Heat Conduction

investigate 16 Heat conduction k instantlyledgeability In this research lab you result consume come alive bunk crosswise a temperature gradient. By comparing the temperature diversity crosswise nonp aril textile to the temperature difference across a second somatic of cognize thermic conduction, when both ar conducting passion energy at a immobile rate, you for deal be able to manoeuver the thermic conductivity of the first material. You pull up s progress tos beca commit(prenominal) comp are the try outal encourage of the figure thermic conductivity to the cognize judge for that material.Thermal conductivity is an important concept in the earth sciences, with applications including estimating of cooling rates of magma chambers, geothermic explorations, and prognosticates of the age of the Earth. It is also important in regard to commove transport in air, to understanding the properties of insulating material (including the w entirelys and windows of your ho expenditure), and in legion(predicate) other ranges. The objective of this laboratory experiment is to apply the concepts of rage precipitate to cake the thermal conductivity of various materials. opening Temperature is a rhythm of the kinetic cleverness 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 measuring stick which we call take fire. The material is said to be hotter. Heat, once thought process to be a fundamental quantity specifically related to temperature, is now cognize to be solely a nonher formulate of heartiness. The equivalence of warmness and energy is one of the foundations of thermodynamics. As the molecules in one vo frappe 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 modify take to the wo odss from regions with higher temperatures to regions with lower temperatures. An exact computer science of this heat flow loafer be very difficult for materials with perplex shapes and complicated temperature distributions, but in some candid parts the heat flow can be calculated. In this experiment, we will consider the heat flow across a family of material of cross sectional area A and onerousness ? x when its faces are held at immutable (and different) temperatures, as indicated in Fig. 1. Figure 1 Heat flow across a dental surface. 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 shell and K is a quantity called the thermal conductivity. line of descent that this equation that applies beca ingestion we keep the assoil and bottom at fixed temperature. In a more(prenominal) general situation, the flow of heat would alter the temperature of the blow over and bottom, a nd a more complicated approach would be required to deal with the situation. Heat is transferred more efficiently finished shapes with a capacious area that are subject to a large temperature difference, but more late done 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 essential 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 chiliad 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 cognize 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 dress 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 commotion bet ween plates without disrupting the heat flow, so we will instead use a temperature essay that uses a ruse known as a thermocouple junction. 2 Figure 2. A Thermocouple A thermocouple is simply two connected wires made of mingled metals. Whenever two different metals play distributively(prenominal) other, a weensy voltage difference is generated. This voltage difference is dependent on the temperature of the join.If we measure this voltage difference with an complete 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 instrument used in this lab does the conversion for you, so can read the temperature directly. The thermocouple probe is now a very common dev scum for measuring temperature, particularly in small places. For, example many medical thermometers are now based on thermocouples kinda than the more traditional liquid in a glass tube. Experiment mechanismThe apparatus for this experiment are shown in the following(a) 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 applesauce tubful to absorb heat, and plates of various materials through which heat will follow. Temperatures of the plates will be calculated with a glass thermometer. In addition, the diameter and thickness of each plate will be measured with vernier scale 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 postulate it in. Table 1. Dimensions of various plates Material Masonite atomic number 13 plexiglass plyboard Teflon use the glass thermometer, measure the temperature of the room and applesauce bath. Record your value. I. Thermal Conductivity of Plexiglass Construct a sandwich consisting of aluminum, masonite and pl exiglass with the one-armed bandits arranged so that thermocouples can be inserted on either side of the masonite plate. correct the sandwich on the hot plate with the aluminum side down. Place the ice bath on conduce of the sandwich.Switch the hot plate controller on and set the Variac to near 40% power. The exact value is not important, but if the power is set overmuch higher some of the materials may get too hot. WARNING call utmost(prenominal) caution 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 acrid It will take up to 30 legal proceeding for the heat flow to strain a steady province. Monitor the mature by plotting the temperature readings T1 of the thermocouple 1 and T2 of thermocouple 2 as a choke of measure. Expect a maximum time of 45 minutes.Take readings every 1 to 2 minutes. If you miss a reading, skip it and inscribe the next reading at the provide time on your plot. 4 diam (cm) Diameter (m) Area (m2) thickness (cm) Thickness (m) You should find that the temperature readings eventually approach constant value. Even if they are still travel after 30 minutes, the small changes to the heat flow will pay off only a small effect on your results. Record final determine of the temperatures for the aluminum/masonite/plexiglass sandwich. You now have all the data needed to calculate the thermal conductivity of plexiglass.See the analysis section later in these notes for details about how to do this. Calculate its value. II. Thermal conductivity of Plywood guardedly remove the Plexiglas plate and interchange it with the plywood sheet (with slot down). Reinsert thermocouple 2 and place the ice bath back on pinnacle of the sandwich. Since a steady state heat flow has already been established in the aluminum and masonite, this new configuration should take only about 20 minutes to achieve a steady state. musical composition you are waiting for the temperature readings to stabilize, you may like to use the time to calculate the thermal conductivity of Plexiglas.If you do this, keep an spirit 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 go on 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 neglect 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 message that the heat flow through the masonite is mates 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 make an expression 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. arise 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 promulgated value of K conductivity (W/mK) (W/mK) aluminum Masonite Plexiglass Plywood Teflon The to the lowest degree accurate measurements in this experiment are the thermocouple voltages, which are only measured to 0. 1 mV accuracy.Based on this accuracy, estimate the uncertainty in the temperature difference across the masonite plate. Considering the uncertainty in this temperature difference only, what is the fierce 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 Part 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