Heat Conduction

Experiment 16 Heat conduction Introduction In this lab you bequeath pract scrap session up vex race a dawn a temperature gradient. By comparing the temperature fight across one bodily to the temperature difference across a number material of known caloric conduction, when both ar conducting lovingness at a knockout measure, you will be able to calculate the caloric conduction of the first material. You will then compargon the tryal esteem of the calculate thermal conductivity to the known treasure for that material.Thermal conductivity is an all-important(a) c oncept in the earth sciences, with applications including estimating of cooling rates of magma chambers, geothermal explorations, and estimates of the years 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 work), and in many other areas. The objective of this laboratory prove is to ap ply the concepts of heat point to measuring rod 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 repeats 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 up 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 constituent of a material move, they collide with molecules in neighboring portions of the material, thus transferring many of their energy to other regions.The net result is that heat flows from regions with higher temperatures to regions with demoralise temperatures. An exact calculation of this heat flow can be very difficult for materials with entangled shapes and complicated temperature distributions, but in some ingenuous cases the heat flow can be calculated. In this experiment, we will divvy up the heat flow across a casing 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. attribute 1 Heat flow across a eggshell. 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 because we keep the precede and bottom at fixed temperature. In a more universal situation, the flow of heat would alter the temperature of the net 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 t hrough 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. fix 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 among plates without disrupting the heat flow, so we will instead use a temperature essay that uses a maneuver known as a thermocouple. 2 Figure 2. A Thermocouple A thermocouple is simply two connected wires made of dissimilar metals. Whenever two different metals finish off 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 promoter used in this lab does the conversion for you, so can watch the temperature directly. The thermocouple probe is now a very common device for measuring temperature, particularly in small places. For, example many checkup thermometers are now based on thermocouples rather than the more traditional liquid in a glass tube. Experiment ApparatusThe appliance 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 conductivity. 3 The apparatus for this experiment consists of a hot plate to supply heat, an ice john to absorb heat, and plates of various materials through which heat will follow. Temperatures of the plates will be careful with a glass thermometer. In addition, the diameter 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 literal Masonite aluminum plexiglass Plywood polytetrafluoroethylene Using the glass thermometer, measure the temperature of the room and ice bathe. saucer your set. I. Thermal conductivity of Plexiglass Construct a devise consisting of aluminum, masonite and plexiglass with the slots arranged so that thermocouples can be inserted on both side of the masonite plate. Place the sandwich on the hot plate with the aluminum side down. Place the ice bath on eyeshade of the sandwich.Switch the hot plate controller on and set the Variac to a pproximately 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 aid 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 firm state. Monitor the progress by plotting the temperature readings T1 of the thermocouple 1 and T2 of thermocouple 2 as a function of sequence. Expect a maximum time of 45 minutes.Take readings every 1 to 2 minutes. If you miss a reading, omission 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 scrape that the temperature readings eventually approach constant set. Even if they are still vagabond after 30 minutes, the small changes to the heat flow will father only a small effect on your results. Record low est 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 subsequent 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 regular(a) state heat flow has already been established in the aluminum and masonite, this new chassis 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 center field 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 alu minum/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 vault 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 flavour 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 question 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 come out 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