tenderness on the temperature readings so that you know when a steady state has been achieved. Record the steady state values of the temperature for the sandwich of aluminum/masonite/plywood. III. Thermal Conductivity of Teflon Carefully remove the plywood plate and replace it with the Teflon plate (with slot down). Reinsert thermocouple 2 and place the ice bath back on top of the sandwich. Again, a steady state will probably be achieved in about 20 minutes. Record the steady state values of the temperatures for the sandwich of aluminum/masonite/Teflon. Analysis If e throw off the heat that escapes from the edges of the plates (due to convection and radiation), all of the heat provided by the hot plate must flow through each of the plates and into the ice bath, once a steady state has been achieved. Thus the heat flow through each plate must be the same throughout the sandwich. In particular, this means that the heat flow through the masonite is equal to the heat flow through the top material. Therefore we can write Hm = Htop . Using Eq. (1) we find that K m Am Tm xm = K top Atop Ttop xtop ( ) ( ) (2) The thermal conductivity of masonite is known to be 0. 0476 W/mK.You can derive an demeanor from Eq. (1) for the thermal conductivity of the top plate. 5 Use your measured values and the known value for the Km to calculate the thermal conductivities of each of the top plates used. Prepare a table like that shown below and fill in the values in your report. Table 2. Thermal conductivities of materials used in this laboratory. Material Calculated thermal Published value of K conductivity (W/mK) (W/mK) Aluminum Masonite Plexiglass Plywood Teflon The least accurate measurements in this experiment are the thermocouple voltages, which are only measured to 0. 1 mV accuracy.Based on this accuracy, estimate the disbelief in the temperature difference across the masonite plate. Considering the uncertainty in this temperature difference only, what is the approximate percentage error in your calculated thermal conductivity values? Questions 1. Use Eq. (1) to calculate the total rate of heat flow H through each of the plates in commence 1. (Note The same value of H must hold for each plate, so you only need to use Eq. (1) once). 2. Do your results agree with the expected values? If not, what measurements, processes, and/or assumptions do you suspect to have been significant sources of error? 6