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Steam power

Tomlinson Carlile Ulbricht · 1916 · Scanned text · Free in the US

100,073 words · about 7 h to read

Period artwork: Interior of the Bodleian Library, 1845
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About this book

Author
Tomlinson Carlile Ulbricht
Language
English
Published
1916
Length
100,073 words · about 7 h
Sections
32 reader sections
Text
Scanned text, read from page scans by OCR; may contain errors
Rights
Public domain in the United States

 

Contents (32)

Continue:

Front matter

Class ZOZaJz:^

Book . Ij,^^

CoEyiiglitJv'?.

Preface

The following pages represent the results of an attempt to collect in a comparatively small book such parts of the field of steam power as should be familiar to engineers whose work does not require that they be conversant with the more complicated thermodjmamic principles considered in advanced treatments. The experience of the authors has led them to believe that a book of this sort should give a correct view-point with regard to the use of heat in the power plant even though it does not enter deeply into the theoretical considerations leading up to that view-point; that it should supply the tools required for the solution of power plant problems of the common sort ; and that it should give sufficient description of power plant apparatus to make the reader fairly familiar with the more common types.

Mathematical treatment of the subject has been eliminated to the greatest possible extent, and anyone familiar with elementary algebra should be able to understand readily such equations as it has been deemed necessary to include.

Brief explanations of physical and chemical concepts

are given in every case in which the text required their use,

so that those who have not studied these subjects, and those

who have but have failed to crystallize and hold the neces-

iii iv PKEFACE

sary ideas, should have httle difficulty in reading the text understandingly.

It is hoped that the book may prove serviceable as a text for steam power courses given to civil engineers in the various colleges and that it may also meet the needs of those instructing power plant operators in industrial schools.

C. F. H.

T. C. U.

Chapter I Page

1. Matter. 2. Energy. 3. Units of Matter and Energy. 4. Work. 5. Mechanical Energy. 6. Heat. 7. Temperature. 8. Measurement of Temperature. 9. The Unit of Heat Energy. 10. Specific Heat. 11. Quantity of Heat. 12. Work and Power.

CHAPTER II The Heat-power Plant 20

13. The Simple Steam-power Plant. 14. Cycle of Events. 15. Action of Steam in the Cylinder. 16. Hydraulic Analogy.

Chapter III

17. Vapors and Gases. 18. Properties of Steam. 19. Generation of Steam, or Water Vapor. 20, Heat of Liquid, q or h. 21. Latent Heat of Vaporization, r or L. 22. Total Heat of Dry Saturated Steam, X or H. 23. Total Heat of Wet Steam. 24. Heat of Superheat. 25. Total Heat of Superheated Steam. 26. Specific Volume of Dry Saturated Steam, V or S. 27. Specific Density of Dry Saturated

Steam, — or 5. 28. Reversal of the Phenomena Just Described. 29. Generation of Steam in Real Steam Boiler. 30. Gauge Pressure.

Chapter IV

31. The Engine. 32. Operation of the Engine. 33. Work Done by the Engine. 34. Heat Quantities Involved. 35. Efficiency. 36. Effect of Wet Steam. 37. Apphcation to vi CONTENTS

PAGE

a Real Engine. 38. Desirability of Other Cycles. 39. The Complete Expansion Cycle. 40. The Incomplete Expansion Cycle.

Chapter V

41. Definitions. 42. Temperature-Entropy Chart for Steam. 43. Quality from T^-Chart. 44. Volume from T<t)- chart. 45. Heat from T</)-chart. 46. The Complete T<^- chart for Steam.

CHAPTER VI Temperature Entropy Diagrams of Steam Cycles 72

47. Complete-expansion Cycle. 48. Area of Cycle Representative of Work. 49. Modifications for Wet and Superheated Steam. 50. Incomplete Expansion Cycle. 51. Effect of Temperature Range on Efficiency.

Chapter VII

52. Operations of Real Engine. 53. Losses in Real Installations. 54. Clearance. 55. Cushion Steam and Cylinder Feed. 56. Determination of Initial Condensation. 57. Methods of Decreasing Cylinder Condensation. 58. Classification of Steam Engines. 59. Rotative Speeds and Piston Speeds. 60. The Simple D-Slide Valve Engine. 61. Engine Nomenclature. 62. Principal Parts of Engines.

CHAPTER VIII The Indicator Diagram and Derived Values 115

63. The Indicator. 64. Determination of I.h.p. 65. Conventional Diagram and Card Factors. 66. Ratio of Expansion. 67. Determination of Clearance Volume from Diagram. 68. Diagram Water Rate. 69. T<^-diagram for a Real Engine, 70. Mechanical and Thermal Efficiencies.

Chapter IX

71. Gain by Expansion. 72. Compounding. 73. The Compound Engine. 74. Cylinder Ratios. 75. Indicator ■ Diagrams and Mean Pressures. 76. Combined Indicator Diagrams.

CONTENTS vii

Chapter X Page

77. Description and Method of Operation. 78. Steam Lap. 79. Lead. 80. Angle of Advance. 8L Exhaust Lap. 82. The Bilgram Diagram. 83. Exhaust and Compression. 84. Diagram for Both Cyhnder Ends. 85. Piston Positions. 86. Indicator Diagram from Bilgram Diagram. 87. Limitations of the D-slide Valve. 88. Reversing Engines. 89. Valve Setting.

CHAPTER XI Corliss and Other High-efficiency Engines 196

90. The Trip-cut-off Corliss Engine. 91. Non-detaching Corliss Gears. 92. Poppet Valves. 93, The Una-flow Engine. 94. The Locomobile Type.

Chapter XII

95. Kinds of Regulation. 96. Governor Regulation. 97. Methods of Varying Mean Effective Pressure. 98. Constant Speed Governing. 99. Governors..

Chapter XIII

100. The Impulse Turbine. 101. Theoretical Cycle of Steam Turbine. 102. Nozzle Design. 103. Action of Steam on Impulse Blades. 104. De Laval Impulse Turbine. 105. Gearing and Staging. 106. The Reaction Type. 107. Combined Types. 108. Economy of Steam Turbines.

Chapter XIV

109. The Advantage of Condensers. 110. Measurement of Vacuum.s. 111. Conversion of Readings from. Inches of Mercury to Pounds per Square Inch. 112. Principle of the Condenser. 113. Types of Condensers. 114. The Jet Condenser. 115. Non-Contact Condensers. 116. Water Required by Contact Condensers. 117. Weight of Water Required by Non-contact Condensers. 118. Relative Advantages of Contact and Surface Condensers. 119. Cooling Towers.

viii CONTENTS

Chapter XV Page

120. Definitions. 121. Combustion of Carbon. 122. Combustion to CO. 123. Combustion to CO2. 124. Combustion of CO to CO2. 125. Conditions Determining Formation of CO and CO2. 126. Flue Gases from Combustion of Carbon. 127. Combustion of Hydrogen. 128. Combustion of Hydrocarbons. 129. Combustion of Sulphur. 130. Combustion of Mixtures. 131. Temperature of Combustion.

Chapter XVI

132. Commercial Fuels. 133. Coal. 134. Coal Analyses. 135. Calorific Value of Coals. 136. Purchase of Coal on Analysis. 137. Petroleum.

Chapter XVII

138. Definitions and Classifications. 139. Functions of Parts. 140. Furnaces and Combustion. 141. Hand Firing. 142. Mechanical Grates. 143. Smoke and its Prevention. 144. Mechanical Stokers. 145. Rate of Combustion. 146. Strength and Safety of Boiler. 147. Circulation in Boilers. 148. Types of Boilers. 149. Boiler Rating. 150. Boiler Efficiencies. 151. Effects of Soot and Scale. 152. Scale. 153. Scale Prevention. 154. Superheaters. 155. Draft Apparatus.

Chapter XVIII

156. Waste Heat in Steam Plant. 157. Utilization of Exhaust for Heating Buildings. 158. Feed-water Heating.

Chapter XIX

159. Boiler-feed Pumps. 160. The Steam Injector. 161. Separators. 162. Steam Traps. 163. Steam Piping.

Chapter I Physical Conceptions And Units

1. Matter. The universe is generally pictured as composed of matter and energy. Matter is regarded as that which is possessed of mass, or as that which is possessed of inertia; i.e., which requires the action of force to put it in motion, to bring it to rest or to change its velocity. These definitions merely enumerate characteristics of matter; they do not tell what it really is. In the present state of knowledge it is, however, impossible to define matter in any other way.

No experiment has yet shown that matter can be created or destroyed by man. It can be changed from one form to another, it can be given certain physical and certain chemical characteristics, more or less at will, but the actual quantity of matter concerned is always the same after and before such changes. It is customary to state this experience in the form of a law known as the Law of the Conservation of Matter, which states that the '^ total quantity of matter in the universe is constant.''

Matter is known to exist in several physical states or conditions of aggregation. The three most familiar are (1) solid, (2) liquid and (3) gaseous. In each of these states matter is conceived as made up of minute particles called molecules which in turn are apparently composed of still smaller parts known as atoms. These atoms can also be broken into parts, but for the purposes of this book it is not necessary to consider such divisions.

Experiment and mathematical reasoning seem to indicate that the molecules of all materials are in constant motion and that there are neutralizing attractive and repulsive forces acting between them. In solids the molecules are apparently bound together in such a way that, although they are in constant motion, the external form or shape of the body tends to remain constant; in fact it requires the expenditure of force to cause a change of form. In liquids the molecular attraction is so altered that practically all rigidity disappears and the shape assumed by the liquid is determined by that of the surrounding surfaces, as, for instance, the shape of the vessel containing the liquid. In gases the molecules are still more free and actually tend to move apart as far as possible, so that a gas will spread in all directions until it fills any closed containing vessel.

2. Energy. Nearly everyone has a conception of what is meant by the term energy, but no one yet knows what energy really is. It is defined as the capacity for doing work, or the ability to overcome resistance. A man is said to be very energetic or to be possessed of a great deal of energy when he has the ability to perform a great amount of work or to overcome great resistances. Matter is sai^ to be possessed of energy when it can perform work or overcome resistance. Actually, matter is not known in any form in which it is not possessed of energy.

There are many different forms of energy. A body in motion can do work and is said to be possessed of mechanical energy. A body which we recognize as hot can do work at the expense of the heat associated with it and is said to be possessed of heat energy. Light, sound and electricity are all forms of energy.

Experiment and experience have never shown that energy can be destroyed or created by man, but they have shown that one form of energy can be converted into another form under proper conditions. The first part of this experience is stated as a law known as the Law of the Conservation of

Energy. This law states that '' the total quantity of energy in the universe is constant."

3. Units of Matter and of Energy. When attempts are made to measure the amount of anything, some unit of measurement is adopted. Matter is measured in numerous ways and many units are used. The common methods of measuring matter are bj^ volume and by weight. Engineers in English-speaking countries use the cubic yard, the cubic foot or the cubic inch as units in measuring matter by volume and they use the pound, the ounce, the grain, etc. as units in measuring matter by weight.

Energy is measured in many units and, in general, there is a characteristic unit or set of units for each form in which it occurs. Thus the foot-pound is very commonly used for measuring mechanical energy; the British thermal unit for measuring heat energy; and the joule for measuring electrical energy. Some of these units will be defined and considered in greater detail in subsequent paragraphs.

4. Work. Work is defined as the overcoming of a resistance through a distance. Thus, work is done when a weight is raised against the resistance offered by gravity; work is done when a spring is compressed against the resistance which the metal offers to change of shape; work is done when a body is moved over another against the resistance offered by friction.

The unit of work is the quantity of work which must be done in raising a weight of one pound through a vertical distance of one foot. It is called the foot-pound. Thus, one foot-pound of work must be done in raising one pound one foot; two foot-pounds of work must be done in raising two pounds one foot or in raising one pound two feet.

If a weight of one pound were suspended from a spring balance as shown in Fig. 1, the balance would indicate a pull or force of one pound. No work would be

Fig. 1.

done by this force as long as the weight remained stationary, because no resistance would be overcome through a distance. If, however, the same weight were slowly or rapidly raised a vertical distance of a foot, one foot-pound of work would be done. A force or pull of one pound would then have overcome a resistance of one pound through a distance of one foot. In general:

Work in ft. -lbs. = Resistance overcome in lb s.X distance. = Force in Ibs.Xdistance in ft.

so that if a force of 10 lbs. pushes or pulls anything which offers a resistance of 10 lbs. while that something travels a distance of, say, 5 ft., the work done will be given by the expression,

Work = 10X5,

A body in falling a certain distance can do work equal to its weight multiplied by the distance it falls because it could theoretically raise an equal weight an equal distance against the action of gravity, and the work done upon this second body would be equal to its weight multiplied by the distance through which it was raised.

It is very important to note that no work is done by a force if there is no motion; resistance must be overcome through a distance in order that work may be done. Thus, a force of 1000 lbs. might be required to hold something in position, that is to balance a resistance, but no work would be done if the body upon which the 1000-pound force acted did not move. Again, a weight of 50 lbs. held at a distance of 10 ft. above the surface of the earth would exert a downward push or pull equal to 50 lbs. on whatever held it in that position; it would, however, do no work if held in that position. If allowed to fall through the distance of 10 ft. it could do 50X10 = 500 ft.-lbs. of work.

It is very convenient to represent graphically the action of forces overcoming resistances, that is, doing work. This is done by plotting points showing the magnitude of the force at the time that the body on which it is acting has traveled different distances. Thus, suppose a constant force of 10 lbs. pushes a body a distance of 15 ft. against a constant resistance of 10 lbs. The force acting on the body will have a value of 10 lbs. just as the body starts to move, a value of 10 lbs. when the body has moved 1 ft., a value of 10 lbs. when the body has moved 2 ft., and so on. This might be represented by points on squared paper as shown

10 9

^ 8

c

3 7

o * o 5 o

5 6 7 8 9 10 11 Distance traveled in Feet

Fig. 2.

12 13 14 15 in Fig. 2 or by a horizontal Hne joining those points as shown in the same figure.

The work done by this force would be 10X15 = 150 ft.-lbs. according to our previous definition. But 10X15 is also the number of small squares under the line representing the action of this force in Fig. 2. The number of these small squares then must be a measure of the work done, but it is also a measure of the area under the line representing the action of the force, so that this area must be a measure of the work done. Each small square represents 1 lb. by its vertical dimension and l.ft. by its horizontal dimension, so that its area must represent 1 lb. XI ft. = 1 ft.-lbo The total number of squares below the line equals 10 X 15 = 150, and since the area of each one represents 1 ft. -lb. the total area under the line represents 150X1 = 150 ft.-lbs.

It is not always convenient to choose such simple scales as those just used. Thus it might be more convenient to plot the action of this force as is done in Fig. 3. Here the height of a square represents 2 lbs. and the width represents 1 ft. ; the area then represents 2X1=2 ft.-lbs. There are 5X15 = 75 squares under the line and as each

«12

S 6 o

5 6 7 8 9 10 n Distance traveled ia Feet

Fig. 3.

12 13 14 15 represents 2 ft.-lbs. the total area under the line represents 2X75 = 150 ft.-lbs. as before.

This is a very useful property of these diagrams and the area under the line representing the action of the force always represents the work done, no matter what the shape of that line.

Thus, assume a force which compresses a spring a distance of 6 ins. Suppose that a force of 10 lbs. is required to compress the spring 1 in., a force of 20 lbs. to compress it 2 ins., and so on up to a force of 60 lbs. to compress it 6 ins. Starting with a force of zero, the force will have to gradually increase as the spring is compressed, as shown by the line in Fig. 4. The area of each of the small squares will represent

10 X -75 = 7^ ft.-lbs. Under the line there is an area equal \.u iz

PHYSICxVL CONCEPTIONS AND UNITS

6X6 o =18 small squares, and the work done in compressing

the spring must then be 18Xr;^= 15 ft. -lbs.

5. Mechanical Energy. Any body which exists in such a position or location that it could do work by dropping or falling is said to be possessed of potential mechanical energy, or of mechanical energy due to position. As long as it remains in this position, it cannot do work at the expense of this energy, but, if allowed to fall, it could do so. The

60 50

3 O Pi

1^30

1"

2"

3"

4"

5" 6

It

K2Ft.

X. Ft.

Ft.

Fig. 4. — Graph Showing Action of Spring.

work it could do would be equal to the product of its weight by the distance it could fall and the potential energy it possesses before starting to fall is measured by this work. Thus, a body weighing 40 lbs. located 10 ft. above the surface of the earth could do 40X10 = 400 ft.-lbs. of work in falhng, and, therefore, it is said to be possessed of 400 ft.-lbs. of potential energy before it starts to fall.

If in falling it raises a weight equal to its own (theoretically) through a distance equal to that through which it falls (theoretically), it will have used up 400 ft.-lbs. of energy in doing 400 ft.-lbs. of work upon the body raised

8 STEAM POWEK

and will no longer be possessed of that amount of potential energy. The body which has been raised will, however, have an equal amount of energy stored in it and will in turn be able to do 400 ft. -lbs. of work if allowed to fall a distance of 10 ft.

If the body assumed above falls through a distance of 10 ft. without raising another body or doing an equivalent amount of work in some other way, it acquires a high velocity. When it arrives at the bottom of the fall of 10 ft., it certainly does not possess the 400 ft. -lbs. of potential energy which it had before dropping nor has it done work at the expense of that energy. Moreover, the energy could not have been destroyed because it is indestructible. The only conclusion is that it must still be possessed of this energy in some way. At the end of the fall it has lost its advantageous position, but it has acquired a high velocity, and experience shows that if brought to rest it can do work upon that which brings it to rest equal to what it could have done in raising a weight as previously described.

At the end of its fall and before being brought to rest, the body is therefore said to be possessed of energy by virtue of its velocity, and this form of energ}^ is called kinetic mechanical energy. The kinetic energy will he exactly equal to the "potential energy which disappeared as the body fell.

Any body which is moving is possessed of kinetic energy because it can do work on anything which brings it to rest. This energy is expressed by the equation,

1 W

Kinetic Energy in ft.-lbs.=-X w^ X V^,

W = the weight of the moving body in pounds. F = the velocity in ft. per second, and 32.2 = a gravitational constant commonly represented by g

6. Heat. One of the most familiar forms of energy is heat, which manifests itself to man through the sense of touch. In reality every body with which man is familiar possesses an unknown amount of heat energy and it is assumed that this heat energy is in some way associated with the motions and relative positions of the molecules and their constituents.

For this reason heat is often described as molecular activity and is regarded as energy stored up in a substance by virtue of its molecular condition. Heat energy can be made to perform work in ways which will be discussed later and this is proof that it is a form of energy and not a material substance, as was once supposed.

Heat is observed and recorded by its effects on matter, producing changes in the dimensions or volumes of objects; changes of internal stress; changes of state, as ice to water and water to steam; changes of temperature; and electrical and chemical effects.

Neglecting certain atomic phenomena not yet well understood, the probable source of all heat energy appearing on the earth is the sun. Heat, however, may be obtained from mechanical and electrical energy; from chemical changes; from changes of physical state; from the internal heat of the earth.

7. Temperature. . Man early realized that under certain conditions bodies felt " hotter " than under other conditions and gradually came to speak of the " degree of hotness " as the temperature of the body. It was later realized that what was really measured as the " hotness " or intensity of heat or temperature of a body was the ability of that body to transmit heat to others and that it had no connection with quantity of heat.

Thus, if the temperature of two adjacent bodies happened to be the same, one of them could not lose heat by transmitting it to the other, but if the temperature of one happened to be higher than that of another, the body at higher temperature would always lose heat to the one at lower temperature.

As a means of measuring temperature certain arbitrary scales have been chosen. The centigrade scale of temperature, for instance, is based upon the temperatures of melting ice and boiling water under atmospheric pressure. The temperature difference between boiling water at atmospheric pressure and melting ice at atmospheric pressure is arbitrarily called one hundred degrees of temperature, and the temperature of the melting ice is called zero, making that of the boiling water 100 degrees.

Any body which has such a temperature that it will not give heat to, or take heat from, melting ice is said to be at a temperature of zero degrees centigrade, represented as 0° C. Similarly, any body in such a condition that it will not give heat to or take heat from water boiling under atmospheric pressure is said to have a temperature of 100° C. A body with a temperature exactly half way between these two limits would then be said to have a temperature of 50° C.

8. Measurement of Temperature. The temperatures of bodies could be determined by bringing them in contact with such things as melting ice and boiling water and determining whether or not a transfer of heat occurred, but this would be a very cumbersome and unsatisfactory method. As a consequence many other means have been devised for the measurement of temperature.

One of the most common and convenient methods involves the use of what are known as mercury thermometers. These depend upon the fact that the expansion of mercury with changing temperature is very uniform over a wide temperature range. Thus, if mercury expands a certain amount when its temperature is raised from that of melting ice to that of boiling water, i.e., 100° C, it will expand just half as much when its temperature is raised half as high, and one-quarter as much when its temperature is raised one-quarter of the range from 0° to 100° C.

fl

The thermometer is made by enclosing a small quantity of mercury in a glass tube fitted with a bulb at one end, as shown in Fig. 5. The lower end of the thermometer is immersed in melting ice and the point on the stem which is reached by the top of the mercury column is marked and labelled 0° C. The thermometer is then immersed in the steam from water boiling under atmospheric pressure and the point reached by the top of the mercury column is marked and labelled 100° C. The distance between the two marks is then divided into one hundred parts and each represents the distance which the end of the column of mercury will move when its temperature changes one centigrade degree.

It is customary to extend this same scale below 0° and above 100°, carrying it, on expensive thermometers, as far in each direction as the approximation to a constant expansion

I w

Fig. 5.— Mercury Theron the part of the mercury and to constant mometer.

properties of the glass justifies.

The temperature of a body can then be found by placing the thermometer in or in contact with that bod}^ and noting the point reached by the end of the mercury column. The division reached gives the temperature directly.

The centigrade scale just described is the one commonly used by scientists the world over, but engineers in this country more often use what is known as the Fahrenheit scale. This is so chosen that the temperature of melting ice is called 32° F. and the temperature of water boiling under atmospheric pressure is called 212° F. There are

-17.8'

i

Fig. 6. — Comparison of Centigrade and Fahrenheit Scales.

thus 180° on this scale for the same temperature difference as is represented by 100° on the centigrade scale. The relation between the two scales is shown diagrammatically in Fig. 6. It is apparent that the temperature of a body at 0° C. will be 32° F. and that of a body at 0° F. will be -17.8° C.

Since 100 centigrade degrees are equal to 180 Fahrenheit degrees, it follows that

180^9 100 5

F.

and that

180~9

Therefore, if tp and tc represent temperatures on the Fahrenheit and centigrade scales respectively.

9 5 and

Cent . ^khs. — ^Fahr.

100^

373- 673

273° 491.4

459.4^

"1459.4

There is still another temperature scale of great importance. It is known as the absolute scale and temperatures measured on it are spoken of as absolute temperatures. The zero on this scale is located at -273° C. or 273 centigrade degrees below centigrade zero, or, what is the same thing, at -459.4° F., or 459.4 Fahrenheit degrees below Fahrenheit zero. The degrees used are either centigrade or Fahrenheit, as convenient, so that there are absolute temperatures expressed in centigrade degrees above absolute zero and there are absolute tempera-

FiG. 7. — Comparison of Absolute and Ordinary Temperature Scales.

tures expressed in Fahrenheit degrees above absolute zero. The relations between the various scales are shown diagrammatically in Fig. 7.

It is apparent from this diagram that, and that if Tf and Tc represent absolute temperatures and if the number 459.4 is rounded out to 460, as is commonly done.

9. The Unit of Heat Energy. The unit used in the measurement of heat energy in the United States is the British Thermal Unit (abbreviated B.t.u). It is defined as the quantity of heat required to raise the temperature of one pound of pure water one degree Fahrenheit. In order to make the definition very exact it is necessary to state the temperature of the water before the temperature rise occurs, because it requires different amounts of heat to raise the temperature of a pound of water one degree from different initial temperatures. For ordinary engineering purposes, however, such refinements generally may be omitted.

Many experimenters have shown that heat energy and mechanical energy are mutually convei'tible, that is, the one can be changed into the other. When such a change occurs no energy can be lost since energy is indestructible, and it follows that, if one form is changed into the other, there must be just as much energy present after the change as there was before.

As the units used in measuring the two forms of energy are very different and as it is often necessary to express quantities of energy taking part in such conversions, it is desirable to determine the relations between these units. This was first accurately done by Joule, who showed that one British thermal unit of heat energy resulted from the conversion of 772 ft. -lbs. of mechanical energy. Later experimenters have shown that the number 778 more nearly expresses the truth than does the number 772 and the larger value is now known as Joule's Equivalent.

Expressed mathematically, the relation between the units is

10. Specific Heat. The specific heat of a substance is defined as that quantity of heat which is used up or recovered when the temperature of one pound of the material in question is raised or lowered one degree. Its numerical value depends upon the specific heat of water since the quantity of heat is measured in units dependent upon the amount required to raise the temperature of water. The specific heat of water is, however, very variable, as shown by the values given in Table L, and it is therefore evident that exact numerical values of specific heats can only be given when the definition of the B.t.u. is exactly expressed.

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