232. Thermodynamics. The more advanced theoretical development of the relationships between work and heat is called thermodynamics. In a general sense it covers the principles relating not only to heat machinery, such as steam and gas engines, but also to other thermal devices, and to many chemical and electrical processes where temperature changes are involved. Some of the principles developed are now accepted as ranking among the fundamental laws of nature. Obviously it would be out of place to enter into details here. However, the first and second laws of thermodynamics will be explained. One important deduction applying to heat machinery will be given in Chapter XXIII.

233. The first law of thermodynamics. The first law is the formal statement of the facts given by equation (19) of section 224:

W = JH.

If the mechanical and the heat energy are measured in the same units, the first law of thermodynamics may be stated as follows: In any transfer of other forms of energy into heat, or of heat into other forms of energy, the heat energy is equal to the amount of transformed energy.

This law is merely a special case of the law of the conservation of energy.

234. The second law of thermodynamics. The second law of thermodynamics may be stated thus: It is impossible to operate continuously any machinery by heat energy obtained from bodies the temperature of which is equal to or lower than that of surrounding bodies.

* The heat of combustion in British thermal units per pound can be found by multiplying the values in the table by 1.80.

The oceans of the earth contain tremendous amounts of heat energy. If we could in some way extract that energy and put it to use, we should have available another great storehouse of energy. If we took heat out of the water, we should cool the water to a temperature below its surroundings. From the second law it follows that it is impossible to get useful work from the heat in the ocean. Useful mechanical energy can be obtained from heat energy only when the heat is taken from bodies which are warmer than their surroundings.

The first and second laws of thermodynamics cannot be proved by theoretical reasoning. They are the result of observation and experiment, and have stood the test of so many different types of experiments that we assume they are always true.

235. Dissipation and degradation of energy. There are two important tendencies in nature:

1. Vast amounts of energy are being transferred into heat energy, which is dissipated throughout space. This is true not only of energy supplied to inanimate machinery but also of that supplied to animal and human life.

2. The tendency is for all bodies to come to the same final temperature. When all bodies are at the same temperature, the heat energy they contain is, according to the second law of thermodynamics, no longer available for use. A hot body in cooling down to its surroundings gives up part of its heat energy to the neighboring bodies, and at the lower temperature this energy is no longer available for use. This process is called the degradation of energy.

These two tendencies show that while the total energy in the universe may remain constant, the part which is available for use by man is steadily becoming less. These conclusions, on account of their serious character, have attracted wide attention.

236. Summary. The old theory that heat was a substance has been abandoned, and heat is now believed to be a form of energy-kinetic energy of the molecules, atoms, and electrons.

The calorie and the British thermal unit are units for measuring energy. The mechanical equivalent of heat is the number of ergs or joules in 1 calorie, or it is the number of foot-pounds in a British thermal unit.

In general, compression of a gas heats it and expansion of a gas cools it. In section 226 is given a reason for this, based on the kinetic theory of gases. It follows also from the law of conservation of energy. The adiabatic compression or expansion of a gas is a process so conducted that heat does not flow into or out of the gas during the compression or expansion.

There are two important cases of expansion: (1) Gas which is escaping from a container has kinetic energy. This energy comes from the thermal energy of the compressed gas in the container. Hence the compressed gas becomes colder. (2) If the pressure in the container is kept constant by some sort of pump, while the gas is escaping, the compressed gas in the container will do work as in (1), but work will be done on it in maintaining the pressure constant. If the gas obeys Boyle's law, the gas in the container will neither lose nor gain energy, and its temperature will not change. However, gases do not strictly obey Boyle's law, and there are slight temperature changes. In most cases the escaping gas is slightly cooled, but hydrogen at ordinary temperatures shows a slight heating effect. Expansion under these conditions is called free expansion, and the slight change in temperature that takes place is called the Joule-Thomson effect.

The specific heat of a gas at constant pressure is always greater than the specific heat of that gas at constant volume. (Why?)

The heat of combustion of a substance is the number of heat units 1 gram or 1 pound will give up when burned.

The first law of thermodynamics states that when mechanical energy is converted into heat energy, or vice versa, the amount of mechanical energy is equal to the amount of heat energy. If the two forms of energy are not measured in the same units, then, by equation (19),

W = JH,

where I is the mechanical equivalent of heat.

The second law of thermodynamics states that it is impossible to operate continuously any machinery by heat energy obtained from bodies the temperature of which is equal to or lower than that of surrounding bodies.

The amount of energy which is available for use by man is steadily decreasing through the dissipation and degradation of energy.

PROBLEMS

1. How does the experiment of Joule show that there must be internal friction or viscosity in water?

2. A motor with an output power of H. P. churns up 209 lb. of water for an hour, and as a result the temperature of the water rises 6.1° F. What value does this indicate for the mechanical equivalent of heat?

3. A bullet of 8 gm. mass has a velocity of 600 m./sec. To how many calories is this energy equivalent ?

4. Find the distance a lead ball must fall if the impact warms the ball 1o C., assuming that half of the energy of fall goes to heat the ball. Neglect air resistance. (The specific heat of lead is 0.031 cal. per gram per degree.)

5. If a man eats 1000 kg.-cal. in 20 min., at what horse power is he receiving energy?

6. A man eats 3800 kg.-cal. each day and performs 600,000 ft.-lb. of useful work. Regarding him as a machine, compute his efficiency.

7. 1000 H. P. is required to run a railroad train at a constant speed on a level track. How many pounds of water could be raised from freezing point to boiling point per hour by this power ?

8. If the earth receives from the sun 2 cal. of heat per minute for each square centimeter of the earth's surface, how many horse power does it receive per square meter?

9. A rifle bullet the weight of which is 0.0124 lb. has a velocity of 3000 ft./sec. To how many British thermal units is this equivalent ?

10. A given type of coal has a heat of combustion of 7500 cal./gm. If 20 per cent of the energy could be converted into useful work, how much coal would be required for each horse-power hour of useful work?

11. H. P. is expended in the frictional losses in the shafting of a machine shop. How many British thermal units are generated per hour?

CHAPTER XX

THE TRANSFER OF HEAT

Methods of transfer of heat, 237. Conduction, 238. Rate of flow of heat; conductivity, 239. Convection, 240. Systems of heating, 241. Winds and ocean currents, 242. Radiation, 243. Heat radiation travels in straight lines, 244. Reflection, 245. Radiation at low temperatures; law of exchanges, 246. Apparent radiation of cold from ice, 247. The mean temperatures of the earth and other planets, 248. Cooling by radiation, 249. Good and poor radiators, 250. The Dewar flask; the thermos bottle, 251. Other illustrations, 252. Radiant energy not a homogeneous radiation, 253. Rate of cooling of hot bodies, 254. Summary, 255.

237. Methods of transfer of heat. Heat is transferred by three different methods: conduction, convection, and radiation. These, with numerous illustrations, will be explained in this chapter.

238. Conduction. If a silver spoon is placed in a cup of very hot coffee, the handle of the spoon becomes hot. When there is a fire in a stove, all metal parts of the stove get hot. In some way heat is conducted from the hotter parts of the spoon or the stove to the colder parts. This is often spoken of as a flow of heat from one part of a body to another. But the word flow may be misleading. Heat is not a fluid: it is the energy of agitation of the extremely small particles of which substances are constructed. When one end of a bar is heated, the molecules and electrons near that end are given greater vibratory motion, greater kinetic energy. In some way, probably by collisions, these particles are able to share their increased energy with their neighbors, the latter, in turn, sharing their increased kinetic energy with those beyond, and so on. Thus energy of agitation is propagated along the bar. The electrons, being very much smaller than the molecules and atoms and being able to move in the interstices between the molecules, are probably the most effective agents in transferring energy from one molecule to its neighbor.