melting and freezing. The middle of the ice stream moves
faster than the sides because the weight there is greater
and the consequent melting more extensive.
40. The Latent Heat of Fusion. - - The nearly sta-
tionary temperature maintained by a solid during its
passage into the liquid state has already been described.
The heat that fuses a crystalline solid does not sensibly
raise its temperature. In the language of the caloric theory
it becomes latent or concealed. The term latent heat has
been retained in the modern theory of heat, but we now
know that the heat which disappears during fusion ceases
to be heat, and is the energy expended or converted into
the potential form in the work of giving mobility to the
The manner of measuring the heat of fusion may be
illustrated by the method of mixtures. If two kilogrammes
of water, one at C. and the other at 100 C., be mixed,
the result will be two kilogrammes at a mean temperature
of 50 C. But if a kilogramme of water at 100 C. be
mixed with one of ice at the freezing point, the ice will
melt and there will be two kilogrammes of water at about
10.4 C. The heat lost by the hot water is 1,000 x 89.6
calories. A portion of this, viz., 1,000 x 10.4 calories, has
been employed to raise the ice-cold water from to 10.4
C., but the remainder has disappeared in the melting of the
ice. Therefore to melt 1,000 gms. of ice, 1,000 (89.6 10.4)
equals 1,000 x 79.2 calories of heat are required. This
is equivalent to 79.2 calories per gm. of ice. In an actual
experiment of this kind, the water equivalent of the calo-
rimeter must be taken into account. It is here supposed
to be included in the kilogramme of hot water. Experi-
ments of this kind have demonstrated that for every unit
of ice melted about 79.2 units of heat disappear.
The latent heat of fusion is denned as the number of
calories required to convert one gramme of a substance
from the solid to the liquid state without change of
Let m^ be the mass and , the temperature of the water
and the calorimeter ; also let m be the water equivalent of
the calorimeter, and let m.> be the mass of the ice whose
heat of fusion I is to be found. If the resulting tempera-
ture of the mixture is t C., then the heat lost by the cal-
orimeter and its contents may be equated to the heat of
fusion of the ice and its gain of heat in rising from zero
to t C., or
(m + MI) (ti ^ m 2 + fn^
Whence ' I = ( + .)(.-*)_ ( .
' m a
The correction for radiation may be avoided by Rumford's
The most probable value of the heat of fusion is 79.25,
though Person found 80.02 and Bunsen 80.03, the mean
specific heat of water between and 100 C. being taken
by Bunseii as the unit.
41. Heat absorbed in Solution (S., 94). - We have
seen that when a solid is changed to the liquid form, heat
is absorbed. If the liquefaction is accomplished by solu-
tion in a proper solvent without chemical action, heat is
still required to give mobility to the molecules, and the
temperature of the solution falls. This effect is often
masked by the generation of heat by chemical action
between the solid and the solvent. If a delicate therrno-
scope be used, such as a thermopile and a galvanometer
(see i' Thermal Electricity "), the heat absorbed by the solu-
tion of sugar in water may be readily detected. A still
larger effect is produced by dissolving common salt, while
quite a notable reduction of temperature is produced by
the dissolving of nitrate of sodium. When glacial acetic
acid is dissolved in water, the absorption of heat necessary
to increase the fluidity exceeds the evolution of heat by
Freezing mixtures are based on the absorption of heat
necessary to give fluidity. Salt water freezes at a lower
temperature than pure water. Hence, when salt and snow
or pounded ice are mixed, both of them become fluid and
absorb heat in the transition from one state to the other.
By this means a temperature of 22 C. may be obtained.
Many other chlorides, as well as some nitrates, form
freezing mixtures with snow or ice. Among them, in the
order of effectiveness, are the chlorides of calcium, copper,
strontium, ammonium, potassium, and barium.
1. Into a mass of water at C. are introduced 100 gms. of
ice at 12 C. ; 7.5 gms. of ice are frozen and the temperature of
all the ice is raised to C. If the latent heat of fusion is 80, find
the specific heat of ice.
2. How much ice at C. will be melted by 30 gms. of copper
(specific heat, 0.095) at 200 C. ?
3. A mass of 100 gms. of platinum (specific heat, 0.0355) is
heated in a furnace and is then dropped into 200 gms. of water at
C. ; the temperature of the water rises to 26 C. What was the
temperature of the furnace ?
4. If a kilo, of copper at 100 C. be placed in a cavity in a
block of ice at C., and if 119 gms. of ice are melted, find the heat
of fusion of ice.
5. 100 gms. of ice at 20 C. were thrown into 1 kilo, of water
at 20 C. contained in a copper vessel weighing 100 gms. When the
ice was melted the temperature of the water was 10. 15 C. Find
the latent heat of fusion of ice.
42. Four Varieties of Vaporization. - - The passage
of a substance into the state of a gas or a vapor is called
vaporization. There are four distinct types depending
upon the conditions under which the process goes on :
1. Evaporation, where a liquid is converted into a gas
quietly at a relatively low temperature and without the
formation of bubbles.
'1. Ebullition, or boiling, a rapid evaporation at a
higher thermal equilibrium, when bubbles of gas form in
the mass of the liquid.
3. The Spheroidal State, where quiet vaporization, at a
rate between evaporation and ebullition, goes on when the
liquid is in apparent contact with a body of relatively high
4. Sublimation, in which a solid passes directly into
the gaseous form without going through the intermediate
Whether the gaseous condition is reached by one of
these processes or another, heat is always absorbed in
considerable quantity, although the vapor is at the same
temperature as the solid or liquid from which it comes ;
we have therefore the expression, "latent heat of vapori-
zation." The latent heat of gases is greater than that of
liquids ; this fact prevents a disastrously sudden conversion
either from the liquid to the gaseous state without chemical
change, or the reverse condensation of vapors to liquids,
since the heat involved in either operation must be supplied
for evaporation, or must be disposed of when generated by
43. Evaporation in a Closed Space. In a solid the
molecules are free to vibrate about fixed positions of equilib-
rium, but have no motion of translation. In a liquid the
conditions of molecular freedom are much more extended.
A molecule is so far released from rigid cohesion that it
may make its way throughout the entire mass; but its
progress is slow because most of its time is spent in en-
counters with other molecules, of which it is never inde-
pendent. There is practically no free path to molecular
motion in liquids, and the migratory track of any mole-
cule depends upon its innumerable chance encounters with
In the interior of a liquid mass a molecule is equally
obstructed in its movements in all directions ; but at the
surface the resultant molecular attraction is normal, and
there results the phenomenon of a surface film, called sur-
face tension (I., 93).
Whenever a molecule at the surface of the liquid has a
normal component of motion sufficient to carry it through
the surface film, it may escape from bondage and wander
about in free space. It is then independent of its fellows,
except for numerous collisions with them, which determine
all the properties of the gaseous state, without, however,
absorbing a large portion of time as compared with that of
the free motion of the molecule. Such molecules consti-
tute the vapor or the gaseous form of the substance, and
the process of entering this state is called evaporation.
If evaporation takes place in a closed space, then the free
molecules may again come within the range of molecular
action at the liquid surface, and may be again entangled
and return into the liquid. This process is called con-
densation. When the number of molecules making their
escape equals the number returning through the surface
film, there is an equilibrium between the loss and the gain,
and at this stage the evaporation is said to cease. This
vapor in. contact with its liquid is then said to be saturated.
Its density will remain unchanged unless there is a change
of temperature. An elevation of the temperature causes
more of the liquid to assume the form of a vapor. If the
volume of the saturated vapor is diminished without change
of temperature, some of the vapor will condense to a
liquid ; and if the volume is increased, more of the liquid
will evaporate so as to maintain the same vapor density.
Dalton concluded that the presence of inert gases, like
air, has no influence on the final density of the vapor ; that
its only effect is to increase the time required to reach the
equilibrium between evaporation and condensation. But
Regnault has shown that the maximum pressure of the
saturated vapor of water, ether, and some other substances,
is slightly diminished when air is present.
The maximum pressures of aqueous vapor in millime-
tivs of mercury are given in the Appendix, Table III.
44. Ebullition. Each molecule carries away heat in
evaporation represented by the additional potential energy
which it gains in entering the gaseous state. If only a
moderate amount of heat is applied, the evaporation is con-
fined to the surface, and it increases till the rate at which
heat is supplied equals the rate of loss by evaporation.
When the evaporation takes place into open space, the
molecules escaping from the surface may never return to
the liquid. There is then no saturated vapor, and the
evaporation continues so long as the heat is supplied and
any liquid remains. But if the surface is limited in area
and the heat supply is in excess, this equilibrium of quiet
evaporation cannot be established. The temperature rises
till bubbles of vapor begin to form in the interior of the
liquid, or at points on the inner surface of the containing
vessel. If the vapor pressure is not sufficient to support
them as they rise, they collapse and produce the familiar
sound of " simmering." With a slightly higher temperature
they rise to the surface, expanding in the ascent under re-
duced hydrostatic pressure; and if the evaporation into
them from their enlarged surface is sufficiently rapid, they
burst through the surface film and escape. This process of
rapid evaporation from the interior, as well as at the
surface, is called ebullition or boiling. An equilibrium is
thus established at a higher temperature than the preced-
ing, and this temperature is called the boiling point of
the liquid. It is constant for the same pressure.
If the heat be supplied at a still more rapid rate the tem-
perature of the liquid does not rise higher, but the boiling
is more violent. So long as the pressure remains the same,
ebullition goes on at any rate of heat supply in excess of
the rate at which silent evaporation at the surface can dis-
pose of it. The vaporization is then no longer confined to
the free surface, but takes place in the interior into small
bubbles initiated by expanding air, ' disengaged from the
liquid by heat, or by other bodies which are very active in
separating vapor from the heated liquid.
When the air has been all boiled out and the containing
vessel is clean, the temperature of water may rise several
degrees above the normal boiling point. Ebullition then
TM POP, 72. 1 TION.
sets in with almost explosive violence, and proceeds till the
excess of heat, due to the elevation of temperature above
the normal boiling point, is disposed of. This abnormally
high boiling point of air-free water probably accounts for
many explosions of stationary boilers at the moment when
.steam is first drawn from them after fresh firing. As a
measure of precaution, a fresh supply of water containing
air should be pumped in before the temperature rises to the
The boiling point is the temperature at which the liquid
boils or gives off bubbles of its own vapor. It has been
found by experiment that at the boiling point the saturated
vapor is given off at a pressure equal to that sustained by the
surface of the liquid.
45. Effect of Pressure on the Boiling Point (T., 135).
- The work done by -\
heat in ebullition is
partly internal and
partly external. The
internal work consists
in separating the mole-
cules beyond the range
of molecular attraction.
The external work de-
pends upon the fact that
the liberated vapor is
formed under pressure.
The work done is meas-
ured by the volume of
vapor formed multi-
plied by the pressure on
it per unit area. Since
this external work is diminished by diminishing the pres-
sure, the lower the pressure the lower the boiling point.
Under diminished pressure water boils at a reduced
temperature. A familiar form of experiment to demon-
strate this fact consists in boiling water in an open flask
till the air is nearly all expelled by the steam. The flask
is then tightly corked and inverted (Fig. 16). The boiling
ceases, but is renewed by
applying cold water to
the flask. The cold water
condenses the vapor and
reduces the pressure with-
in the flask so that the
boiling begins again. If
the air has been thorough-
ly expelled, the water may
be kept boiling till the
temperature has fallen to
that of the air of the
A convenient modifica-
tion of this experiment
consists in fitting into the
flask a rubber stopper
traversed by a small glass tube, so that the flask is air-tight
except through the tube. The tube should be bent twice
at right angles in order that the outer end may dip down
below the surface of cold water in a beaker (Fig. 17).
Boil the water in the flask till the air is expelled, and then
dip the open end of the tube under water, at the same time
removing the lamp. If the apparatus is air-tight the cold
water will rise in the tube as the flask cools, and will at
length pass the beiid and pour into the flask in a stream.
The cold water condenses the vapor and causes violent
ebullition, which will continue, though the water all the
time becomes cooler. The only precaution to be observed
is to make sure that the air shall enter the tube before the
flask is filled; otherwise the shock due to the sudden
stopping of the stream when the flask is full will break it.
Beyond the normal boiling point the pressure of saturated
vapor rises rapidly with the temperature. The rise of
temperature from 100 to 180 C. increases the pressure of
water vapor from one to nearly ten atmospheres, and an
additional rise of 40 C. raises the pressure to about 23
The relation between temperature and the vapor press-
ure of water is represented by the curve of Fig. 18.
Above 150 C. this curve rises very rapidly as the tem-
46. The Spheroidal State. When a drop of water is
placed on a clean hot stove it will often take a flattened
globular form and roll around with rapid but silent
evaporation. This phenomenon is known as the spheroidal
state. It may be beautifully exhibited by heating a small
flat platinum dish red hot over a Bunsen burner, and care-
fully placing in it a large globule of water by means of a
pipette. It will not boil, but will assume the spheroidal
state. The globule is not in contact with the hot metal,
but rests on a cushion of its own vapor, which escapes
rhythmically from its edge and often throws it into beauti-
ful undulations. If the lamp be removed the temperature
will fall till a point is reached at which the drop comes into
contact with the hot metal, when violent ebullition will
If the drop is not too large, light may be projected
through between it and the hot metallic surface, thus
demonstrating that the drop is not in contact with the
Boutigny, by placing a small thermometer in the drop
of water, found that its temperature remained below the
boiling point ; and Berger afterwards found that in a
large globule the temperature varied from 96 or 98 C.
near the bottom to about 90 C. at the upper surface.
Budde has shown that under the exhausted receiver of
an air-pump the spheroidal state of water may persist at
temperatures as low as 80 or 90 C. The vapor pressure
under the drop is then only what is required to support the
drop itself, the air pressure having been removed.
Water is not the only substance that assumes the
spheroidal form. The temperature of spheroidal sulphur
dioxide is low enough to freeze a drop of water placed in
it. This may happen in a red-hot crucible because the
sulphur dioxide in the spheroidal state is below its boiling
point, and this is below the freezing point of water.
Solid carbon dioxide may be touched with the hand or
even the tongue without danger if no pressure 4s applied,
because it is kept out of contact by an intervening film of
the substance in the gaseous form. Faraday succeeded in
freezing mercury in a mixture of ether and solid carbon
dioxide contained in a red-hot crucible. The contents of
the crucible were cushioned on their vapor in a state
analogous to the spheroidal form.
Quite a remarkable example of the spheroidal state,
because it takes place at a low temperature, is exhibited by
liquid oxygen on water. The liquid oxygen boils gently
at about 180 C., and when placed on water it imme-
diately exhibits all the aspects of a globule of water on
a hot plate. The water is at a high temperature relative
to the oxygen. So much heat, however, is abstracted from
the water by the evaporation of the liquid oxygen that the
spheroidal globule soon encases itself in an envelope of ice,
with only a small blowhole for the escape of the gas.
47. Sublimation. The usual course from the solid to
the gaseous state is through that of a liquid. But a num-
ber of solids slowly waste away by evaporation without
liquefying. Ice and snow at temperatures below freezing
gradually lose in volume by evaporation. So carbon dioxide
snow when exposed in the air wastes away by evaporation,
and can be liquefied only with difficulty in an open tube.
A solid brick of it will remain unmelted for many hours
even in warm weather. It evaporates only so fast as it
gets heat to do the work of evaporation.
Other substances, such as camphor and ammonium car-
bonate, sublime at ordinary temperatures. Iodine, ammo-
nium chloride, and arsenic sublime when heated under
atmospheric pressure. But if the pressure is increased
arsenic may be fused ; and below a certain critical pressure
for each, ice, mercuric chloride, and camphor do not melt,
but pass directly into the gaseous state.
If by reduction of pressure the boiling point of a liquid
is reduced to the fusing point of its solid, then the solid
may pass directly into the gaseous state. A solid will,
therefore, sublime when the pressure upon it is less than
the vapor pressure of its saturated vapor at the tempera-
ture of fusion. The vapor pressure of carbon dioxide at
its fusing point of 65 C. is three atmospheres ; under a
lower pressure than three atmospheres it therefore sub-
limes. If the pressure of mercuric chloride is below 420
mms. it must evaporate without liquefaction. The same
is true of iodine at pressures under 90 mms., and of ice
under 4.6 mms. of mercury.
48. Latent Heat of Vaporization (P., 3O4). The
latent heat of vaporization is the quantity of heat required
to convert one gramme of the liquid into vapor without
change of temperature. The temperature at which the
vaporization takes place is often understood to be the
boiling point of the liquid under a pressure of one stand-
ard atmosphere. The investigations of Regnault on the
latent heat of steam enable us to express the latent heat of
VA PORIZA TION. 75
vaporization, for water vapor at least, by one formula appli-
cable through a considerable range of temperature. By
the total heat of steam at any temperature Regnault meant
the amount of heat necessary, first, to raise one gramme of
water to that temperature without evaporation, and then
to convert it wholly into saturated vapor at the same tem-
perature. If L is the latent heat of vaporization, , and t
the initial and final temperatures, and s the mean specific
heat between these temperatures, then the total number of
heat units required to convert a gramme of water at ^
into saturated vapor at t is
Regnault's experiments were conducted under pressures
ranging from 0.22 to 13.625 atmospheres, and from to
230 C. ; and between these limits he found that the total
heat was represented by the equation
H= 606.5 + 0.305*.
Taking the mean specific heat of water to be unity and the
initial temperature zero, the formula for the latent heat at
any temperature t C. becomes
L=H-t = 606.5 -0.695*.
If t is 100 C. the latent heat of steam is therefore 53T ; that
is, .">:-.> 7 calories are required to convert one gramme of water
at 100 C into steam at the same temperature.
Taking into account the very small variation in the
specific heat of water, the latent heat of steam falls from
606.5 at C. to 536.5 at 100, and to 464.5 at 200 C.
Prior to Regnault's investigations it was generally ad-
mitted on insufficient evidence that the heat required to
change a gramme of water at C. into steam was inde-
pendent of the pressure. If that were true, the sums of the
three pairs of numbers above, representing latent heats
and temperatures, should be approximately the same. On
the contrary they increase by nearly five per cent for every
100 degrees rise of temperature.
Andrews found the latent heat of evaporation of a few
common liquids boiling under atmospheric pressure to be
as' follows :
Alcohol . 202.4
49. Cold due to Evaporation. If the heat required
is not supplied from some external source, the evaporation
of a liquid will be accompanied by a
lowering of its temperature. This fact
accounts for the coolness felt when ether,
alcohol, or benzine evaporates from the
hand. While their latent heat of evapo-
ration is smaller than that of steam, their
boiling points are lower and the rapid
F |9 evaporation absorbs much heat.
In Leslie's experiment a thin flat dish,
containing about 10 c.c. of water, is supported by a tripod
over a large shallow glass vessel containing strong sulphuric
acid, and the whole is placed under the receiver of an air-
pump (Fig. 19). The dish should be held in such a manner
that it cannot receive heat from below by conduction.
On exhausting the air rapidly the pressure is reduced till
the boiling point falls to the temperature of the water.
The water then begins to boil briskly ; and if the vapor is
removed rapidly, both by working the pump and by ab-
sorption by the acid, the pressure may be kept low enough
to keep the water boiling till it freezes. The conditions are
such as to produce rapid evaporation, while- the heat re-
quired to do the internal work is drawn entirely from the
water itself and the thin dish. Not infrequently the
bubbles may be frozen before they burst.
Wollaston's cryophorus (Fig. 20) is also designed to
show the freezing of water by evaporation. It consists of
a bent tube with a bulb at each end. Before it is sealed
some water is introduced and boiled to expel all the air
from the tube, which is then sealed by fusing the glass.
In performing the experiment the water is all collected
in the upper bulb J., and the lower one
is imbedded in a freezing mixture. The
vapor condenses rapidly in E and forms at
the same rate in A. Heat is thus carried
by the vapor from A to B ; and as A parts
with its heat, if none is supplied to it, the
temperature of the water in it will fall to
the freezing point.
Much lower temperatures may be se-
cured by the rapid evaporation of liquids
which boil at a temperature below the
boiling point of water. Thus with liquid sulphur diox-
ide, which boils under atmospheric pressure at 10 C.,