Physics for university students (Volume 2) online

mercury may be frozen. By the rapid evaporation of
liquid carbon dioxide Pictet obtained a temperature of
140 C. Liquid oxygen boiling in air reduces the tem-
perature to 182 C. ; and by increasing the rate of evap-
oration by reducing the pressure, Dewar has reached a
temperature of 200 C., or even lower.

This property of heat absorption by liquids that evap-
orate at a low temperature has been applied to the con-
struction of ice machines. Ammonia is first condensed by
pressure and cooling to 'a liquid with about one-tenth of




Fig. 20.



78 HEAT.

its weight of -water. It is then evaporated under reduced
pressure secured by powerful pumps, and its temperature
falls low enough to freeze water in vessels about it or
within it. The process is made continuous by returning
the ammonia to a condensing chamber cooled with water.
It thus passes repeatedly through the same cycle of changes.

50. Relative Humidity. The atmosphere always con-
tains aqueous vapor, whose pressure is the same as if it
alone were present. When its pressure at any temperature
of the air equals the saturation pressure for that tempera-
ture, it will condense on the surface of bodies, or fall as
rain or snow.

The humidity or dampness of the air does not depend
alone on the quantity of aqueous vapor present, but on the
nearness of the vapor pressure to the saturation point.
The saturation pressure at any temperature is the same as
that under which water boils at that temperature.

The saturation pressure rises rapidly with the tempera-
ture (Appendix, Table III.). Thus the maximum pressure
of aqueous vapor at 10 C. is 9.17 mms., while at 21 C. it
is 18.5 mms., or a little more than twice as great. There-
fore the quantity of aqueous vapor that would saturate the
air at the lower temperature would only half saturate it at
the higher. The air is said to be damp when it is nearly
saturated with vapor. Hence the heating of the atmos-
phere, while the quantity of aqueous vapor remains un-
altered, removes it further from the saturation point and
diminishes its dampness. When damp air from outdoors
passes through a hot-air furnace it becomes dry air, not
because it has lost any aqueous vapor, but because its
capacity to take up vapor of water has been increased by
the rise of temperature. The requisite saturation pressure






VAPORIZATION. 79

of the aqueous vapor is then much higher ; and hence the
necessity of adding more vapor of water to bring the air
of the rooms nearer to the saturation point. In winter the
humidity is usually greater than in summer, not because
the quantity of vapor present is greater, but because the
temperature is lower and the amount of vapor required to
produce saturation is less.

Humidity must therefore be expressed relatively as the
ratio of the pressure of the aqueous vapor present at a
given temperature to the saturation pressure at the same
temperature. This ratio can be measured by determining
the actual pressure of the aqueous vapor in the air and
comparing it with the maximum pressure at the same
temperature obtained from the tables. This is the method
applied by means of all dew-point instruments, called
hygrometers.

51. The Dew-Point. If a mass of air containing
aqueous vapor be gradually cooled, a temperature will at
length be reached at which the vapor will begin to con-
dense. This temperature is called the dew-point. Con-
densation of aqueous vapor may be beautifully illustrated
by passing a beam of strong light through a large glass
receiver on an air-pump in a darkened room. If the air
be only moderately moist, a single stroke of the pump will
produce a thick cloud of precipitated vapor with splendid
iridescent diffraction effects. The expansion of the air
under pressure cools it below the dew-point, and the vapor
at once condenses as a visible cloud, consisting of water in
a state of fine division. Each minute mote of dust floating
in the air serves as a nucleus of condensation and acquires
a coating of liquid.

Aitken has shown that the presence of such particles of



80 HEAT.

dust is necessary to produce condensation of moisture,
and that a dustless atmosphere may be supersaturated
without the formation of a cloud.

52. Dew. Any cool body lowers the temperature of
the air in contact with it ; and if the temperature is by this
means reduced to the dew-point, the cool body will become
covered with a film of water. Hoar frost is formed when
the temperature of deposition is below freezing.. If the
reduction of temperature to the dew-point occurs in the
interior of a mass of air, the condensation results in rain
or snow ; but if it be in contact with bodies on the earth's
surface, the condensation takes the form of dew or frost,
according as the temperature of deposition is above or below
the freezing point.

The first correct explanation of the conditions attend-
ing the formation of dew was given by Wells. He ex-
plained the free deposition of dew on cloudless nights by
the uncompensated radiation of heat from the earth toward
a clear sky. Hence objects which readily lose heat by
radiation, particularly if their specific heat be low, receive
the largest deposit of dew. On cloudy nights the clouds
absorb heat and radiate it back to the earth, or return it
by reflection, so that the ground does not cool to the same
extent as when the sky is clear.

Another condition favoring a heavy dew is a quiet atmos-
phere. When the wind blows, the air in contact with any
body is replenished so rapidly that it has not time to be
chilled to the dew-point.



53. Regnault's Hygrometer. - The Ir^grometer is an
instrument for determining the relative humidity of the
atmosphere. The form devised by Regnault is considered
superior to all others.



VAPORIZATION.



81



It consists of two thin polished silver thimbles into
which are fitted glass tubes open at both ends (Fig. 21).
The tube A is half filled with sulphuric ether, and is closed
with a stopper through which pass a thermometer t? and a
bent tube C extending down nearly to the bottom of the
silver thimble. The other tube contains only a ther-
mometer t. The two are connected
by means of the cross tube sup-
ported by the exhaust tube DE,
which is connected to an aspirator. c {

To make an observation, the
air is drawn in through C by the
aspirator and bubbles up through
the ether, causing it to evaporate
rapidly. The temperature of A
is thus lowered ; and when the
dew-point is reached, it is indicated
by a dimming of the silver tube A
in comparison with -5, which re-
mains at the temperature of the
atmosphere, as indicated by the
thermometer t. The agitation of
the ether makes it certain that
the thermometer t' indicates the
correct temperature of A. The thermometer t' is read as
soon as the dimming is apparent. The aspiration is
stopped at the same time, and the temperature is again
read at the instant when the dew disappears. The obser-
vations are made with a telescope at a distance.

The temperature given by t' is then the dew-point.
The corresponding vapor pressure for both temperatures
read on t 1 and t may then be taken from the table, and
their ratio is the relative humidity. For example, if the




Fig. 21.



82



HEAT.



dew-point were 7 and the temperature of the air 20 C.,
the corresponding saturation pressures are 7.49 and 17.39
mms. respectively. The pressure of the aqueous vapor
present would be therefore 7.49, and the maximum possible
pressure at 20 C. is 17.39. Hence the relative humidity

would be 7 _' 49 or 0.431.



17.39




Fig. 22.



Regnault's hygrometer may be
roughly imitated by using two test-
tubes (Fig. 22) and forcing air
through by means of a foot bellows.
The escaping vapor may be condensed
in a cooled flask further removed
from the apparatus than the figure
shows. 1

54. Liquefaction of Gases. Un-
der atmospheric pressure a number of
substances are known to us in both
the liquid and the gaseous states.
Water is liquid below 100 and a
vapor at higher temperatures. Alco-



hol is a liquid below 78 C. and a vapor above. Sulphuric
ether is a liquid below 35 C. and a vapor above. If we had
no means of obtaining temperatures below freezing, sulphur
dioxide would be known to us only as a gas at atmospheric
pressure, since it boils at 10 C. In the cold of Arctic
regions it would always remain liquid, since under a press-
ure of one atmosphere it is always liquid below 10 C.

The two facts that some vapors condense to liquids by
lowering their temperatures, and that the boiling point of
a liquid is raised by pressure, suggest the combined appli-

i Wright's Heat, p. 201.



VAPORIZATION. 83

cation of cold and pressure to effect the liquefaction of
substances which are ordinarily known only in the gaseous
form. When the temperature of a substance in the form
of a gas is lowered by artificial means, and its boiling
point is raised by pressure, the two temperatures approach
each other; and if the two simultaneous processes are
carried far enough to make the two temperatures coincide,
liquefaction ensues.

Faraday was the first to liquefy chlorine, carbon dioxide,
cyanogen, and ammonia. His apparatus was of the simplest
character, consisting merely of a bent tube (Fig. 23) into
which the materials to produce the
gas could be placed and hermeti-
cally sealed. The pressure employed
was the pressure of the gas itself.
The shorter limb of the tube was
surrounded with a freezing mixture
for lowering the temperature.

When crystals of hydrate of chlo- Fig 23

rine, made by passing chlorine gas

into water just above the freezing point, were heated in
the longer limb a, they decomposed and formed a greenish
liquid floating on a clear one. The lighter liquid distilled
over and condensed in the shorter arm b. When the
tube was opened, this condensed liquid was found to
be liquid chlorine.

Carbon dioxide was condensed to a liquid in a similar
way by heating sodium carbonate in the limb a. When
cyanide of mercury was placed in a and heated, cyanogen
was liberated and was liquefied in b. To liquefy ammonia
advantage was taken of the fact that chloride of silver
absorbs about 200 times its volume of this gas. Before
sealing either end of the tul>e, the longer limb was nearly




84 HEAT.

filled with dry precipitated silver chloride. Dry ammonia
was then passed through the tube, and when the air had
been expelled and the chloride was fully charged, both
ends were sealed. The end b was then placed in a freez-
ing mixture, and a Bunsen flame was carefully applied to
a. The silver chloride melts at 38, and begins to part
with its ammonia at about 115 C. As the pressure of the
liberated ammonia rose, the gas was condensed to a clear,
highly refrangible liquid in b.

The pressure at which condensation took place was
determined by introducing into the experimental tube a
smaller one, open at one end, and containing air confined
by a small piston of mercury. The pressure was indicated
by the extent to which the air in the small tube was com-
pressed. Tn every case the pressure was observed to
increase up to the point where condensation began, and
after that it remained constant so long as the condensed
liquid Avas kept at the same temperature. This pressure
was that of the saturated vapor at the given temperature.

55. Continuity of the Liquid and Gaseous States
(P., 368; M., 119; S., ISO). If water or other liquids
be heated in a closed vessel, it is well known that the
pressure of the vapor rises very rapidly with the tempera-
ture (45). Steam formed at 100 C. has a density of only
Tji\nr, while steam formed at 231 C. has a density of ^V,
the maximum density of water being the unit. Hence not
very far above this latter temperature there will be no
difference in density between the steam and the water.
At such a temperature liquefaction will not be accom-
panied by condensation, and the usual distinctions between
water and steam vanish.

Tn 1822 Cagniard de la Tour heated water and other






VAPORIZATION. 85

liquids in closed tubes and observed that they appeared to
be converted into a gas occupying only from two to four
times the volume of the liquid. When a tube, about one-
fourth full of water, was slowly heated to 360 C., the
curvature of the surface gradually diminished and finally
all demarkation between the liquid and the vapor dis-
appeared. When the gas had cooled a little a thick cloud
suddenly made its appearance, and soon the surface of
separation between the liquid and the vapor was again
visible. De la Tour found the same phenomenon with
ether, alcohol, and bisulphide of carbon, but the tempera-
ture at which the liquid disappeared was different in each
case. This temperature has since been called the critical
temperature, and the corresponding pressure is the criti-
cal pressure. The inference is easy that above its critical
temperature a gas cannot be liquefied by any pressure,
however great.

This conclusion was fully justified by the extended
investigations of Dr. Andrews * on the conditions of the
liquefaction of a gas, and especially of carbon dioxide,
for which he found a critical temperature of 30.92 C.
If the pressure on this gas, when above this temperature,
be increased to 150 atmospheres, a steady decrease of
volume will be observed, but there will be no sudden
change of volume at any point. The temperature may
then be gradually lowered until the carbon dioxide has
reached the temperature of the air. It will then be found
to be a liquid. The substance has passed from the gaseous
state to the liquid state by imperceptible gradations and
without the sudden evolution of heat. Andrews concluded
that a gas and a liquid are only widely separated forms of
the same condition of matter, and that the passage from

*Phil. Trans., 1869, Part 2, p. 575.



86 HEAT.

one to the other may be made without breach of
continuity.

The following are the critical temperatures for several
substances :

Ether 196.2 C.

Acetone 246.1

Alcohol 258.6

Carbon bisulphide 276.1

Water 365

56. Distinction between a Gas and a Vapor. - The

discovery of Andrews permits us to distinguish between a
gas and a vapor. By a vapor is meant a substance in the
gaseous state at any temperature below the critical point.
A vapor can be reduced to a liquid by pressure alone, and
can therefore exist in contact with its own liquid. A gas,
on the other hand, cannot be liquefied by pressure alone,
but only by combined pressure and cooling. A gas is
the form which any liquid assumes above its critical tem-
perature. A substance can exist partly in the liquid and
partly in the vaporous state in contact only at tempera-
tures below the critical point. Thus, below 30. 92 C.
carbon dioxide may exist as a vapor, but above that tem-
perature it cannot be reduced to the liquid state and is a
gas.

Below the critical temperature the liquid and the vapor
of any substance may be readily distinguished ; above
that temperature they have not as yet been differentiated
by any decisive characteristics. They have apparently
the same density and refrangibility, and their molecular
attractions are equalized to the extent that there is no
surface tension. At the critical temperature the latent
heat of vaporization is reduced to zero.



VAPORIZATION.



87



57. Liquefaction of Oxygen and Nitrogen. On
Dec. 24, 1877, two announcements were made to the Paris
Academy of Sciences by Cailletet and Pictet that they
had liquefied oxygen. It had previously resisted low tem-
peratures and enormous pressures because its low critical
temperature had not been reached.

Their plan of operations was to reduce the temperature
of carbon dioxide by the rapid evaporation of liquid
sulphur dioxide under reduced pressure secured by a
vacuum pump ; then to
carry the lowering of the
temperature one step fur-
ther by the similar rapid
evaporation of the cooled
liquid carbon dioxide. The
gas was carried back in
each case and again con-
densed by a compression
pump. The cycle of oper-
ations was thus complete.

Fig. 24 illustrates Pic-
tet's apparatus. The oxy-
gen was produced in the heavy iron retort L, and toward
the close of the decomposition of the potassium chlorate the
manometer indicated a pressure of 500 atmospheres in the
copper tube MN. J?~and K are filled with carbon dioxide
and C and D with sulphur dioxide. The two double-acting
pumps, A and B, are coupled together so that A exhausts
the sulphur dioxide vapor from the cylinder (7, and B
compresses it under a pressure of 3 atmospheres in the
receiver D, where it is cooled by a stream of cold water.
From D it is returned by the small pipe d to C as a liquid.
Its rapid evaporation in C lowers the temperature of the




Fig. 24.



liquid to 65 or 70 C. The purpose of this operation
is to produce and maintain a sufficient quantity of liquid
carbon dioxide in H and K. The two pumps, E and F,
perform the same offices as A and B. As fast as E ex-
hausts the vapor from H, F compresses it in K, where it
condenses under a pressure of from 4 to 7 atmospheres
on account of the low temperature produced by the evap-
oration of the liquid sulphur dioxide. The evaporation
of the carbon dioxide reduces the temperature to 130 C.
At this stage the pressure of the manometer R sinks to
320 atmospheres, indicating that the oxygen begins to
liquefy. On opening the stop-cock N the liquid issues
with great violence as a white jet, and is further cooled
by the evaporation and expansion to such an extent that
some of it may be obtained in the liquid state.

Professor Dewar has more recently improved on the
older process by the employment of nitrous oxide and
ethelene in the two successive cycles. The chamber con-
taining the oxygen is protected by a heavy felt covering
and is surrounded by two tubular circuits, one traversed
by nitrous oxide and the other by ethelene. After the
two successive reductions of temperature by the evapora-
tion of first the one liquid and then the other, the cold
oxygen under pressure is allowed to rush out through a
stop-cock at the bottom of the chamber. It is received in
a flask and becomes in part liquid by the further cooling
due to the work done in pushing back the atmosphere to
make way for itself. It is mixed with some solid carbon
dioxide from which it is freed by filtering through .an ordi-
nary filter paper. It has a delicate sky-blue color, and its
temperature when evaporating under atmospheric pressure
is 182 C. Nitrogen is liquefied by the same apparatus.
The advantage over the older method is in point of the
quantity of gas condensed.



VAPORIZATION. 89

The critical temperature of oxygen is about 112 C.,
and its critical pressure 50 atmospheres. The critical tem-
perature of nitrogen is 145 C. ; that of hydrogen is still
lower. Thus gases which are condensed only with great
difficulty have very low critical temperatures, while sub-
stances ordinarily liquid have very high ones.

PROBLEMS.

1. If a mass of aqueous vapor occupies a volume of 500 c.c.
under a pressure of 5.9 mms. at 25 C., find the pressure when the
volume has been reduced to 200 c.c. ; also the volume at which
the vapor becomes saturated at the same temperature (Appendix,
Table III.).

2. A vessel is filled with a gas at 15 C. and a pressure of 100
mms. of mercury ; find the pressure at 100 C.

3. If 25 grns. of steam at the boiling point be passed into 500
gins, of ice-cold water, to what temperature will the water be raised?
The latent heat of steam is 536.5.

4. A block of ice weighing 100 grns. is enveloped in steam at
100 C., and when the ice is all melted the water has a temperature
of 50 C. Assuming no loss of heat, how many gms. of steam have
been condensed ? The latent heat of water is 79.25.

5. How many calories are required to evaporate 100 gms. of ice-
cold water if the evaporation takes place under a pressure of 91.98
mms. ? (Appendix, Table III.).

6. How many calories are required to change 100 gms. of ice at
15 C. into steam at 150 C. ? (Art. 48).



90 HEAT.



CHAPTER VII.

TRANSMISSION OF HEAT.

58. Three Modes of Transmission. The distribu-
tion of heat takes place by three distinct modes, which
are called conduction, convection, and radiation. By the
first method heat is transmitted from particle to particle
of a body, or from one body to another in contact with it,
by a slow process, which depends upon difference of tem-
perature between contiguous parts, and upon the nature
of the conducting substance.

In convection heat is taken up by matter, and is carried
with it in its motion. Convection is the transfer of heat
from place to place by sensible masses of matter. In this
way buildings are heated by the circulation of hot water,
and heat is conveyed by hot air. It is chiefly in this way
that a uniform temperature in large masses of fluid is
established.

Heat is also distributed as radiant energy, which is
propagated by a wave-motion in the ether, and by the same
physical process as the one involved in the transmission of
light. It is by this method that heat and light are con-
veyed to us from the sun, or from a lamp or a fire. During
the transit the heat and light are both radiant energy, or
simply radiation. Ity the first two modes heat is dis-
tributed through the agency of matter ; while in the third
method the ether is the medium of propagation.



77M.VS-V/.S>70A' OF HEAT. 91

59. Conduction by Solids (T., 178; S., 268; P., 5O5 ;
G., 160). Heat should not be confused with its effects.
The melting of iron, the boiling of water, the energetic
out rush of steam under pressure, and the leaping aloft of
flames are not heat, but the results of converting the
motion of heat into mechanical motion. Heat is the
energy of molecular motion ; and when the molecules of
a solid or a liquid are agitated by the motion of heat, they
are not free to oscillate without imparting motion to other
molecules. The slow transmission of the motion of heat
from molecule to molecule of ordinary matter is con-
duction.

If one end of an iron rod
be placed in a fire, the other
end will in course of time
become hot ; the heat travels
slowly along the rod from
particle to particle, and finally
appears at the distant end.
This mode of conveyance, by
which heat is transmitted Fj 25

from the hotter to the colder

parts of a body, or from one body to another of lower
temperature, is called conduction. It tends to establish
equilibrium of temperatures.

Different substances possess this power of transmitting
heat in very different degrees. As a general rule metals
are the best conductors, while glass, wood, chalk, fire-clay,
gypsum, water, wool, and feathers are very poor conduc-
tors. If a cylinder be made one-half of wood and the
other half of brass, joined end to end, and if a piece of
thin writing-paper be wrapped tightly round it and a
flame be applied to the junction (Fig. 25), the paper round




92 TIE A T.

the wood will soon be scorched, while round the brass it
will not be injured. The metal conducts away the heat so
rapidly that the paper remains below the temperature
of ignition ; but the sluggishness of the wood in the same
process of passing on the heat permits it to accumulate in
the paper.

A Norwegian cooking-stove is a box heavily lined with
felt, into which fits a metallic dish with a cover. The dish
is covered with a felt cushion. The materials to be cooked
are placed in the dish with water, which is first boiled for
a short time. The dish is then transferred to the box, and
is enclosed in it. The conductivity of the felt and the
imprisoned air is so poor that in three hours the tempera-
ture does not fall more than 10 or 15 degrees C., and the
cooking is completed without further application of heat.

Differences in the apparent temperature of bodies are
due to their different conductivities. If pieces of metal,
marble, wood, and woollen cloth in the same room be
touched with the hand, the metal will feel cold, the marble
less so, and the woollen cloth least so of all. The sensation
of coldness is due to the rapid withdrawal of heat from
the hand by the good conducting power of the metal and
the marble. In a similar way, if the temperature of these
objects were higher than that of the hand, the metal
would feel the warmest of the series, because the rate at
which heat would flow from it to the hand would be
greatest. For this reason we handle hot objects by inter-
posing a poor conductor, like flannel, between them and
the hand ; and ice is kept from melting by wrapping in