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holding it in the hand so that it nearly reaches the bottom. According to Archimedes' principle, the thermometer is now buoyed up by a force equal to the weight of the displaced water and, conversely, the water is pushed down by an equal force, so some additional weight must be put on the other pan to restore the balance. Since the density of water is unity, this additional weight in grams is numerically equal to the volume in cubic centimeters of the submerged part of the thermometer. Multiply this volume by 0.46 and by the rise in temperature of the water and the product is the number of calories absorbed by the thermometer.
Express in the form of an equation the fact that the heat lost by the metal is equal to the heat gained by the water, cup and stirrer, and thermometer. By solving this equation for the unknown quantity, S, the specific heat of the substance is found.
Make two trials, obtaining two values of the specific heat, and take the mean for the final value. Repeat with a different metal.
In this experiment, the chief source of error lies in the temperature readings, so they should be taken as accurately as possible, estimating fractions of degrees, if the thermometer is not divided into divisions smaller than whole degrees. The transfer of the metal from the boiler to the calorimeter must be made very rapidly or else both metal and water may change from the temperatures indicated by the thermometers when they were read. Avoid all splashing of water in the transfer and be sure that ALL the metal gets into the calorimeter.
EXPERIMENT NO. 206
THE MECHANICAL EQUIVALENT OF HEAT.
References: Stewart, Physics, Sect. 223, 224; Kimball, College Physics, Sect. 407-409; Duff, College Physics, Sect. 171, 199, 240; Spinney, Text-Book of Physics, Sect. 221.
When a certain amount of work, W, is done without storing mechanical energy, certain amount of heat, H, appears; and the mechanical equivalent of the heat is defined as,
To determine J we must measure the work done (in ergs), and the heat produced (in calories). The apparatus for doing this consists of a pair of metal cones, one revolving inside the other. A weighed mass of water is placed in the inner one, which is held still while the outer one revolves. The heat produced by friction warms the water and the two cones, so H is determined as in any heat experiment. Let t' be the temperature at the beginning of the experiment, t" the temperature at the end, m the mass of the water, m' that of the stirrer and two cones, s' their specific heat. Then
In order to equalize the losses and gains of heats, the experiment should be started about 8 degrees below the room temperature and carried about 8 degrees above it. Read the thermometer to tenths of degrees.
A cord is fastened to a wooden wheel attached to the inner cone. This cord is passed over a pulley and a weight of 100 to 200 grams attached to it. By means of a preliminary trial this weight is made of such size that, when the outer cone is rotated at constant speed the friction is just sufficient to keep it lifted off the floor, oscillating between the floor and the pulley with the cord wound part way around the wheel. Then on the average, the moment of the weight equals the moment of the frictional force, since they tend to rotate the wheel in opposite directions, yet balance. The moment of the weight is MgR, where M is the mass hung on the cord, and R is the radius of the disc. The moment of friction is Fr, where F is the unknown force of friction between the cones, and r is the mean outside radius of the inner cone. Therefore:
Now if the outer cone makes n revolutions, the work done by friction is
Hence, to find the work done, we need only measure the radius of the disk, know the mass, M, and know the total number of revolutions made. The last is obtained by means of the revolution counter attached to the apparatus.
One observer must rotate the hand-wheel which drives the apparatus, while the other stirs, and watches the thermometer. Make two trials.
EXPERIMENT NO. 207
THE HEAT OF FUSION OF ICE.
References: Stewart, Physics, Sect. 258-260; Kimball, College Physics, Sect. 422, 424; Duff, College Physics, Sect. 208; Spinney, Text-Book of Physics, Sect. 175.
The heat of fusion of ice is defined as the quantity of heat per gram necessary to melt ice without change of temperature. If the ice is melted, the heat is absorbed; if the resulting water freezes, the same amount of heat is given out. The heat of fusion of ice may be determined by the method of mixtures described below.
The water equivalent of a calorimeter cup and stirrer is computed and the displacement of a thermometer found as described in Experiment No. 205. Fill the calorimeter at least half-full of water warmed to about 15° C above room temperature. Find the mass and temperature of this water accurately. Add a few pieces of ice, which have been carefully dried with absorbent paper, and stir the mixture. Keep on adding ice until the temperature falls to about 15° below that of the room. Read this temperature carefully and then make a weighing to find the mass of the ice which has been added. No ice must be left unmelted, and none must be taken out of the calorimeter. If the pieces are too small, they cannot be thoroughly dried; if they are too large, they will take so long to melt that radiation errors will spoil the results.
Compute the quantity of heat given out by the calorimeter, stirrer, water, and thermometer in cooling from the original
temperature to the final temperature. This heat has been used to melt the known mass of ice and to raise the resulting ice-water from the freezing point to the final temperature. Compute the quantity used in raising the temperature of the ice-water by multiplying the mass of the ice by the rise in temperature, then subtract the result from the total quantity of heat given out by the warm materials. The difference is the number of calories used in melting the ice, so the heat of fusion can be found by dividing this difference by the mass of the ice.
Make three to five trials, using a fresh supply of warm water each time. If the thermometers used are not graduated to fractions of degrees, the fractions should be estimated as closely as possible. The experiment should be carried out as rapidly as conditions will permit, so as to minimize radiation errors, and precautions should be taken to see that heat is not introduced by handling the calorimeter, breathing on it, etc. If any water is spilled from the calorimeter during the experiment, or, if any splashes out when ice is introduced or the stirrer is manipulated, the work must be begun again with a freshly weighed mass of warm water. The thermometer must be left in the calorimeter till the end of the trial as it will carry out some water, if removed. The mass of ice introduced must be determined especially carefully, and any such losses of water will cause errors in the apparent mass of the ice.
EXPERIMENT NO. 208
COOLING, FREEZING, UNDERCOOLING.
References: Stewart, Physics, Sect. 258, 264; Kimball, College Physics, Sect. 422, 424, 427; Duff, College Physics, Sect. 206, 208; Spinney, Text-Book of Physics, Sect. 181.
(a) Take two test-tubes, containing crystals of naphthalene and acetamide respectively, and place in each a thermometer with its bulb completely buried in the substance and held in place by a perforated cork. Grooves must be cut in each cork to permit gases to enter or escape from the tube. Fasten the tubes in burette clamps and set them side by side in a vessel of water which can be heated. Heat the water until the substances
are completely melted and at a temperature above 90° C, then remove the tubes from the hot water and allow them to cool in air. Do not shake or jar the tubes after beginning to take temperature readings. Read the thermometers every half minute. until the temperature of the naphthalene has fallen to about 50° C and that of the acetamide to about 30° C. (If the weather is warm, it may be necessary to cool the acetamide in water. If so, it must be put in water at the start of the cooling operation.) If any sudden changes in temperature are observed, take readings as frequently as needed to obtain a full record of the changes, noting both temperature and time at each reading. Watch especially the range between 80° and 70° C. There should be a marked difference between the behaviors of the two substances. If water gets into the tube of acetamide, it is best to obtain a fresh sample, and the material should be discarded. after it has been used five or six times. Sodium thiosulphate (photographer's hypo) may be used in place of the acetamide, but it will have to be cooled in water, as its change-point is between 40° and 30° C. Plot the cooling curve for each substance, using temperatures as ordinates and times as abscissæ.
(b) Support a tube of distilled water, with thermometer and cork, in a burette clamp and immerse the tube in a freezing mixture of ice and salt. Take temperature readings at intervals, as in part (a), until the water freezes or is cooled below 0° C without freezing. If it is successfully undercooled a few degrees, jar the tube or drop in a very small bit of ice and note carefully what temperature changes occur, recording the time intervals as in part (a). Stop readings when the ice has cooled a few degrees below zero. If the first trial does not result in undercooling the water, try again. Plot the cooling curve for water.
What change of state is occurring while the temperature of the substances remains constant? As the substances are warmer than their surroundings, they are giving off heat continually. How can the temperature remain constant for some time, if this is true? What happens to the rate of cooling as the temperatures approach that of the surroundings? Does this change of rate agree with a law of cooling stated in your text-book? State the difference in behavior of the various substances tested.