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The maximum density of water occurs at 4° C.

The general gas law is, by equation (12),

pv = RT,

where T is temperature measured on the gas scale. The gas scale is practically identical with the Kelvin, or absolute, scale. The temperature T is the temperature in centigrade plus 273. The following are convenient working equations:

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PROBLEMS

1. How much will the length of 200 ft. of copper wire change for a change in temperature of 50° C.? (The coefficient is .000016.)

2. An iron steam-pipe line is 100 ft. long at 20° C. What will be the increase in its length when steam at 105° C. passes through it? (The coefficient of expansion is .000012.)

3. Calculate the change in length of a steel bridge 300 ft. long between a winter minimum of 30° C. and a summer maximum of + 40° C. if the coefficient for steel is .000012.

4. A steel scale which was correct at 0° C. was used to measure a certain distance. The reading, 84.12 cm., was taken at a temperature of 30° C. What was the error? (The coefficient of steel is .000012.)

5. How long must a brass bar be in order that its change of length may be the same as that of a steel bar 100 cm. long? (The coefficient of steel is 000012; of brass, .000018.)

6. A steel ball displaces 400 cc. of water at 0°C. How many cubic centimeters will be displaced at 30° C.?

7. A steel rod has its temperature raised 20°C. How much compressional stress must be applied to this rod in order to prevent it from expanding? (The coefficient of expansion is 000012, and Young's modulus is 28 × 106 lb./sq. in.)

8. A certain mass of gas has a volume of 1000 cc. at 50° C. What will be the volume if the temperature is raised to 90° C., the pressure remaining constant?

9. Air passing through a hot-air furnace has its temperature changed from 15° C. to 60° C. What is the percentage increase of its volume?

10. A steel vessel holds 500 gm. of mercury at 0° C. How many grams will it hold at 30° C.? (The linear coefficient of steel is .000012; the volume coefficient of mercury is .00018, and its density is 13.60 at 0° C.) 4.17.

11. A glass vessel contains 200 cc. of alcohol, and is full at a temperature of 15° C. How many cubic centimeters will spill over when the temperature is raised to 40° C.? (The volume coefficient of glass is .00002; of alcohol, .00110.) 5,400

12. The air in an automobile tire had a pressure of 80 lb./sq. in. (above atmospheric pressure, which is 15 lb./sq. in.) at a temperature of 20° C. What will be the pressure in the tire when, from fast driving, its temperature is raised to 60° C.? (Assume the volume to be constant.).

13. A constant-volume gas thermometer was used to measure temperature. At 0° C. the observed pressure was 86.2 cm. At another temperature the pressure was 98.8 cm. Compute the temperature.;

14. A gram of air occupies 774 cc. at 0° C. and at a pressure of 76 cm. of mercury. What will be its volume at 20° and at a pressure of 73 cm. of mercury?

844,500

15. A certain mass of dry air at a temperature of 20° C. and a pressure of 74 cm. of mercury has a volume of 500 cc. Find the pressure at a temperature of 30° C. when the volume is 600 cc.

CHAPTER XVIII

QUANTITY OF HEAT

Quantity of heat, 213, Heat a form of energy, 214. Units for measuring quantity of heat, 215. Method of mixtures, 216. Calorimetry, 217. Thermal capacity, 218. Specific heat, 219. Experimental determination of specific heat, 220. Summary, 221.

213. Quantity of heat. A comparatively simple experiment will bring out an important fact. To perform this two Bunsen burners giving the same kind and type of flame are used. One of them is placed under a suspended block of iron weighing about a pound, and the other is at the same time placed under a pound of water in a thin-walled vessel. In a few minutes the iron will be heated above the boiling point of water, as can be shown by dropping a little water on it, while the equal mass of water will still be cool enough for one to hold his fingers in it. If we assume that the two, the iron and the water, receive heat at the same rate, it is obvious that the increase in temperature of the two is not the same thing as the quantity of heat they have received. Other experiments might be cited to support this. For example, if a pan of crushed ice is placed on a hot stove, the mixture of ice and water will remain at a constant temperature of 0° C. until most of the ice is melted. In this case, adding heat did not produce at once an increase in temperature. Hence it is necessary to distinguish between quantity of heat and temperature. The distinction should be seen clearly before the student has completed this chapter.

214. Heat a form of energy. The old theory was that heat was a material substance, called caloric, which in some way was able to penetrate bodies. A hot body contained a large amount of it, while a cold body contained a smaller amount. It was necessary to assume that this substance was not like ordinary matter; for example, it possessed neither inertia nor weight.

The modern theory regards heat as a form of energy. According to this theory the molecules, atoms, and electrons in all bodies are in a continual state of vibration. In a hot body these small particles have relatively large amounts of kinetic energy, while in a cold one they have less. From this point of view it is easy to understand how friction develops heat in a body, for when one body slides over another the molecules on the two surfaces are given an increased vibration. It is also important to look at this from the standpoint of the principle of conservation of energy. Because the small particles are given motion, and hence kinetic energy, work must be done to slide one body over the other. Mechanical energy apparently disappears. But the "lost" energy is now kinetic energy of the small subdivisions of matter, -a form of energy we call heat.

It will appear later that what we now call quantity of heat is really the energy of these small subdivisions of matter.

215. Units for measuring quantity of heat. Three different units are commonly used in measuring quantity of heat. They are defined as follows:

The calorie, or gram-calorie, is equal to the amount of heat required to change the temperature of 1 gram of water 1 degree centigrade.

The kilogram-calorie is equal to the amount of heat required to change the temperature of 1 kilogram of water 1 degree centigrade.

The British thermal unit (B.T.U.) is equal to the amount of heat required to change the temperature of 1 pound of water 1 degree Fahrenheit.

To aid in fixing these units in mind the student should mentally verify the following calculations:

The quantity of heat required to raise 1 gram of water from 10° C. to 30° C. is 20 calories.

The quantity of heat required to raise 400 grams of water from 10° C. to 40° C. is 12,000 calories, or 12 kilogram-calories.

The quantity of heat required to raise 5 pounds of water from 40° F. to 65° F. is 125 British thermal units.

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The preceding definitions are only approximations, although they are sufficiently close for all except very accurate work. More precise definitions should state the exact temperature range. For example, the precise definition of the calorie may be stated as the quantity of heat necessary to change 1 gram of water from 15° C. to 16° C. The reason for this explicit statement is that it is not true that the same amount of heat is required to change 1 gram of water 1 degree whatever the initial temperature may be. The amount is slightly different for different ranges.

216. Method of mixtures. The solution of the following problem brings out a principle which has a very wide use in quantitative work in heat.

Problem. 200 gm. of water at 10° C. are mixed with 500 gm. of water at 30° C. Compute the temperature of the mixture.

Solution. In this mixture 20 gm. of water gain heat, while 500 gm. lose heat. If the mixing takes place under such circumstances that heat is not gained from, or given up to, other bodies in the neighborhood, the heat gained by the one must equal that lost by the other part (if it is granted that heat is a form of energy, this follows from the principle of conservation of energy).

The heat gained is 200 (t - 10) cal., and the heat lost is 500 (30 - t) cal., where t is the temperature of the mixture. Equating these, 200 (t − 10) = 500 (30 – t),

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The important principle is expressed by saying that the number of calories gained by one part is equal to the number of calories lost by the other part.

217. Calorimetry. Since the usefulness of coal is proportional to the quantity of heat that it gives off when burned, it is often bought and sold on the basis of the number of British thermal units that 1 pound gives off. The heat from a sample can be measured by an apparatus in which all the heat given up by the coal goes into a water jacket which surrounds the combustion chamber. If the weight of the water and the change of temperature are known, the number of British thermal units can be computed. This is one example of many cases in which it is important to measure the

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