# -1- Lab 14: Thermal Conductivity , James J. DeHaven, Ph.D and , Sandra Ceraulo Ph.D. 1 T2

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1 -1- Lab 14: Thermal Conductivity , James J. DeHaven, Ph.D and , Sandra Ceraulo Ph.D. Suppose you have a sheet of some sort of structural material, and you want to find the rate at which heat is transferred from one surface to another. The process by means of which the heat moves through the material is called conduction, and the rate at which it is transferred from one place to another is governed by the so-called heat conduction equation: [1] Δ Q κa( T _ 1 T2 ) l /ΔT rate of heat transferred (SI unit are watts) T1 temperature on the hot side of material T2 temperature on the cold side of material l thickness of insulator A cross sectional area over which the transfer takes place κ thermal conductivity of material (a constant for each substance) Figure 1 (next page) shows a schematic drawing for heat conduction across a surface, and you should consult it to get a good picture of the meaning of each of these variables. In this lab, you will measure the thermal conductivity, κ, of five different insulators: 1) Glass 2) Wood (plywood) 3) Lexan (plexiglass) 4) Sheet Rock (wall board) 5) Masonite Substances for which the thermal conductivity is large conduct heat rapidly and are said to be good conductors. Most metals fall into this category. Substances with the low values of κ such as down and asbestos are called insulators and are poor conductors. On the basis of this lab, you should be able to evaluate the suitability of these materials for construction from the perspective of their insulating properties. Method The experimental setup for determining κ is show in figure 2. A steam generator is used to provide a high temperature region inside a steam chamber. A piece of insulating material is placed on top of the steam chamber, and a cylindrical block of ice is placed on the insulator. The rate at which the ice melts tells us how fast heat is flowing across the insulator.

2 -2- l A Surface area T 2 T 1 ΔT κ thermal conductivity coefficient Figure 1: Schematic diagram of heat conduction across a slab of material.

3 -3- Ice Block Insulator Clamped off Steam Hose Tared 200ml Beaker for Melted water Steam Chamber Wooden Block 250ml Beaker for condensed steam Support Stand Steam Generator Figure 2: Experiment Apparatus for determining the coefficient of thermal conductivity. To find κ we must measure all the other quantities in equation [1]. Our principal efforts will be aimed at finding the rate of heat transfer, / Δt, for the heat that penetrates the insulator separating the steam chamber from the ice. We find this by using the heat of fusion of water and by measuring the mass of ice melted during a time Δt. The rate at which heat is absorbed by the block is easily calculated by: [2] Δ Q ΔH fusion m water

4 However, even if no steam is applied, some of the ice will melt anyway due to the fact that room temperature is warm enough to melt ice. We have to take this into account, and so, at the beginning of the experiment we find [3] Δ Q Δ t ambient ambient -4- ΔH fusion m water, ambient ambient where m water, ambient is the mass of ice melted without applying any steam. This ice melts in a measured amount of time Δt ambient, which we can measure. We can then find the rate of heat transferred from the steam to the ice separately, by subtracting the rate of heat transferred from the room (ambient conditions) from the combined rate subtracting the rate of heat transfer, which is what we measure when the steam is operating. To put this algebraically: [4] ( ) Δ ( ) _ ( ) t steam only steam + ambient where ( / Δt) steam+ambient is what you measure when you measure the mass of ice melted after the steam has been running at a stable temperature for a time Δt ( / Δt) ambient is what you measure with the steam turned off, prior to commencing the experiment with the steam on. ( / Δt) steam only is what you use to calculate the thermal conductivity of the insulator. In addition to this you will have to measure the other quantities in the heat conduction equation. You will have to measure l, the thickness of the sample material. You can do this using either the ruler or calipers provided. You will have to know T 1 and T 2. The low temperature will be the melting point of ice. The high temperature will be the condensation point of steam. To obtain an accurate value for the condensation point you will have to include the variation (if any) due to the deviation of the current atmospheric pressure from 1 atmosphere (760 torr). To do this, you will need to know the current barometric pressure. You can obtain this from the barometer located in the lab. Near 100 degrees centigrade, each additional torr of atmospheric pressure adds degrees to the boiling point, and for every torr less than 760, the boiling point is lowered by degrees centigrade. In other words: [5] Boiling point 100 C + (0.037 C/torr) (Barometric pressure - 760torr)

5 -5- Finally, it will be necessary to measure the area. Normally you might be inclined to simply measure the area of the insulator. But, in this experiment, we are only interested in the heat that is conducted to the ice--consequently, the surface area will simply be equal to the area of the bottom of the cylinder of ice. Since the block of ice may shrink as you proceed through an experiment, you will need to use an average area. To do this, you will need to measure the diameter of the ice before and after each experiment. A Surface area of ice T 2 l T 1 Inside Steam Chamber A Figure 3 : side and bottom view of ice cylinder. Note that the cross sectional area of the ice, not the area of the insulator, governs the rate of heat transfer fro the steam chamber to the ice. Procedure Set up the apparatus as shown in figure 2 but clamp off the line to the steam chamber and leave the other vent open. Make sure that the unused steam nozzle in the steam generator is clamped off. Make sure to use boiling chips in the steam generator. Fill the generator about 3/4 full of water and turn the knob to the highest setting. Again--do not open the line to the steam chamber until you have completed part 1 below. Part 1. Determination of Heat Transfer Rate at Room Temp ( / Δt) ambient 1) Run the cylinder of ice under warm water to free the ice from the mold. With the glass insulator in place, find ( / Δt) ambient by measuring the mass of water that melts and the time it takes it to melt (see equation [3]). Steps 2-6 outline how to do this in greater detail. 2) Measure and record l, the thickness of the sample material

6 3) Mount the glass sample material onto the steam chamber using the plates and thumb screws 4) Make sure that the material sample (insulator) is flush against the water channel so water will not leak. A bit of vaseline put between the channel and the sample will create a good seal. Tighten the thumbscrews to press the glass against the red rubber gasket. DO NOT OVER TIGHTEN!! Do not remove the ice completely from the mold. Instead, allow it to slide out as the experiment proceeds. You only need to be sure that the ice is capable of sliding freely out of the mold. 5) Let the ice sit for several minutes until it begins to melt and comes in full contact with the sample material. The ice may be at a temperature lower than zero degrees. Since the ice may be rough on top at the beginning of the experiment give it a chance to melt so that the entire top surface area rests against the glass. During a phase change, the temperature remains constant. For example, during the melting of the ice, the temperature remains at zero degrees C. During the waiting period, you may determine the mass in kg of the 200 ml tall-form beaker used to collect the melted ice and record it. 6) To determine the rate of melting due to room temperature, do the following: a) If you have not already done so, determine the mass in kg of the 200 ml tall-form beaker used to collect the melted ice and record it. b) Collect the meting ice in the beaker for a measured amount of time (approximately 10 minutes). Determine the precise time interval by measuring it with a stopwatch. This is Δt ambient c) Determine the combined mass (in kg) of the beaker and melted ice after the time t ambient d) Subtract the mass in 6a from the mass in step 6c to determine the mass of the melted ice at ambient temperature. You now have all the information needed to determine the heat absorbed by the ice at ambient (room) temperature. Part II. Calculation of Heat Transfer / Δt of Steam plus Ambient Temp -6-7) Make sure the steam generator is connected and that the small piece of tubing is clamped off, and that the tubing leading from the generator to the steam chamber is NOT clamped. Place a container under the drainer spout of the steam chamber to collect condensed steam that escapes from the chamber. 8) Run steam into the steam chamber. Let the steam run for a few minutes until the temperature stabilizes. Then the heat flow will be steady. 9) Measure the diameter of the ice block. Record the value as d before 10) Empty the cup used to collect the melted ice. Repeat step 6 but this time with the steam running into the steam chamber. Record the mass of the melted ice (remember to subtract the mass of the beaker) as before.

7 -7- Record the exact time Δt during which the ice melted while the steam was running. This quantity corresponds to Δt steam+ambient 11) Measure the diameter of the ice block, d after d after. When calculating A, use the average of d before and 12) Repeat this procedure for the other materials provided, a total of 5 in all. Part III. Calculations This experiment is ideal for a spreadsheet because it contains many simple calculations involving several measured quantities. Prepare an EXCEL spreadsheet showing your calculations (attach this to your lab report). Below is a rough outline of the calculations that need to be done. For each material: 1) Calculate / Δt for the ambient temperature (equation 3). Be sure to take into account the mass of water melted at room temperature in your calculations. 2) Calculate / Δt for steam and ambient temperature (equation 2) 3) Calculate / Δt for steam only using equation 4 4) Using the measured values for l, d before, d after, T1 and T 2, in your spreadsheet, calculate κ using equation 1. Remember to use the average diameter of the ice to calculate its cross sectional area, A. 5) Write up your lab using the usual report format. Report: Introduction: Write a brief introduction stating the objectives of the experiment, and a concise summary of the methods that will be used. Experimental: Describe the experimental apparatus and precisely what variables will be measured and how they will be measured. Results: Summarize the results of the experiment. Show sample calculations. If you are attaching computer generated tables or graphs, briefly explain them here. Discussion: Explain the significance of your results and their connection with more general physical principles. Where it is possible, compare your numbers with accepted values. Explain any sources of error.

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