When a given weight of a perfect gas is compressed or expanded at a
constant temperature, the product of the pressure and volume is a
constant. Vapors, which are liquids in aeriform condition, on the other
hand, can exist only at a definite pressure corresponding to each
temperature if in the saturated state, that is, the pressure is a
function of the temperature only. Steam is water vapor, and at a
pressure of, say, 150 pounds absolute per square inch saturated steam
can exist only at a temperature 358 degrees Fahrenheit. Hence if the
pressure of saturated steam be fixed, its temperature is also fixed, and
_vice versa_.
Saturated steam is water vapor in the condition in which it is generated
from water with which it is in contact. Or it is steam which is at the
maximum pressure and density possible at its temperature. If any change
be made in the temperature or pressure of steam, there will be a
corresponding change in its condition. If the pressure be increased or
the temperature decreased, a portion of the steam will be condensed. If
the temperature be increased or the pressure decreased, a portion of the
water with which the steam is in contact will be evaporated into steam.
Steam will remain saturated just so long as it is of the same pressure
and temperature as the water with which it can remain in contact without
a gain or loss of heat. Moreover, saturated steam cannot have its
temperature lowered without a lowering of its pressure, any loss of heat
being made up by the latent heat of such portion as will be condensed.
Nor can the temperature of saturated steam be increased except when
accompanied by a corresponding increase in pressure, any added heat
being expended in the evaporation into steam of a portion of the water
with which it is in contact.
Dry saturated steam contains no water. In some cases, saturated steam is
accompanied by water which is carried along with it, either in the form
of a spray or is blown along the surface of the piping, and the steam is
then said to be wet. The percentage weight of the steam in a mixture of
steam and water is called the quality of the steam. Thus, if in a
mixture of 100 pounds of steam and water there is three-quarters of a
pound of water, the quality of the steam will be 99.25.
Heat may be added to steam not in contact with water, such an addition
of heat resulting in an increase of temperature and pressure if the
volume be kept constant, or an increase in temperature and volume if the
pressure remain constant. Steam whose temperature thus exceeds that of
saturated steam at a corresponding pressure is said to be superheated
and its properties approximate those of a perfect gas.
As pointed out in the chapter on heat, the heat necessary to raise one
pound of water from 32 degrees Fahrenheit to the point of ebullition is
called the _heat of the liquid_. The heat absorbed during ebullition
consists of that necessary to dissociate the molecules, or the _inner
latent heat_, and that necessary to overcome the resistance to the
increase in volume, or the _outer latent heat_. These two make up the
_latent heat of evaporation_ and the sum of this latent heat of
evaporation and the heat of the liquid make the _total heat_ of the
steam. These values for various pressures are given in the steam tables,
pages 122 to 127.
The specific volume of saturated steam at any pressure is the volume in
cubic feet of one pound of steam at that pressure.
The density of saturated steam, that is, its weight per cubic foot, is
obviously the reciprocal of the specific volume. This density varies as
the 16/17 power over the ordinary range of pressures used in steam
boiler work and may be found by the formula, D = .003027p^{.941}, which
is correct within 0.15 per cent up to 250 pounds pressure.
The relative volume of steam is the ratio of the volume of a given
weight to the volume of the same weight of water at 39.2 degrees
Fahrenheit and is equal to the specific volume times 62.427.
As vapors are liquids in their gaseous form and the boiling point is the
point of change in this condition, it is clear that this point is
dependent upon the pressure under which the liquid exists. This fact is
of great practical importance in steam condenser work and in many
operations involving boiling in an open vessel, since in the latter case
its altitude will have considerable influence. The relation between
altitude and boiling point of water is shown in Table 12.
The conditions of feed temperature and steam pressure in boiler tests,
fuel performances and the like, will be found to vary widely in
different trials. In order to secure a means for comparison of different
trials, it is necessary to reduce all results to some common basis. The
method which has been adopted for the reduction to a comparable basis is
to transform the evaporation under actual conditions of steam pressure
and feed temperature which exist in the trial to an equivalent
evaporation under a set of standard conditions. These standard
conditions presuppose a feed water temperature of 212 degrees Fahrenheit
and a steam pressure equal to the normal atmospheric pressure at sea
level, 14.7 pounds absolute. Under such conditions steam would be
generated _at_ a temperature of 212 degrees, the temperature
corresponding to atmospheric pressure at sea level, _from_ water at 212
degrees. The weight of water which _would_ be evaporated under the
assumed standard conditions by exactly the amount of heat absorbed by
the boiler under actual conditions existing in the trial, is, therefore,
called the equivalent evaporation "from and at 212 degrees."
The factor for reducing the weight of water actually converted into
steam from the temperature of the feed, at the steam pressure existing
in the trial, to the equivalent evaporation under standard conditions is
called the _factor of evaporation._ This factor is the ratio of the
total heat added to one pound of steam under the standard conditions to
the heat added to each pound of steam in heating the water from the
temperature of the feed in the trial to the temperature corresponding to
the pressure existing in the trial. This heat added is obviously the
difference between the total heat of evaporation of the steam at the
pressure existing in the trial and the heat of the liquid in the water
at the temperature at which it was fed in the trial. To illustrate by an
example:
In a boiler trial the temperature of the feed water is 60 degrees
Fahrenheit and the pressure under which steam is delivered is 160.3
pounds gauge pressure or 175 pounds absolute pressure. The total heat of
one pound of steam at 175 pounds pressure is 1195.9 B. t. u. measured
above the standard temperature of 32 degrees Fahrenheit. But the water
fed to the boiler contained 28.08 B. t. u. as the heat of the liquid
measured above 32 degrees Fahrenheit. Therefore, to each pound of steam
there has been added 1167.82 B. t. u. To evaporate one pound of water
under standard conditions would, on the other hand, have required but
970.4 B. t. u., which, as described, is the latent heat of evaporation
at 212 degrees Fahrenheit. Expressed differently, the total heat of one
pound of steam at the pressure corresponding to a temperature of 212
degrees is 1150.4 B. t. u. One pound of water at 212 degrees contains
180 B. t. u. of sensible heat above 32 degrees Fahrenheit. Hence, under
standard conditions, 1150.4 - 180 = 970.4 B. t. u. is added in the
changing of one pound of water into steam at atmospheric pressure and a
temperature of 212 degrees. This is in effect the definition of the
latent heat of evaporation.
Hence, if conditions of the trial had been standard, only 970.4 B. t. u.
would be required and the ratio of 1167.82 to 970.4 B. t. u. is the
ratio determining the factor of evaporation. The factor in the assumed
case is 1167.82 ÷ 970.4 = 1.2034 and if the same amount of heat had been
absorbed under standard conditions as was absorbed in the trial
condition, 1.2034 times the amount of steam would have been generated.
Expressed as a formula for use with any set of conditions, the factor
is,
H - h
F = ----- (2)
970.4
Where H = the total heat of steam above 32 degrees Fahrenheit from steam
tables,
h = sensible heat of feed water above 32 degrees Fahrenheit from
Table 22.
In the form above, the factor may be determined with either saturated or
superheated steam, provided that in the latter case values of H are
available for varying degrees of superheat and pressures.
Where such values are not available, the form becomes,
H - h + s(t_{sup} - t_{sat})
F = ---------------------------- (3)
970.4
Where s = mean specific heat of superheated steam at the
pressure existing in the trial from saturated
steam to the temperature existing in the trial,
t_{sup} = final temperature of steam,
t_{sat} = temperature of saturated steam, corresponding to
pressure existing,
(t_{sup} - t_{sat}) = degrees of superheat.
The specific heat of superheated steam will be taken up later.
Table 19 gives factors of evaporation for saturated steam boiler trials
to cover a large range of conditions. Except for the most refined work,
intermediate values may be determined by interpolation.
Steam gauges indicate the pressure above the atmosphere. As has been
pointed out, the atmospheric pressure changes according to the altitude
and the variation in the barometer. Hence, calculations involving the
properties of steam are based on _absolute_ pressures, which are equal
to the gauge pressure plus the atmospheric pressure in pounds to the
square inch. This latter is generally assumed to be 14.7 pounds per
square inch at sea level, but for other levels it must be determined
from the barometric reading at that place.
Vacuum gauges indicate the difference, expressed in inches of mercury,
between atmospheric pressure and the pressure within the vessel to which
the gauge is attached. For approximate purposes, 2.04 inches height of
mercury may be considered equal to a pressure of one pound per square
inch at the ordinary temperatures at which mercury gauges are used.
Hence for any reading of the vacuum gauge in inches, G, the absolute
pressure for any barometer reading in inches, B, will be (B - G) ÷ 2.04.
If the barometer is 30 inches measured at ordinary temperatures and not
corrected to 32 degrees Fahrenheit and the vacuum gauge 24 inches, the
absolute pressure will be (30 - 24) ÷ 2.04 = 2.9 pounds per square inch.