Figure 2
Equipment
The apparatus is shown in Figure 2. The hand crank and ring stand in the version used in this lab is integral with the apparatus baseplate. Paper is used between the cone surfaces to provide smooth operation, and prevent damage to the cones.
Figure 2
Setup
IMPORTANT: The tapered brass cones are machined in pairs and must not be interchanged with another set. They must be handled carefully and not dropped, marred or scratched.
Friction Cones. Remove the brass calorimeter cones from the calorimeter jacket, and inspect for smoothness. Remove the metal torque disk from the inner cone and weigh the brass cones, recording the mass. Note the disc is separated from the inner brass cone with thermal insulating material.
The contact surfaces of the cones must be separated by a sheet of ordinary paper, cut in the proper shape, a template is provided. Trim if necessary until the piece fits smoothly in the outer cone without overlapping. Insert the inner cone and rotate one cone with respect to the other to make sure they turn smoothly. Fill the inner cone about half full with tap water, since the temperature doesn't matter during the trial runs. Place the cone assembly into the calorimeter jacket and re-attach the metal disk to the cone assembly.
Torque Device. Position the pulley and forked-spring assembly on the ring stand so that the cord feeds out of the pulley tangential to the groove in the large disk and in the same plane. The fingers of the fork-spring should contact the large disk at the center and apply a downward force to hold the cones in uniform contact. The downward force may be varied by means of the knurled screw.
Hang the dial spring balance from the hook located near the top of the ring stand post. Attach a length of string to the small hole in the large disk, placing it in the groove on the edge of the disk for about 1/2 to 3/4 of its circumference. This insures the force is perpendicular to the radius, which is required if equation (2) is to be valid. Pass the cord under the small pulley and attach the hook on the spring balance. The dial spring balance measures the torque on the large disk required to counter-balance the frictional drag between the cones when the outer one is rotating.
Note: In order for the spring balance to read the correct force, the cord must pass through the pulley and make a 90 angle!
Calorimeter. Now fasten the split rubber stopper around the lower end of the thermometer so that a length of several centimeters of the sensor end projects below the stopper. Slip the sensor end through the hole in the stirrer in such a way that the handle of the stirrer extends upward freely through the open slot in the stopper. Insert this assembly into the hole in the large disk, making certain that the end of the sensor is submerged in the water in the cone and the stirrer is free to move up and down.
Preliminary Trial. The successful performance of this experiment requires careful technique to control the speed properly. A preliminary trial will acquaint you with the apparatus and verify the adjustments that will give optimum functioning, with easy operation and control.
Turn the hand wheel slowly and then gradually increase the speed until you reach a convenient rate that is easy to maintain. You will need to maintain the rate and the balance reading as closely as you can for several minutes. It may be helpful to increase the downward pressure of the fork spring device on the large disk and thus give a higher force balance reading at the same rotational speed.
Try stirring the water by moving the stirrer up and down while rotating the crank. Familiarize yourself with the thermometer. Crank steady and gently. Within a minute or two the temperature should begin rising. You should get a "feel" for the work and for the time required to raise the temperature 1 C. When you are satisfied that the necessary technique has been acquired, quantitative measurements may begin.
Measurement of Mechanical Equivalent.
1. Thermal Loses - If the temperature of the calorimeter is above room temperature some of the heat is lost to the environment by conduction even with thermally insulating material surrounding the cones. This loss is proportional to the temperature difference between cones and environment. The temperature rise of the water during the preliminary trial will therefore not reflect all the heat transferred and would result in a significant error (systematic) in J. This error can be minimized by starting at some temperature below room temperature, and finishing at exactly the same temperature difference above room temperature. Then the calorimeter cones will gain from the environment as much heat below room temperature as they lose while above, leaving a nearly net zero effect due to extraneous heat transfer. A starting temperature of 5-10 C below room temperature is recommended.
2. Final Procedure
A. Weigh both cones empty. You will have to partially disassemble the apparatus if this was not done during the setup.
B. Weigh the stirrer. Determine the volume of the submerged portion of the thermometer with the small graduated cylinder using the "displacement" method. Record the room temperature at this time.
C. The effective diameter (2R) of the metal torquing disk is the value measured at the bottom of the grove. Determine this value.
D. Fill the inner cone with ice water to about one centimeter from the top. There will be a significant temperature rise in the water as the brass cools down, and the calorimeter reaches thermal equilibrium.
E. Weigh both cones plus water. Meaurement of all these masses is required to accurately determine the net heat input from the temperature changes, and knowledge of specific heats.
F. Place stirrer in water and stir occasionally until the temperature of water and cones is stabilized at about 2¡ below the desired starting temperature of 5¡-10¡ C below room temperature. Record the desired temperature.
G. Now quickly re-assemble apparatus, read and record initial temperature and counter reading. Begin rotating the outer cone, adjusting speed and pressure to give a satisfactory force balance reading. Try to maintain constant speed and balance reading throughout the experiment.
H. The water should be stirred at frequent intervals, but not constantly. A team of two students can arrange their tasks so one records the data and stirs the water, while the other rotates the crank.
I. Stop the rotation when the temperature is about 0.5¡ C below the final temperature you desired to reach. Continue to stir until the water reaches the highest temperature. Record this value.
J. Record the final counter reading.
ANALYSIS AND RESULTS
The equation to be evaluated is
J =
obtained from equation (4) and (5).
The combined heat capacity of the system is the sum of four terms
C = Cb + Cw + Cs + CT
Specific heats per gram are:
brass 0.093 cal/g C
water 1.00 cal/g C
stirrer 0.1 cal/g C
aluminum 0.215 cal/g C
Compare your value of J with the accepted value. Obtain a value for the error
in your measured value of J by estimating and propagating the uncertainties in
F, R, 
T, and Cx. In this experiment various systematic
effects are likely to dominate, and at the sophistication level of this lab,
there is no easy method to evaluate the corrections. Thus, a difference
(Jmeasured - Jaccepted) in excess of 2
is
probably due to systematic errors. Try to identify some sources of these
systematics.