5. Air temperature is 30° C., and the relative humidity 60 per cent. Estimate the value of the dew point.

6. How many grams of water must be evaporated into a room 10 m. square and 4 m. high to raise the relative humidity from 30 per cent to 70 per cent when the temperature is 20° С.?

7. The dew point near the ground was 24° C. The air rose until its volume was doubled, and it became saturated at 0° C. Compute the number of grams of water vapor condensed from each cubic meter of the air, measured at the ground.

8. A cubic meter of air has at normal pressure a thermal capacity of about 250 cal. How much would its temperature be increased if it received all the heat liberated by the condensation of 10 gm. of water vapor? (Assume the heat of vaporization to be 600 cal./gm.)

CHAPTER XXIII

HEAT ENGINES

Heat engines, 304. The reciprocating steam engine, 305. Efficiency of an engine, 306. Steam turbines, 307. Maximum theoretical efficiency, 308. Internal-combustion engines, 309.

304. Heat engines. The earliest heat engine was probably the toy invented by Hero, a pupil of Archimedes. Steam was generated in a hollow ball which was partly filled with water. This steam escaped through two tubes on opposite sides of the ball. The ends of the tubes were bent so that the reaction from the steam jets supplied the motive force to set the ball in rotation. This reaction principle is today used in some types of the steam turbine.

There are many types of machines now in use for converting heat energy into mechanical energy. The great development of these has been due in part to the large supplies of fuel from which energy in the form of heat can be conveniently obtained. In several types of engines the fuel is used to generate steam, and the energy in the steam is used to drive the engine, as was the case in Hero's toy. In another class the fuel is actually burned inside the engine. The commonly used gasoline engine is one type of these internal-combustion engines. There are other special types (the hot-air engine, for example), but space will not permit an explanation here of all the various types which have been developed.

305. The reciprocating steam engine. The development of the modern steam engine has been one of gradual evolution, many men making important contributions; but the work of James Watt (1736-1819) was so important that he is often given the credit for its invention. Watt's engine was far more efficient than any of the earlier types, requiring for the development of the same mechanical energy only about one fourth as much coal as its predecessor.

An understanding of the way steam under pressure can be used to run an engine may be obtained by aid of the simplified diagram of Fig. 179. The piston P is connected by the driving-rod R to the shaft S by a crank, as shown. The eccentric rod R' is connected to the slide valve B, which, as it slides to and fro, first uncovers the passageway N into the right end of the cylinder and then, closing it, uncovers M, leading into the left end. When steam under pressure enters at A, it flows through N into the right end

of the cylinder, forcing the piston P toward the left. At this stage the steam on the left side of the piston can escape through M and out of the exhaust E. As the piston moves, it turns the shaft S by means of the driving-rod and crank. This causes the slide valve B to move to the right. The slide valve thus first cuts off the supply of steam through N, and then a little later closes the exhaust from the left end of the cylinder. When the piston has reached the far end, the right end of the cylinder is connected through N to the exhaust E, and live steam is admitted to the left end of the cylinder through M. Thus, as the piston P moves back and forth, the slide valve also moves back and forth, first admitting steam into one

side of the cylinder, then at the proper time turning the steam into the other, while the first side is connected to the exhaust, and so on. Thus a continuous reciprocating motion is given to the piston, and a continuous rotation to the shaft. In a stationary engine a heavy flywheel is necessary to insure the passing of dead centers and to keep the motion uniform.

More energy can be extracted from the same amount of steam if the supply to one end of the cylinder is cut off before the piston has reached the end of its motion. Before the steam supply is cut off, the steam in the cylinder is at high pressure and temperature, nearly that of the boiler. After the valve is closed, the steam in the cylinder expands, driving the piston on. In this way the vapor does work and loses energy; hence its temperature and pressure fall. If the valve is properly adjusted, the pressure of the steam will fall to nearly that of the place into which it passes from the exhaust. If the steam had been kept at high pressure in the cylinder, the work it could do by its own expansion would have been lost. The lower the temperature at which the steam is released, the more heat energy of the steam has been utilized.

If the steam escapes into the atmosphere, the engine is called noncondensing; but if the steam is led into some place where it is condensed at a low temperature and pressure, the engine is called a condensing engine. The condenser is an air-tight chamber the interior of which is maintained much below the atmospheric pressure. As the steam enters this chamber it is condensed by a spray of cold water. If the temperature of the condenser is very low, the pressure of the vapor in it cannot be higher than the pressure of water vapor saturated at that temperature. It should be obvious that when the steam is forced out from the cylinder into the atmosphere, it exerts a back pressure on the piston of about 15 pounds per square inch. But in a high-grade condensing engine the pressure in the condenser may be as low as 1 pound per square inch, or about 14 pounds per square inch lower than atmospheric pressure. When the steam exhausts into such a condenser, the back pressure on the piston is very small. Hence the steam driving the piston forward can expand to a lower pressure and temperature, thus giving up more of its heat energy.

In the compound engine the steam passes through several cylinders in succession. In the first cylinder the steam expands to an intermediate pressure. At this reduced pressure the steam goes into the second cylinder, and from there it may exhaust into the condenser. In the triple-expansion engine the steam passes through three cylinders, the pressure being reduced in each one. Quadrupleexpansion engines are now in use, where the same steam passes in turn through four cylinders. The most effective steam engines today are quadruple-expansion condensing engines.

It is important for the student to understand the general transfers of energy that take place in a steam-power plant. In the first place, the fuel has a definite amount of energy. When the fuel is burned, the energy is converted into heat energy. Part of this heat energy is used to raise water to its boiling point and to convert it into steam under pressure. The steam under pressure does work in two steps. First, when steam is forced into the cylinder, the steam in the boiler does work in expanding. This is a cooling process, and the steam in the boiler loses energy. Then, when the steam in the cylinder is cut off from the boiler, it expands, doing work, and loses heat energy as its pressure and temperature fall. In both steps expanding steam does work on the piston. In this way mechanical work is done at the expense of heat energy.

306. Efficiency of an engine. There are several different quantities which are called the efficiency of an engine. Inasmuch as all these are commonly used, it is important to know the differences between them.

The thermal efficiency may be defined as the ratio of mechanical work per hour to the available energy in steam supplied per hour (the two must be measured in the same units). The "available" energy of the steam is the difference between the heat energy the steam has at the high temperature of the boiler and the heat energy it has after it has condensed into water. It may be stated as the amount of energy required to put the water from the condenser back into steam in the boiler. The "mechanical work" usually includes the total mechanical energy developed, including that lost in the engine on account of the friction of its bearings. The rate at which this energy is developed is often referred to as