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is being formed which too, has the same temperature as the water. Not until 970.4 B.t.u. or sufficient heat units to raise ten pounds of water almost one hundred degrees in temperature have been added to the pound of water at 212°F. will the pound of water become entirely converted into steam at 212°F. This quantity of heat necessary is important in steam engineering and is known as the latent heat of evaporation for water under atmospheric pressure conditions. To be succinct, in steam engineering practice the quantity of heat necessary to convert one pound of water at a given temperature and pressure into dry steam at the same temperature and pressure is known as the latent heat of evaporation for that temperature and pressure and is usually expressed by the symbol L. Steam boilers seldom operate at a pressure so low as that of atmospheric conditions. Indeed, while such a pressure is but 14.7 lb. per sq. in., the modern boiler in the central station operates at something like ten to fifteen times this pressure. This fact materially complicates computation in steam engineering, for it is found that at pressures different than that of standard atmospheric conditions the latent heat of evaporation is wholly different. Indeed, so complex is this law of variation that no one as yet has been able to give an exact formula for its determination, although in subsequent chapters approximate equations will be set forth. Hence, it has become necessary to refer to carefully compiled steam tables for such information and a later chapter will set forth the manner of their use.
Other Variations Occur With Changes of Pressure. When water passes into steam, the volume-say of one pound-vastly increases. At atmospheric pressure the volume of steam is about sixteen hundred times what it was when existing as water. At other pressures the volume relationships will of course be different. Again when the pressure increases at which steam is formed, the volume becomes less in proportion. No accurate mathematical formula has been found for this relationship hence once again must we appeal to the steam tables.
Data Easily Taken from Steam Tables.-By experiment it has been found that varying amounts of heat are required to raise water from a particular initial temperature to the boiling point, for the boiling point is not reached until a higher temperature is attained as the pressure is increased. On the other hand, less heat is required to convert a pound of water at these higher
boiling points into steam. Since the volume and density too vary under varying pressures, the entire problem now becomes one of picking the proper constants for the particular temperature and pressure under discussion and when one by a little practice can use the steam tables with facility, it is surprising to see how simply and directly most problems in steam computation may be solved.
Total Heat of Steam.-Often in steam engineering practice problems arise in which we must express the total heat of steam quantitatively represented in each pound under consideration. It makes little difference at what point we begin to estimate such heat relationships, but by common consent the freezing point of water has been adopted. Hence, the total heat of steam is the heat required to raise one pound of water from 32°F. to the boiling point added to the heat required to convert this water into steam at that temperature. If the steam exist as superheated steam, there must also be added the heat required to raise dry saturated steam to the temperature of superheat. The various mathematical formulas for computing these numerical results will be taken up later in a chapter entitled Quality of Steam. At this particular time we shall write down the simplest of these formulas as an illustration.
Total Heat of Dry Saturated Steam.-The total heat of dry saturated steam, written H, for a given temperature t, is the sum of the heat of liquid and latent heat of evaporization for that temperature.
Hence we may write this important fundamental equation
Other Instances of Total Heats.-If, however, the steam is evaporated from the water and then superheated, that is, an additional quantity of heat is added after all the water has become steam, it will then begin to rise in temperature and the quantity of heat necessary for each degree rise in temperature is about one half that required per degree rise when it existed as water. This exact ratio is however quite variable and ranges between .46 and .60 depending upon the pressure and degree of superheat attained. Hence once again appears the necessity of steam tables.
It is now readily seen that in general three definite and distinct considerations present themselves in the solution of problems involving the computation of total heat. The first instance is one in which the steam exists in a dry state and at the temperature and pressure at which it is generated from the water. Such steam is known as dry saturated steam. The second instance is that in which the steam is not completely dry, but holds in suspension small particles or globules of water, and in this instance the mixture is known as wet steam. The third instance is of especial importance in modern central station practice and involves what is known as superheated steam. In this case the steam is first formed by evaporation from water into dry saturated steam, after which it is conveyed through pipes that are exposed to high temperatures, thus causing the temperature of the steam to be still further raised, although the pressure practically remains constant.
The complete solution of these three instances for computation of total heats will be found in the chapter on Quality of Steam as stated above. Meanwhile the thorough mastery of the fundamentals of the physical properties of water as herein set forth will be of vast assistance in a clear understanding of this later discussion.
1. The water entering a feed-water heater is at a temperature of 75°F. and leaves the heater at 190°F., what is the heat absorbed per lb. of water? From the steam tables the heat of liquid at 75°F. is 43.05 B.t.u. and at 190°F. it is 157.91 B.t.u. Hence the heat absorbed per lb. of water is 114.86 B.t.u.-Ans.
2. Water enters a boiler at 160°F. and is converted into dry saturated steam at 200 lb. pres. per sq. in. abs., what is the total heat required to evaporate each lb. of steam?
The heat in the entering water at 160°F. is from the steam tables 127.86 B.t.u. The total heat of dry saturated steam at 200 lb. pres. abs., is 1198.1 B.t.u. Hence the actual heat necessary to evaporate each lb. of steam is 1198.10 127.86 = 1070.24 B.t.u.-Ans.
3. If the heat of liquid for boiling water at 212°F. is 180 B.t.u. and the latent heat of evaporation is 970.4 B.t.u., how much heat is required to evaporate a pound of water from an open water heater which is receiving its supply at 64°F.?
Each lb. of water entering at 64°F. has a heat of liquid of 32.07 B.t.u. Water evaporating into steam at 212°F. has a heat of liquid of 180 and a latent heat of evaporation of 970.4 B.t.u., making a total heat of evaporation of 1150.4 B.t.u. for every lb. of water so evaporated. Hence the net heat required is
THE STEAM TABLES
FIG. 36. The book of steam tables.
IT has already been shown that since no simple mathematical laws have as yet been devised to express the temperature, pressure, latent heat, heat of liquid and other fundamental properties of steam and water that are absolutely necessary in the solution of steam engineering problems, we must resort to carefully compiled steam tables.
Practically all the research and scientific investigation along the lines of pure steam engineering of the last half century have been devoted to the more complete establishment of some of the fundamental constants involved in the steam tables.
The three most important of these are the zero point of the absolute temperature scale, the proper value for a constant employed in the conversion of mechanical energy into heat energy, and the exact determination of the heat required to evaporate one pound of water from 212°F. into dry saturated steam at 212°F. Since these values are continually found by more careful and exacting experimental work to be slightly different than formerly held, we find that the steam tables of recent publication are different than those of former years.
The Steam Tables as Adopted in this Discussion. The Steam Tables and Diagrams as computed by Marks and Davis and published by Longmans, Green & Company, are today universally recognized and are adopted as the standard compilation for the problems cited in this discussion.
In the rear of these steam tables an interesting discussion of the methods employed by these investigators in arriving at the
three fundamental constants mentioned above is given. The result of these investigations shows that the absolute zero is to be taken at 459.6°F., the mechanical equivalent of heat at 777.5, and the latent heat of steam at 212°F. to be 970.4 B.t.u.
Recapitulation of Fundamental Evaluations.-These three constants are 'so important that they should be memorized and for emphasis let us recapitulate their exact interpretation.
The absolute zero is now found to be a point situated at 459.6° F. below the zero point on the Fahrenheit scale or 491.6°F. below the freezing point of water. At such a temperature it is supposed to be impossible to further draw off heat from any substance for at this temperature the heat storage is supposed to be absolutely exhausted.
The mechanical equivalent of heat as given above means that the energy represented by one B.t.u. or British thermal unit of heat is equivalent to 777.5 ft. lb. of mechanical energy. Or if one pound of crude petroleum contains 18,500 B.t.u., it possesses as stated in a previous chapter, sufficient energy to raise a human being weighing 175 lb. a vertical upward distance of over 18 miles.
The latent heat of steam at 212°F. and atmospheric pressure means that the quantity of heat necessary to evaporate one pound of water at 212°F. into dry saturated steam at 212°F. is found experimentally to be 970.4 B.t.u.
Analysis of a Typical Page of Steam Tables.-Let us now proceed to analyze a page of Marks & Davis' steam tables, column by column. The illustration as given is found on page 12 of this compilation and we shall follow across the page the line. corresponding to a temperature of 231°F.
Temperatures in Fahrenheit Units. Since all steam engineering computation is based on temperatures represented in the Fahrenheit scale instead of the Centigrade system, the temperatures are here listed in the Fahrenheit units.
Pressures in Absolute Notation. This column means that the pressures here given represent the pressure in pounds per sq. in. at which water will boil when the temperature is that as listed in the first column. Further on in the steam tables an exactly similar table may be found to the one cited except in this latter instance the pressures are made to vary pound by pound and the corresponding boiling temperature of water given.
In this instance, then, we read that a pressure of 21.16 lb.