American Technical Society. # Cyclopedia of engineering : a general reference work on steam boilers, pumps, engines, and turbines, gas and oil engines, automobiles, marine and locomotive work, heating and ventilating, compressed air, refrigeration, dynamos motors, electric wiring, electric lighting, elevators, etc. (Volume 2) online

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Online Library → American Technical Society → Cyclopedia of engineering : a general reference work on steam boilers, pumps, engines, and turbines, gas and oil engines, automobiles, marine and locomotive work, heating and ventilating, compressed air, refrigeration, dynamos motors, electric wiring, electric lighting, elevators, etc. (Volume 2) → online text (page 9 of 30)

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different degrees of heat for comparison, so we must resort to some

other means. A simple method is to use some substance whose

volume changes a definite amount for a definite change in temper-

ature and always has the same volume for the same temperature.

Mercury and alcohol are suitable substances and may be placed in

a glass bulb, to which is connected a glass tube of small bore. All

the air is drawn out of the tube, and the end is sealed so that the

thermometric substance can expand or contract in a vacuum.

The tube having been sealed, the bulb is placed in melting ice and

the height of the mercury in the tube noted. It is then placed

130

THE STEAM ENGINE. 79*

in steam (or boiling water) at atmospheric pressure and the height

of the column again noted. On the Fahrenheit scale the melting

point is called 32, and the boiling point 212, and the intervening

space is divided into 180 equal parts. In the Centigrade scale

the melting point is called and the boiling point 100; there are

100 equal intervals between them. Thus we see that 180 F =:

100 C, or 1 C = 1.8 F.

Example : What is the temperature of 50 C on the F scale ?

50 C = 50 X 1.8 = 90 F above the melting point

or 90 -f 32 = 122 F above zero.

In order to compare temperatures, we place the thermometer

in contact with the substance whose degree of heat we wish to

know and then observe the height of the liquid column in the ther-

mometer. The height of this column depends upon the expansion

of the thermometric substance and indicates the intensity of heat,

or the temperature as we commonly call it. We use a thermom-

eter to measure the intensity of heat, but not the quantity of

heat.

For measuring the intensity of heat, the degree is the unit-,

for measuring the quantity of heat we have another unit, which is

the amount of heat necessary to raise one pound of water from 61

F to 62 F. This is called the British thermal unit (B. T. U.).

To raise one pound of water from 60 F to 62 F, or to raise two

pounds from 60 F to 61 F, will require 2 B. T. U.

Suppose we have a small bar of iron heated to a white heat ;

its temperature will be high, but it will contain a relatively

small quantity of heat, that is, it will not require a great many

B. T. U. to raise its temperature to this high point. But suppose

this same number of heat units were transferred to a ton of iron ;

the temperature would scarcely be changed, for the infinitely

greater number of particles would have a correspondingly less

number of vibrations.

Experience teaches us that when a rifle-ball strikes a target

it stops, and that the energy which it possesses by virtue of its

bodily motion is suddenly transformed into energy of molecular

motion. Energy is indestructible; the molecular motion of the

impinging body is at once increased and heat is developed. In

general, whenever moving bodies are brought to rest, either sud-

131

SO THE STEAM ENGINE.

denly as by impact or gradually as by friction, the kinetic energy

of the moving mass is transformed into molecular kinetic energy,

and we say that the bodies become heated.

We have now seen that we can transform energy of motion

into heat. Also by means of suitable apparatus we can transform

heat into energy of motion. Heat is the lowest form of energy,

and while it is comparatively easy to transform other forms into

heat, it is not as easy to change heat into the higher forms oi

energy. The principle of the transformation is simple enough, but

if we are to have an efficient engine, we must be able to extract

practically all of the heat f rom the working substance. This, how-

ever, is impossible, because the ordinary ranges of temperature

used in practice are so far removed from the absolute zero o(

temperature, that with the most perfect machines we can at best

recover but a fraction of the heat; the rest passing out of the

engine.

The transformation is accomplished by means of a working

substance which passes from the temperature of a heat generator

into a refrigerator; the heat given up during the change is trans-

formed into work. By the term refrigerator we mean the low

temperature of the working substance at exhaust. The greater

the temperature of the source of heat, or the lower the temperature

of the refrigerator, the greater will be the amount of heat that can

be abstracted and converted into useful work. If the temperature

of the refrigerator could be reduced to the absolute zero, all the

heat would be removed from the working substance, and the only

loss would be that due to mechanical imperfections of the engine ;

but since the absolute zero is 461 below the zero on the Fahren-

heit scale, or 493 below the freezing point, we must at best allow

a relatively large amount of heat to pass out of the engine into

the refrigerator without having done any work at all.

The unit of work is the foot-pound ; that is, the work done

in raising one pound one foot. By means of careful experiments

it has been determined that for every 778 foot-pounds of work

transformed into heat there is developed one B. T. U. This value

778 is known as the Mechanical Equivalent of heat. It means

that one B. T. U. and 778 foot-pounds of work are mutually

interchangeable.

132

THE STEAM ENGINE.

EXPANSION OF OASES.

A perfect gas, strictly speaking, is one that cannot be lique-

fied ; ordinarily, however, we apply the term to those gases that can

be liquefied only with great difficulty, that is, under extreme pres-

sure and a great reduction of temperature. For every perfect gas

there is a definite relation between the pressure and volume, and

what is known as Boyle's Law has been found to hold true, viz. :

The pressure of a perfect gas at constant temperature varies in-

versely as the volume ; that is, if the temperature remains constant

the pressure becomes less as fast as the volume becomes greater,

or conversely the volume becomes less as fast as the pressure

becomes greater. Now if the pressure becomes twice as great, the

volume becomes half as large, and if the volume becomes three

times as great, the pressure will be only one-third as much. Hence

we see that however the pressure may vary, the volume will change

in such a way that the pressure multiplied by the volume will

always be constant, provided the temperature remains the same,

This simple law is expressed thus :

P X V = C

in which

P pressure in pounds per square inch (absolute)

V volume in cubic feet

C a constant which has different values for different gases.

Gases that are not easily liquefied, such as hydrogen, oxygen

and air, follow this law fairly well, but those that are easily lique-

fied, such as steam and ammonia, do not follow it at all.

The value of C is not the same for all gases, and as no gas is,

strictly speaking, a perfect gas, >ts value varies slightly with the

temperature. For air, which is nearly a perfect gas, its value is

182.08 at 32 F.

Example. What is the absolute pressure per square inch of

one pound of air if the temperature is 32 F, and the volume

4.129 cubic feet?

V = 4.129

P = 44.1 pounds per square inch, absolute.

133

THE STEAM ENGINE.

Let us discuss this law by means of a diagram. Fig. 1 is

drawn with O Y and O X at right angles to each other ; pressures

are measured to any convenient scale on O Y and volumes on O X.

O C represents 12.387 cubic feet and O D represents 14.7 pounds,

since P X V = 1 82.08. O F represents 24.774 cubic feet and O G

7.35 pounds. I.nlike manner O L represents 6.19 cubic feet and O N

29.41 pounds. Then if we draw perpendiculars to O X at L, C

and F, and perpendiculars to O Y at N, D and G, they will meet

in the points M, E and H. The curve A B is drawn through

these points. Then for

any pressure we can find

the corresponding volume

or vice versa. The area of

the rectangle O D E C

equals that of the rectangle

O G H F and also that of

the rectangle O N M L.

That this is so is readily

seen from the fact that the

product of the pressure and

its corresponding volume

is constant.

If we plot a curve

using this equation we will

get a rectangular hyperbola, as shown in " Steam Engine Indi-

cators." This curve is called an isothermal curve or curve of

equal temperatures.

If the volume of a perfect gas remains constant, the pressure

will vary as the temperature. Or, if the pressure remains constant,

the volume will vary as the temperature. This is known as the

Law of Charles. From this we see that, as the temperature

decreases, either the pressure or the volume will decrease a pro-

portionate amount, and this must continue as long as there is any

heat in the gas; finally a low temperature (the absolute zero)

will be reached, where there is no more heat, and consequently

either the pressure or the volume must be zero, provided this law

holds true at such a very low temperature.

The law states that any change of pressure or volume is pro-

VOLUME

Fig. 1.

134

THE SfEAM ENGINE. 83

portional to the change in temperature, that is, the new volume is

equal to the first volume plus or minus some fractional part of

this volume, called the coefficient of expansion, multiplied by the

change in temperature. We may express the formula thus:

Pj Vj =P V+(PV)& X t

p V(l-f kf).

Where P l and V x are the new pressure and volume

P and V are the first pressure and volume

Jc is the coefficient of expansion for the gas

t is the change in temperature.

From Boyle's Law we know that P V = C ; hence we may

write the above equation :

P 1 V,=0(l + *0

= * C(T +

From careful experiments on the expansion of air, Regnault

determined the value of the coefficient k to be .003654 for Centi-

grade units. This value is constant between freezing point, 0,

and boiling point, 100. Substituting this value of k in our last

equation, we have :

= k C (273.7 + f).

Now if we should make the change of temperature, t, equal

to 273.7 we should have:

P, Y! = k C (273.7 273.7) =

r, v t = o.

Therefore we must have reached the absolute zero at 273.7

below the freezing point, because here P l X V t has reached 0, as

we have previously seen must be the case at the absolute zero.

273.7 X 1.8 = 492.7 for the F scale. Therefore the absolute

zero is 492.7 32 = 460.7 below zero on the Fahrenheit scale.

For ordinary work 461 will be sufficiently accurate.

If we let P = absolute pressure in pounds per square inch

V = volume of one pound in cubic feet

T = absolute temperature on Fahrenheit scale,

Then, PV = CT&.

I' C equals .3693 for air.

135

THE STEAM ENGINE.

Example. If one pound of air occupies 16.606 cubic feet at

a pressure of 14.7 pounds per square inch, what is its temperature?

P X V = C X T

14.7 X 16.606 = .3693 X T

T _ 244.108

.3693

T = 661.

This value 661 is absolute temperature, and to find the

Fahrenheit temperature 461 must be subtracted from it. Thus,

061 461 =:200 F.

Saturated Vapor. The process of converting a liquid into

a vapor is known as vaporization; the product thus formed is

readily condensed and

therefore does not follow

the laws of perfect gases

at all. A dry saturated

vapor is one that has

just enough heat in it

to keep it in the form

of a vapor; if we add

more heat it becomes

Fig. 2.

superheated. A super-

heated vapor may lose

a part of its heat without condensation ; a saturated vapor cannot.

When a saturated vapor loses a part of its heat some of it will

condense and we say that the vapor is wet.

Steam is simply the vapor from water and we shall confine

our discussion to this alone. Suppose we have a vertical cylinder,

as shown in Fig. 2, fitted with a light piston free to move up and

down, yet so constructed that it may be loaded at will. Suppose

that there is one pound of water at a temperature of 32 F in the

bottom of this cylinder, and that the piston rests upon its surface.

Now, if we apply heat by means of a gas flame or fire, we shall

notice the following effects:

First. The temperature of the water will gradually rise until

it reaches the temperature at which steam is formed. This

temperature will depend upon the pressure, or the load on the

136

THE STEAM ENGINE. 85

piston. If the piston is very light, we may neglect its weight and

consider that there is simply the atmospheric pressure of 14.7

pounds per square inch acting on the water surface. At this

pressure steam will begin to form at 212 F.

Second. As soon as 212 F is reached, steam will begin to

form and the piston will steadily rise, but no matter how hot the

fire may be, the temperature of both water and steam will remain

at 212 until all the water is evaporated. We had one pound of

water at 32 F and at 14.7 pounds absolute pressure, and found

that steam formed at a temperature of 212 F and remained at

that temperature. We added 180.9 B. T. U., the heat of the

liquid, to bring the water from 32 to the boiling point. To con-

vert water at 212 into steam at 212, we added 965.7 B. T. U.

more. This quantity, known as the latent heat, or heat of vapor-

ization, makes the total heat 1,146.6 B. T. U. If we should

measure the volume carefully after all the water was evaporated,

we should find that there was just 2G.36 cubic feet of dry saturated

steam. We had one pound of water, and therefore must have one

pound of steam, for none of it could escape ; hence one cubic foot

will weigh . ; . = 0.03794 pounds, which is known as the

26. 36

density of steam at 14.7 pounds absolute pressure or 212 F.

In the Table of Properties of Saturated Steam (see page 14)

all these quantities are found in the order given and at the pres-

sure of 14.7 pounds above vacuum.

Suppose now we place a weight of 85.3 pounds on the piston.

The pressure is 85.3 pounds plus 14 7 pounds, or 100 pounds abso-

lute. We shall now find that no steam will form until a temper-

ature of 327.58 is reached. Starting with water at 32, it will

be necessary to add 297.9 B. T. U. before a temperature of

327.58 is reached, and also we must add 884.0 B. T. U. more to

vaporize it, making a total heat of 1,181.9 B. T. U. Under this

greater pressure the steam occupies a volume of only 4.403 cubic

feet, or one cubic foot of it weighs . = 0.2271 pound.

4.403

Of course it would be impossible to determine all these dif-

ferent quantities by actual experiment, and at all pressures varying

from vacuum to the high pressures, used in water-tube boilers.

137

86 ME STEAM

Fortunately \ve are able to compute them all from equations which

have been carefully determined by experiment. If saturated

steam were a perfect gas, we could easily calculate all the relations

of pressure, volume and temperature from the equation PV= CT,

but steam is so far removed from the state of a perfect gas that

these relations do not hold, and the true equations become very

complex. The following equation proposed by Rankine is one of

the simplest, and gives fairly good results:

, A B C

Iog 10 l = A _ _ 2

in which P = pressure in pounds per square inch above vacuum.

A = 6.1007

B = 2,732

C = 396,945

T = absolute temperature in Fahrenheit degrees.

By the aid of such equations as this, all the different quan-

tities found in the steam tables may be calculated. These equations

are based on careful experiments and give very satisfactory results.

Steam Tables. We have already seen that any change in

the temperature of saturated steam produces a change of pressure,

and that every change of pressure corresponds to a certain change

in temperature. There are several properties of saturated steam

that depend upon the temperature and pressure ; and the values

of all these different properties when arranged for all temperatures

and pressures are called Steam Tables. The following are the

principal items that are found in the tables :

1. The absolute pressure in pounds per square inch; it is

equal to the gage pressure plus the atmospheric pressure of 14.7

pounds.

2. The temperature of the steam, or boiling water, at the

corresponding pressure.

3. The heat of the liquid ; or the number of B. T. U. neces-

sary to raise one pound of water from 32 F to the boiling point

corresponding to the given pressure.

4. The heat of vaporization, or the latent heat ; this is the

number of B. T. U. necessary to change one pound of water, at

the boiling point, into dry saturated steam at the same temperature

and pressure.

138

THE STEAM ENGINE. 87

5. The total heat- or the number of B. T. U. necessary to

change one pound of water from 32 F into steam at the given

temperature or pressure. The total heat is evidently equal to the

sum of the heat of the liquid and the heat of vaporization.

6. The density of the steam ; that is, the weight in pounds

of one cubic foot of steam at the given temperature or pressure.

7. The specific volume ; or volume in cubic feet of one

pound of steam at the required temperature or pressure. Evi-

dently the specific volume is equal to .

density

All these properties have been calculated by means of various

formulas which have been deduced from the results of actual

experiment. There are several formulas for the temperatures and

pressures of steam ; as some computers have used one and some

another, there is likely to be a slight discrepancy between the

tables computed by different authors. Rankin's formula, already

given, is the simplest, but is not generally considered to be quite

as accurate as some of the later ones ; it has probably been used,

however, more than any other.

The total heat may be calculated by means of the formula

H = 1,091.7 + 0.305 (t 32) [1]

in which H = total heat

t =; temperature in degrees Fahrenheit.

The heat of the liquid is equal to q.

q = t + 0.00002 *a _j_ 0.0000003*3 [2]

in which t =. temperature in degrees Centigrade.

These constants are for use in the Centigrade system only.

To calculate the heat of the liquid for any Fahrenheit temper-

ature it is necessary to change the Fahrenheit into equivalent

Centigrade degrees and then substitute in the above formula.

The formula used for the calculation of specific volume is too

complex for consideration here, but^the relation of pressure and

volume may be approximately expressed by means of an equation

of the form P V n = C, in which n is an exponent, C a constant,

P the absolute pressure, and V the specific volume ; n is usually

taken to be , and C to be 475.

lo

On pages 14 ind 15 are given tables of the properties of

139

THE STEAM ENGINE.

TABLE OF PROPERTIES OF SATURATED STEAM.

Pressure

in

pounds

persq.in

above

vacuum

Tenpera-

ture in

degrees

Fahren-

heit.

Heat

in

liquid

from

32 in

units.

Heat of

vaporiza-

tion, or

latent

heat in

teat units

Total

heat in

heat

units

from

water at

32.

Density o

weight

of cubic ft

in pounds

Volume

of 1

pound in

cubic

feet.

Total

pressure

above

vacuum.

1

101.99

700

1043.0

1113.1

0.00299

334.5

1

2

126.27

91.4

1026.1

1120.5

0.00576

173.6

2

3

141.62

109.8

1015.3

1125.1

0.00844

118.5

3

4

153.09

121.4

1007.2

1128.6

0.01107

90.31

4

6

162.34

130.7

1000.8

1131.5

001366

73.21

5

6

170.14

138.6

995.2

1133.8

0.01622

61.67

6

7

176.90

145.4

990.5

1135.9

0.01874

53.37

7

8

182.92

151.5

986.2

1137.7

0.02125

47.06

8

9

188.33

156.9

982.5

1139.4

0.02374

42.12

9

10

193.25

161.9

979.0

1140.9

0.02621

38.15

10

147

212.00

180.9

965.7

1146.6

0.03794

26.36

14.7

15

213.03

181.8

965.1

1146.9

0.03826

26.14

15

20

227.95

196.9

954.6

1151.5

0.05023

19.91

20

25

240.04

209.1

946.0

1155.1

0.06199

16.13

26

30

250.27

219.4

938.9

1158.3

0.07360

13.59

30

35

259.19

228.4

932.6

1161

0.08508

11.75

35

40

267.13

236.4

927.0

1163.4

0.09644

10.37

40

45

274.29

243.6

922.0

1165.6

0.1077

9287

45

60

280.85

250.2'

917.4

1167.6

0.1188

8414

60

65

286.89

256.3

913.1

1169.4

0.1299

7.696

65

60

292.51

261.9

909.3

1171.2

0.1409

7.097

60

65

297.77

267.2

905.5

1172.7

0.1519

6583

65

70

302.71

272.2

902.1

1174.3

0.1628

6.143

70

75

307.38

276.9

898.8

1175.7

0.1736

5.762

75

80

S11.80

281.4

895.6

1177.0

0.1843

6 426

80

85

316.02

285.8

892.5

1178.3

0.1951

5126

85

90

320.04

290.0

889.6

1179.6

0.2058

4.859

90

95

323.89

294.0

886.7

1180.7

0.2165

4.619

96

100

327.58

297.9

884.0

1181.9

0.2271

4.403

100

105

331.13

301.6

881.3

1182.9

0.2378

4.205

105

110

334.56

305.2

878.8

1184.0

0.2484

4.026

110

115

337.86

308.7

876.3

1185.0

0.2589

3.862

116

120

341.05

3120

874.0

1186.0

0.2695

3 711

120

125

344.13

315.2

871.7

1186.9

0.2800

3.571

125

130

347.12

318.4

869.4

1187.8

0.2904

3.444

130

140

352.85

324.4

865.1

1189.5

0.3113

3.212

140

150

358.26

330.0

861.2

1191 2

0.3321

3.011

160

160

363.40

335.4

857.4

1192.8

0.3530

2833

160

170

368.29

340.5

853.8

1194.3

0.3737

2.676

170

180

372.97

345.4

850.3

1195.7

0.3945

2.535

180

190

377.44

350.1

847.0

1197.1

04153

2.408

190

200

381.73

354.6

843.8-

1198.4

04359

2.294

200

225

391.79

365.1

836.3

1201.4

0.4876

2.051

225

250

400.99

374.7

829.5

1204.2

0.5393

1.854

260

275

409.50

383.6

823.2

1206.8

0.5913

1.691

275

300

417.42

391.9

817.4

1209.3

0.644

1.553

300

325

424.82

399.6

811.9

1211.5

0.696

1.437

325

350

431.90

406.9

806.8

1213.7

0.748

1.337

350

375

438.40

414.2

801.5

1215.7

0.800

1.250

375

400

445.15

421.4

796.3

1217.7

0.853

1.172

400

600

466.57

444.3

779.9

1224.2

1.065

.939

600

140

THE STEAM ENGINE.

TABLE OF PROPERTIES OF SATURATED STEAM.

Temper-

ature in

degrees

Fahren-

heit.

Total

pressure

above

vacuum.

Heat

in

liquid

from

32 in

units.

Heat of

vaporiza-

tion, or

latent

heat in

heat units

Total

heat in

heat

units

from

water at

32.

Density o

weight

of cubic ft

in pounds

. Volume

of one

pound in

cubic

feet.

Tempera

ture in

degrees

Fahren-

heit.

32

0.089

0.

1091.7

1091.7

0.0003

3387.

32

60

0.254

28.12

1072.1

1100.2

0.0008

1234.

60

90

0.692

58.04

1051.4

1109.4

0.002J

474.6

90

120

1.683

88.10

1034.4

1118.5

0.0049

204.4

120

140

2.877

108.2

1016.4

1124.6

00081

123.2

140

160

3.706

118.3

1009.4

1127.7

0.0103

97.03

150

160

4.729

128.4

1002.3

1130.7

0.0130

77.14

160

170

6.98

138.5

995.3

11338

0.0162

61.85

170

180

7.50

148.5

988.3

1136.8

0.0200

50.01

180

190

9.33

158.6

981.3

1139.9

0.0245

40.73

190

200

11.52

168.7

974.2

1142.9

00299

33.40

200

210

14.12

178.8

967.2

1146.0

0.0363

27.57

210

220

17.19

188.9

960.1

1149.0

0.0435

22.98

220

225

1891

193.9

956.7

1150.6

0.0476

20.99

225

230

20.78

198.9

953.2

1152.1

0.0521

19.20

230

935

22.80

204.0

949.6

1153 6

0.0569

17.59

235

240

24.98

209.0

946.1

1156.1

0.0619

16.14

240

245

27.33

214.1

942.6

1156.7

0.0674

1483

245

250

29.86

219.1

939.1

11582

0.0733

13.65

250

255

32.57

224.1

935.6

1159.7

0.0795

12.57

255

260

35.48

229.2

932.0

1161.2

0.0862

11.60

260

265.

38.60

234.2

928.6

11628

0.0933

10.72

265

270

41.94

239.3

925.0

1164.3

0.1008

9.918

270

275

45.51

244.3

921.5

1165.8

0.1088

9.187

275

280

49.33

249.3

918.0

1167.3

0.1173

8521

280

285

53.39

254.4

914.5

1168.9

0.1264

7913

other means. A simple method is to use some substance whose

volume changes a definite amount for a definite change in temper-

ature and always has the same volume for the same temperature.

Mercury and alcohol are suitable substances and may be placed in

a glass bulb, to which is connected a glass tube of small bore. All

the air is drawn out of the tube, and the end is sealed so that the

thermometric substance can expand or contract in a vacuum.

The tube having been sealed, the bulb is placed in melting ice and

the height of the mercury in the tube noted. It is then placed

130

THE STEAM ENGINE. 79*

in steam (or boiling water) at atmospheric pressure and the height

of the column again noted. On the Fahrenheit scale the melting

point is called 32, and the boiling point 212, and the intervening

space is divided into 180 equal parts. In the Centigrade scale

the melting point is called and the boiling point 100; there are

100 equal intervals between them. Thus we see that 180 F =:

100 C, or 1 C = 1.8 F.

Example : What is the temperature of 50 C on the F scale ?

50 C = 50 X 1.8 = 90 F above the melting point

or 90 -f 32 = 122 F above zero.

In order to compare temperatures, we place the thermometer

in contact with the substance whose degree of heat we wish to

know and then observe the height of the liquid column in the ther-

mometer. The height of this column depends upon the expansion

of the thermometric substance and indicates the intensity of heat,

or the temperature as we commonly call it. We use a thermom-

eter to measure the intensity of heat, but not the quantity of

heat.

For measuring the intensity of heat, the degree is the unit-,

for measuring the quantity of heat we have another unit, which is

the amount of heat necessary to raise one pound of water from 61

F to 62 F. This is called the British thermal unit (B. T. U.).

To raise one pound of water from 60 F to 62 F, or to raise two

pounds from 60 F to 61 F, will require 2 B. T. U.

Suppose we have a small bar of iron heated to a white heat ;

its temperature will be high, but it will contain a relatively

small quantity of heat, that is, it will not require a great many

B. T. U. to raise its temperature to this high point. But suppose

this same number of heat units were transferred to a ton of iron ;

the temperature would scarcely be changed, for the infinitely

greater number of particles would have a correspondingly less

number of vibrations.

Experience teaches us that when a rifle-ball strikes a target

it stops, and that the energy which it possesses by virtue of its

bodily motion is suddenly transformed into energy of molecular

motion. Energy is indestructible; the molecular motion of the

impinging body is at once increased and heat is developed. In

general, whenever moving bodies are brought to rest, either sud-

131

SO THE STEAM ENGINE.

denly as by impact or gradually as by friction, the kinetic energy

of the moving mass is transformed into molecular kinetic energy,

and we say that the bodies become heated.

We have now seen that we can transform energy of motion

into heat. Also by means of suitable apparatus we can transform

heat into energy of motion. Heat is the lowest form of energy,

and while it is comparatively easy to transform other forms into

heat, it is not as easy to change heat into the higher forms oi

energy. The principle of the transformation is simple enough, but

if we are to have an efficient engine, we must be able to extract

practically all of the heat f rom the working substance. This, how-

ever, is impossible, because the ordinary ranges of temperature

used in practice are so far removed from the absolute zero o(

temperature, that with the most perfect machines we can at best

recover but a fraction of the heat; the rest passing out of the

engine.

The transformation is accomplished by means of a working

substance which passes from the temperature of a heat generator

into a refrigerator; the heat given up during the change is trans-

formed into work. By the term refrigerator we mean the low

temperature of the working substance at exhaust. The greater

the temperature of the source of heat, or the lower the temperature

of the refrigerator, the greater will be the amount of heat that can

be abstracted and converted into useful work. If the temperature

of the refrigerator could be reduced to the absolute zero, all the

heat would be removed from the working substance, and the only

loss would be that due to mechanical imperfections of the engine ;

but since the absolute zero is 461 below the zero on the Fahren-

heit scale, or 493 below the freezing point, we must at best allow

a relatively large amount of heat to pass out of the engine into

the refrigerator without having done any work at all.

The unit of work is the foot-pound ; that is, the work done

in raising one pound one foot. By means of careful experiments

it has been determined that for every 778 foot-pounds of work

transformed into heat there is developed one B. T. U. This value

778 is known as the Mechanical Equivalent of heat. It means

that one B. T. U. and 778 foot-pounds of work are mutually

interchangeable.

132

THE STEAM ENGINE.

EXPANSION OF OASES.

A perfect gas, strictly speaking, is one that cannot be lique-

fied ; ordinarily, however, we apply the term to those gases that can

be liquefied only with great difficulty, that is, under extreme pres-

sure and a great reduction of temperature. For every perfect gas

there is a definite relation between the pressure and volume, and

what is known as Boyle's Law has been found to hold true, viz. :

The pressure of a perfect gas at constant temperature varies in-

versely as the volume ; that is, if the temperature remains constant

the pressure becomes less as fast as the volume becomes greater,

or conversely the volume becomes less as fast as the pressure

becomes greater. Now if the pressure becomes twice as great, the

volume becomes half as large, and if the volume becomes three

times as great, the pressure will be only one-third as much. Hence

we see that however the pressure may vary, the volume will change

in such a way that the pressure multiplied by the volume will

always be constant, provided the temperature remains the same,

This simple law is expressed thus :

P X V = C

in which

P pressure in pounds per square inch (absolute)

V volume in cubic feet

C a constant which has different values for different gases.

Gases that are not easily liquefied, such as hydrogen, oxygen

and air, follow this law fairly well, but those that are easily lique-

fied, such as steam and ammonia, do not follow it at all.

The value of C is not the same for all gases, and as no gas is,

strictly speaking, a perfect gas, >ts value varies slightly with the

temperature. For air, which is nearly a perfect gas, its value is

182.08 at 32 F.

Example. What is the absolute pressure per square inch of

one pound of air if the temperature is 32 F, and the volume

4.129 cubic feet?

V = 4.129

P = 44.1 pounds per square inch, absolute.

133

THE STEAM ENGINE.

Let us discuss this law by means of a diagram. Fig. 1 is

drawn with O Y and O X at right angles to each other ; pressures

are measured to any convenient scale on O Y and volumes on O X.

O C represents 12.387 cubic feet and O D represents 14.7 pounds,

since P X V = 1 82.08. O F represents 24.774 cubic feet and O G

7.35 pounds. I.nlike manner O L represents 6.19 cubic feet and O N

29.41 pounds. Then if we draw perpendiculars to O X at L, C

and F, and perpendiculars to O Y at N, D and G, they will meet

in the points M, E and H. The curve A B is drawn through

these points. Then for

any pressure we can find

the corresponding volume

or vice versa. The area of

the rectangle O D E C

equals that of the rectangle

O G H F and also that of

the rectangle O N M L.

That this is so is readily

seen from the fact that the

product of the pressure and

its corresponding volume

is constant.

If we plot a curve

using this equation we will

get a rectangular hyperbola, as shown in " Steam Engine Indi-

cators." This curve is called an isothermal curve or curve of

equal temperatures.

If the volume of a perfect gas remains constant, the pressure

will vary as the temperature. Or, if the pressure remains constant,

the volume will vary as the temperature. This is known as the

Law of Charles. From this we see that, as the temperature

decreases, either the pressure or the volume will decrease a pro-

portionate amount, and this must continue as long as there is any

heat in the gas; finally a low temperature (the absolute zero)

will be reached, where there is no more heat, and consequently

either the pressure or the volume must be zero, provided this law

holds true at such a very low temperature.

The law states that any change of pressure or volume is pro-

VOLUME

Fig. 1.

134

THE SfEAM ENGINE. 83

portional to the change in temperature, that is, the new volume is

equal to the first volume plus or minus some fractional part of

this volume, called the coefficient of expansion, multiplied by the

change in temperature. We may express the formula thus:

Pj Vj =P V+(PV)& X t

p V(l-f kf).

Where P l and V x are the new pressure and volume

P and V are the first pressure and volume

Jc is the coefficient of expansion for the gas

t is the change in temperature.

From Boyle's Law we know that P V = C ; hence we may

write the above equation :

P 1 V,=0(l + *0

= * C(T +

From careful experiments on the expansion of air, Regnault

determined the value of the coefficient k to be .003654 for Centi-

grade units. This value is constant between freezing point, 0,

and boiling point, 100. Substituting this value of k in our last

equation, we have :

= k C (273.7 + f).

Now if we should make the change of temperature, t, equal

to 273.7 we should have:

P, Y! = k C (273.7 273.7) =

r, v t = o.

Therefore we must have reached the absolute zero at 273.7

below the freezing point, because here P l X V t has reached 0, as

we have previously seen must be the case at the absolute zero.

273.7 X 1.8 = 492.7 for the F scale. Therefore the absolute

zero is 492.7 32 = 460.7 below zero on the Fahrenheit scale.

For ordinary work 461 will be sufficiently accurate.

If we let P = absolute pressure in pounds per square inch

V = volume of one pound in cubic feet

T = absolute temperature on Fahrenheit scale,

Then, PV = CT&.

I' C equals .3693 for air.

135

THE STEAM ENGINE.

Example. If one pound of air occupies 16.606 cubic feet at

a pressure of 14.7 pounds per square inch, what is its temperature?

P X V = C X T

14.7 X 16.606 = .3693 X T

T _ 244.108

.3693

T = 661.

This value 661 is absolute temperature, and to find the

Fahrenheit temperature 461 must be subtracted from it. Thus,

061 461 =:200 F.

Saturated Vapor. The process of converting a liquid into

a vapor is known as vaporization; the product thus formed is

readily condensed and

therefore does not follow

the laws of perfect gases

at all. A dry saturated

vapor is one that has

just enough heat in it

to keep it in the form

of a vapor; if we add

more heat it becomes

Fig. 2.

superheated. A super-

heated vapor may lose

a part of its heat without condensation ; a saturated vapor cannot.

When a saturated vapor loses a part of its heat some of it will

condense and we say that the vapor is wet.

Steam is simply the vapor from water and we shall confine

our discussion to this alone. Suppose we have a vertical cylinder,

as shown in Fig. 2, fitted with a light piston free to move up and

down, yet so constructed that it may be loaded at will. Suppose

that there is one pound of water at a temperature of 32 F in the

bottom of this cylinder, and that the piston rests upon its surface.

Now, if we apply heat by means of a gas flame or fire, we shall

notice the following effects:

First. The temperature of the water will gradually rise until

it reaches the temperature at which steam is formed. This

temperature will depend upon the pressure, or the load on the

136

THE STEAM ENGINE. 85

piston. If the piston is very light, we may neglect its weight and

consider that there is simply the atmospheric pressure of 14.7

pounds per square inch acting on the water surface. At this

pressure steam will begin to form at 212 F.

Second. As soon as 212 F is reached, steam will begin to

form and the piston will steadily rise, but no matter how hot the

fire may be, the temperature of both water and steam will remain

at 212 until all the water is evaporated. We had one pound of

water at 32 F and at 14.7 pounds absolute pressure, and found

that steam formed at a temperature of 212 F and remained at

that temperature. We added 180.9 B. T. U., the heat of the

liquid, to bring the water from 32 to the boiling point. To con-

vert water at 212 into steam at 212, we added 965.7 B. T. U.

more. This quantity, known as the latent heat, or heat of vapor-

ization, makes the total heat 1,146.6 B. T. U. If we should

measure the volume carefully after all the water was evaporated,

we should find that there was just 2G.36 cubic feet of dry saturated

steam. We had one pound of water, and therefore must have one

pound of steam, for none of it could escape ; hence one cubic foot

will weigh . ; . = 0.03794 pounds, which is known as the

26. 36

density of steam at 14.7 pounds absolute pressure or 212 F.

In the Table of Properties of Saturated Steam (see page 14)

all these quantities are found in the order given and at the pres-

sure of 14.7 pounds above vacuum.

Suppose now we place a weight of 85.3 pounds on the piston.

The pressure is 85.3 pounds plus 14 7 pounds, or 100 pounds abso-

lute. We shall now find that no steam will form until a temper-

ature of 327.58 is reached. Starting with water at 32, it will

be necessary to add 297.9 B. T. U. before a temperature of

327.58 is reached, and also we must add 884.0 B. T. U. more to

vaporize it, making a total heat of 1,181.9 B. T. U. Under this

greater pressure the steam occupies a volume of only 4.403 cubic

feet, or one cubic foot of it weighs . = 0.2271 pound.

4.403

Of course it would be impossible to determine all these dif-

ferent quantities by actual experiment, and at all pressures varying

from vacuum to the high pressures, used in water-tube boilers.

137

86 ME STEAM

Fortunately \ve are able to compute them all from equations which

have been carefully determined by experiment. If saturated

steam were a perfect gas, we could easily calculate all the relations

of pressure, volume and temperature from the equation PV= CT,

but steam is so far removed from the state of a perfect gas that

these relations do not hold, and the true equations become very

complex. The following equation proposed by Rankine is one of

the simplest, and gives fairly good results:

, A B C

Iog 10 l = A _ _ 2

in which P = pressure in pounds per square inch above vacuum.

A = 6.1007

B = 2,732

C = 396,945

T = absolute temperature in Fahrenheit degrees.

By the aid of such equations as this, all the different quan-

tities found in the steam tables may be calculated. These equations

are based on careful experiments and give very satisfactory results.

Steam Tables. We have already seen that any change in

the temperature of saturated steam produces a change of pressure,

and that every change of pressure corresponds to a certain change

in temperature. There are several properties of saturated steam

that depend upon the temperature and pressure ; and the values

of all these different properties when arranged for all temperatures

and pressures are called Steam Tables. The following are the

principal items that are found in the tables :

1. The absolute pressure in pounds per square inch; it is

equal to the gage pressure plus the atmospheric pressure of 14.7

pounds.

2. The temperature of the steam, or boiling water, at the

corresponding pressure.

3. The heat of the liquid ; or the number of B. T. U. neces-

sary to raise one pound of water from 32 F to the boiling point

corresponding to the given pressure.

4. The heat of vaporization, or the latent heat ; this is the

number of B. T. U. necessary to change one pound of water, at

the boiling point, into dry saturated steam at the same temperature

and pressure.

138

THE STEAM ENGINE. 87

5. The total heat- or the number of B. T. U. necessary to

change one pound of water from 32 F into steam at the given

temperature or pressure. The total heat is evidently equal to the

sum of the heat of the liquid and the heat of vaporization.

6. The density of the steam ; that is, the weight in pounds

of one cubic foot of steam at the given temperature or pressure.

7. The specific volume ; or volume in cubic feet of one

pound of steam at the required temperature or pressure. Evi-

dently the specific volume is equal to .

density

All these properties have been calculated by means of various

formulas which have been deduced from the results of actual

experiment. There are several formulas for the temperatures and

pressures of steam ; as some computers have used one and some

another, there is likely to be a slight discrepancy between the

tables computed by different authors. Rankin's formula, already

given, is the simplest, but is not generally considered to be quite

as accurate as some of the later ones ; it has probably been used,

however, more than any other.

The total heat may be calculated by means of the formula

H = 1,091.7 + 0.305 (t 32) [1]

in which H = total heat

t =; temperature in degrees Fahrenheit.

The heat of the liquid is equal to q.

q = t + 0.00002 *a _j_ 0.0000003*3 [2]

in which t =. temperature in degrees Centigrade.

These constants are for use in the Centigrade system only.

To calculate the heat of the liquid for any Fahrenheit temper-

ature it is necessary to change the Fahrenheit into equivalent

Centigrade degrees and then substitute in the above formula.

The formula used for the calculation of specific volume is too

complex for consideration here, but^the relation of pressure and

volume may be approximately expressed by means of an equation

of the form P V n = C, in which n is an exponent, C a constant,

P the absolute pressure, and V the specific volume ; n is usually

taken to be , and C to be 475.

lo

On pages 14 ind 15 are given tables of the properties of

139

THE STEAM ENGINE.

TABLE OF PROPERTIES OF SATURATED STEAM.

Pressure

in

pounds

persq.in

above

vacuum

Tenpera-

ture in

degrees

Fahren-

heit.

Heat

in

liquid

from

32 in

units.

Heat of

vaporiza-

tion, or

latent

heat in

teat units

Total

heat in

heat

units

from

water at

32.

Density o

weight

of cubic ft

in pounds

Volume

of 1

pound in

cubic

feet.

Total

pressure

above

vacuum.

1

101.99

700

1043.0

1113.1

0.00299

334.5

1

2

126.27

91.4

1026.1

1120.5

0.00576

173.6

2

3

141.62

109.8

1015.3

1125.1

0.00844

118.5

3

4

153.09

121.4

1007.2

1128.6

0.01107

90.31

4

6

162.34

130.7

1000.8

1131.5

001366

73.21

5

6

170.14

138.6

995.2

1133.8

0.01622

61.67

6

7

176.90

145.4

990.5

1135.9

0.01874

53.37

7

8

182.92

151.5

986.2

1137.7

0.02125

47.06

8

9

188.33

156.9

982.5

1139.4

0.02374

42.12

9

10

193.25

161.9

979.0

1140.9

0.02621

38.15

10

147

212.00

180.9

965.7

1146.6

0.03794

26.36

14.7

15

213.03

181.8

965.1

1146.9

0.03826

26.14

15

20

227.95

196.9

954.6

1151.5

0.05023

19.91

20

25

240.04

209.1

946.0

1155.1

0.06199

16.13

26

30

250.27

219.4

938.9

1158.3

0.07360

13.59

30

35

259.19

228.4

932.6

1161

0.08508

11.75

35

40

267.13

236.4

927.0

1163.4

0.09644

10.37

40

45

274.29

243.6

922.0

1165.6

0.1077

9287

45

60

280.85

250.2'

917.4

1167.6

0.1188

8414

60

65

286.89

256.3

913.1

1169.4

0.1299

7.696

65

60

292.51

261.9

909.3

1171.2

0.1409

7.097

60

65

297.77

267.2

905.5

1172.7

0.1519

6583

65

70

302.71

272.2

902.1

1174.3

0.1628

6.143

70

75

307.38

276.9

898.8

1175.7

0.1736

5.762

75

80

S11.80

281.4

895.6

1177.0

0.1843

6 426

80

85

316.02

285.8

892.5

1178.3

0.1951

5126

85

90

320.04

290.0

889.6

1179.6

0.2058

4.859

90

95

323.89

294.0

886.7

1180.7

0.2165

4.619

96

100

327.58

297.9

884.0

1181.9

0.2271

4.403

100

105

331.13

301.6

881.3

1182.9

0.2378

4.205

105

110

334.56

305.2

878.8

1184.0

0.2484

4.026

110

115

337.86

308.7

876.3

1185.0

0.2589

3.862

116

120

341.05

3120

874.0

1186.0

0.2695

3 711

120

125

344.13

315.2

871.7

1186.9

0.2800

3.571

125

130

347.12

318.4

869.4

1187.8

0.2904

3.444

130

140

352.85

324.4

865.1

1189.5

0.3113

3.212

140

150

358.26

330.0

861.2

1191 2

0.3321

3.011

160

160

363.40

335.4

857.4

1192.8

0.3530

2833

160

170

368.29

340.5

853.8

1194.3

0.3737

2.676

170

180

372.97

345.4

850.3

1195.7

0.3945

2.535

180

190

377.44

350.1

847.0

1197.1

04153

2.408

190

200

381.73

354.6

843.8-

1198.4

04359

2.294

200

225

391.79

365.1

836.3

1201.4

0.4876

2.051

225

250

400.99

374.7

829.5

1204.2

0.5393

1.854

260

275

409.50

383.6

823.2

1206.8

0.5913

1.691

275

300

417.42

391.9

817.4

1209.3

0.644

1.553

300

325

424.82

399.6

811.9

1211.5

0.696

1.437

325

350

431.90

406.9

806.8

1213.7

0.748

1.337

350

375

438.40

414.2

801.5

1215.7

0.800

1.250

375

400

445.15

421.4

796.3

1217.7

0.853

1.172

400

600

466.57

444.3

779.9

1224.2

1.065

.939

600

140

THE STEAM ENGINE.

TABLE OF PROPERTIES OF SATURATED STEAM.

Temper-

ature in

degrees

Fahren-

heit.

Total

pressure

above

vacuum.

Heat

in

liquid

from

32 in

units.

Heat of

vaporiza-

tion, or

latent

heat in

heat units

Total

heat in

heat

units

from

water at

32.

Density o

weight

of cubic ft

in pounds

. Volume

of one

pound in

cubic

feet.

Tempera

ture in

degrees

Fahren-

heit.

32

0.089

0.

1091.7

1091.7

0.0003

3387.

32

60

0.254

28.12

1072.1

1100.2

0.0008

1234.

60

90

0.692

58.04

1051.4

1109.4

0.002J

474.6

90

120

1.683

88.10

1034.4

1118.5

0.0049

204.4

120

140

2.877

108.2

1016.4

1124.6

00081

123.2

140

160

3.706

118.3

1009.4

1127.7

0.0103

97.03

150

160

4.729

128.4

1002.3

1130.7

0.0130

77.14

160

170

6.98

138.5

995.3

11338

0.0162

61.85

170

180

7.50

148.5

988.3

1136.8

0.0200

50.01

180

190

9.33

158.6

981.3

1139.9

0.0245

40.73

190

200

11.52

168.7

974.2

1142.9

00299

33.40

200

210

14.12

178.8

967.2

1146.0

0.0363

27.57

210

220

17.19

188.9

960.1

1149.0

0.0435

22.98

220

225

1891

193.9

956.7

1150.6

0.0476

20.99

225

230

20.78

198.9

953.2

1152.1

0.0521

19.20

230

935

22.80

204.0

949.6

1153 6

0.0569

17.59

235

240

24.98

209.0

946.1

1156.1

0.0619

16.14

240

245

27.33

214.1

942.6

1156.7

0.0674

1483

245

250

29.86

219.1

939.1

11582

0.0733

13.65

250

255

32.57

224.1

935.6

1159.7

0.0795

12.57

255

260

35.48

229.2

932.0

1161.2

0.0862

11.60

260

265.

38.60

234.2

928.6

11628

0.0933

10.72

265

270

41.94

239.3

925.0

1164.3

0.1008

9.918

270

275

45.51

244.3

921.5

1165.8

0.1088

9.187

275

280

49.33

249.3

918.0

1167.3

0.1173

8521

280

285

53.39

254.4

914.5

1168.9

0.1264

7913

Online Library → American Technical Society → Cyclopedia of engineering : a general reference work on steam boilers, pumps, engines, and turbines, gas and oil engines, automobiles, marine and locomotive work, heating and ventilating, compressed air, refrigeration, dynamos motors, electric wiring, electric lighting, elevators, etc. (Volume 2) → online text (page 9 of 30)