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604 Chapter 14 | Heat and Heat Transfer Methods
. The distance, however, simply doubles. Because the temperature difference and the coefficient of thermal conductivity are independent of the spatial dimensions, the rate of heat transfer by conduction
increases by a factor of four divided by two, or two:
(14.37)
Applying the Science Practices: Estimating Thermal Conductivity
The following equipment and materials are available to you for a thermal conductivity experiment:
1 high-density polyethylene cylindrical container 1 steel cylindrical container
1 glass cylindrical container
3 cork stoppers
3 glass thermometers
1 small incubator
1 cork base (2 cm thick) crushed ice
1 digital timer
1 metric balance
1 meter stick or ruler
1 Vernier caliper
1 micrometer
Notes: The three cylindrical containers have equal volumes and are tested in sequence. All cork stoppers fit snugly into the open tops of the containers and have small holes through which a thermometer can be placed securely. There is enough ice to fill each of the containers. Each container with thermometer fits inside the incubator on the cork base. The incubator has been uniformly pre-heated to a temperature of 40°C. The thermometers can be observed through the incubator window
Exercise 14.1
Describe an experimental procedure to estimate the thermal conductivity (k) for each of the container materials. Point out what properties need to be measured, and how the available equipment can be used to make all of the necessary measurements. Identify sources of error in the measurements. Explain the purpose of the cork stoppers and base, the reason for using the incubator, and when the timer should be started and stopped. Draw a labeled diagram of your setup to help in your description. Include enough detail so that another student could carry out your procedure. For assistance, review the information and analysis in ‘Example 14.5: Calculating Heat Transfer through Conduction.’
Solution
The dimensions of each container are measured, so that the side surface area (A) and the thickness of the sides (d) are determined. Weigh an empty container, fill it with ice, weigh it again, insert the cork stopper, and insert the thermometer through the stopper so that the bulb is near the bottom of the container. Place the container in the incubator on the cork base. The incubator provides a uniform high temperature, which evenly surrounds the container and will melt the ice within 20 minutes. Because the cork is an effective insulator, most of the heat transfer will occur through the sides of the containers. By using the incubator temperature of 40° (T2) and the temperature of the ice , the
temperature difference is uniform until all of the ice melts, and the temperature of the water in the container rises. During the time (t) the container is placed in the incubator and the ice completely melts, the amount of heat transferred into the container is almost all of the heat needed to melt the ice, which equals the mass of the ice (m) multiplied by the latent heat of ice (Lf). By using all the measured quantities in the rearranged equation (14.26) for thermal conductivity,
the thermal conductivity (k) can be estimated for each of the container materials. Sources of error
include the measurements of the length and radius of the container, which are affected by the precision of the calipers and meter stick, and the measurement of the container thickness, which is made with the micrometer. The mass of the ice, the measured temperatures, and the time interval are also subject to precision limits of the balance, thermometers, and timer, respectively.
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