Adolphe Ganot.

Elementary treatise on physics online

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ice at zero, and m a weight of water at f sufficient to melt the ice. The
ice is immersed in the water, and as soon as it has melted the final
temperature 6 is noted. The water, in cooling from f to fc has parted
with a quantity of heat, m(t - ' ). If x be the latent heat of the ice, it
absorbs, in liquefying, a quantity of heat, M.r; but, besides this, the water
which it forms has risen to the temperature f, and to do so has required
a quantity of heat, represented by M^. We thus get the equation
M;r + M0 = m(t - 0),

from which the value of x is deduced.

By this method, and avoiding all sources of error, MM. Desains and De
la Provostaye found that the latent heat of the liquefaction of ice is ?9'25 ;
that is, a pound of ice, in liquefying, absorbs the quantity of heat which
would be necessary to raise 79-25 pounds of water, i, or, what is the same
thing, one pound of water from zero to 79*2 5.

This method is thus essentially that of the method of mixtures ; the
same apparatus may be used, and the same precautions are required in
the two cases. In determining the latent heat of liquidity of most solids,
the different specific heats of the substance in the solid and in the liquid
state require to be taken into account. In such a case, let ;;/ be the weight
of the water in the calorimeter (the water equivalents of the calorimeter
and thermometer supposed to be included); M the weight of the substance
operated on; t the original and -, the final temperature of the calorimeter ;

-433] Latent Heat of Vapours. 371

T the original temperature of the substance ; C its melting (or freezing)
point ; C the specific heat of the substance in the solid state between the
temperature C and ( ; c its specific heat in the liquid state between the
temperatures T and ( ; and let L be the latent heat sought.

If the experiment be made on a melted substance which gives out heat
to the calorimeter and is thereby solidified (it is taken for granted that a
body gives out as much heat in solidifying as it absorbs in liquefying), it is
plain that the quantity of heat absorbed by the calorimeter, m(l /), is
made up of three parts : first, the heat lost by the substance in cooling
from its original temperature T to the solidifying point C ; secondly, the
heat given out in solidification, L ; and, thirdly, the heat it. loses in sink-
ing from its solidifying point ( to the temperature of the water of the
calorimeter. That is :


m(9 - /) =
whence, L - - (T - EX - (C -

M. Person, who has made several researches on this subject, has
obtained the following numbers for the latent heats of fusion of several
bodies :

Water . . . . 79*24 Bismuth . . . .1264

Nitrate of sodium . . 62-97 Sulphur .... 9-37

Zinc ..... 28-13 Lead ..... 5-37

Silver . . . . .21*07 Phosphorus . . 5-03

Tin ..... 14*25 D'Arcet's alloy . . . 4-50

Cadmium .... 13*66 Mercury .... 2*83

These numbers represent the number of degrees through which a pound
of water would be raised by a pound of the body in question in passing
from the liquid to the solid state ; or, what is the same thing, the number
of pounds of water that would be raised i C. by one of the bodies in

On modern views the heat expended in melting is consumed in moving
the atoms into new positions; the work, or its equivalent in heat required
for this, the potential energy they thus acquire, is strictly comparable to
the expenditure of work in the process of raising a weight. When the liquid
solidifies, it reproduces the heat which had been expended in liquefying
the solid; just as when a stone falls it produces by its impact against the
ground the heat, the equivalent x)f which in work, had been expended in
raising it, and a similar explanation applies to the latent heat of

433. Determination of tbe latent heat of vapours. Liquids, as we
have seen in passing into the state of vapour, absorb a very considerable
quantity of heat, which is termed latent heat of vaporisation. In deter-
mining the heat absorbed in liquids, it is assumed that a vapour, in
liquefying, gives out as much heat as it had absorbed in becoming con-
verted into vapour.

The method employed is essentially the same as that for determining


On Heat.


the specific heat of gases. Fig. 322 represents the apparatus used by
M. Despretz. The vapour is produced in a retort, Q where its tempera-
ture is indicated by a thermometer. It passes into a worm immersed in
cold water, where it condenses, imparting its latent heat to the condensing

water in the vessel B. The con-
densed vapour is collected in a
vessel, A, and its weight represents
the quantity of vapour which has
passed through the worm. The ther-
mometers in B give the change of

Let M be the weight of the con-
densed vapour, T its temperature
on entering the worm, which is
that of its boiling point, and x the
latent heat of vaporisation. Simi-
larly, let m be the weight of the
condensing water (comprising the

F; 22 weight of the vessel B and of the

worm SS reduced in water), let t

be the temperature of the water at the beginning, and 6 its temperature
at the end of the experiment.

It is to be observed that, at the commencement of the experiment, the
condensed vapour passes out at the temperature t, while at the conclusion
its temperature is fc> ; we may, however, assume that its mean temperature

during the experiment is ^ + '. The vapour M after condensation has

therefore parted with a quantity of heat M I T - _ J c, while the heat

disengaged in liquefaction is represented by MX. The quantity of heat
absorbed by the cold water, the worm and the vessel is m(0 /). Therefore,

_ *J>\ c = m(0 - /),

from which x is obtained. M. Despretz found that the latent heat of
aqueous vapour at 100 is 540 ; that is, a pound of water at 100 absorbs
in vaporising as much heat as would raise 540 pounds of water through
i. M. Regnault found the number 537, and MM. Favre and Silbermann

As in the case of the latent heat of -water we may say,

Steam at ioo = Water at ioo + latent heat of gaseifi cation.

In the conversion of a body from the liquid into the gaseous state, as in
the analogous process of fusion, one part of the heat is used in increasing
the temperature and another in internal work. For vaporisation the
greater portion is consumed in the internal work of overcoming the
reciprocal attraction of the particles of liquid, and in removing them to
the far greater distances apart in which they exist in the gaseous state. In

-434] Favre and Silbermami s Calorimeter. 373

addition to this there is the external work namely, that required to over-
come the external pressure, usually that of the atmosphere ; and as the
increase of volume in vaporisation is considerable, this pressure has to be
raised through a greater distance. Vaporisation may take place without
having external work to perform, as when it is effected in vacuo ; but
whether the evaporation is under a high or under a low pressure, on the
surface of a liquid or in the interior, there is always a great consumption
of heat in internal work.

434. Favre and Silbermann's calorimeter. The apparatus (fig. 323)
furnishes a very delicate means of determining the calorific capacity of
liquids, latent heats of evaporation, and the heat disengaged in chemical

The principal part is a spherical iron reservoir, A, full of mercury, of
which it holds about 50 pounds, and represents, therefore, a volume of more
than half a gallon. On the left there are two tubulures, B, in which are
fitted two sheet-iron tubes or muffles, projecting into the interior of the
bulb. Each can be fitted with a glass tube for containing the substance
experimented upon. In most cases one muffle and one glass tube are
enough ; the two are used when it is desired to compare the quantities of
heat produced in two different operations. In a third verticle tubulure, C,
there is also a muffle, which can be used for determining calorific capacities
by Regnault's method (425), in which case it is placed beneath the r of
fig. 320.

The tubulure d contains a steel piston ; a rod, turned by a handle, ;;/,
and which is provided with a screw thread, transmits a vertical motion to
the piston ; but, by a peculiar mechanism, gives it no rotatory motion. In
the last tubulure is a glass bulb, a, in which is a long capillary glass tube,
bo, divided into parts of equal capacity.

It will be seen from this description that the mercury calorimeter is
nothing more than a thermometer with a very large bulb and a capillary
stem : it is therefore extremely delicate. It differs, however, from a ther-
mometer in the fact that the divisions do not indicate the temperature of
the mercury in the bulb, but the number of thermal units imparted to it
by the substances placed in muffle.

This graduation is effected as follows : By working the piston the
mercury can be made to stop at any point of the tube, bo, at which it is
desired the graduation should commence. Having then placed in the
iron tube a small quantity of mercury, which is not afterwards changed, a
thin glass tube, e, is inserted, which is kept fixed against the buoyancy of
the mercury by a small wedge not represented in the figure. The tube
being thus adjusted, the point of a bulb tube (see fig. 324) is introduced
containing water, which is raised to the boiling point : turning the position
of the pipette, then, as represented on n', a quantity of the liquid flows
into the test tube.

The heat which is thus imparted to the mercury makes it expand ; the
column of mercury in bo is lengthened by a number of divisions, which we
shall call n. If the water poured into the test glass be weighed, and if its
temperature be taken when the column fois stationary, the product of the

374 On Heat. [434-

weight of the water into the number of degrees through which it has
fallen indicates the number of thermal units which the water gives up to
the entire apparatus (419). Dividing by this number of thermal units,

Fig. 323.

the quotient gives the number a of thermal units corresponding to a
single division of the tube bo.

In determining the specific heat of liquids, a given weight M, of the
liquid in question is raised to the temperature T, and is poured in the
tube C. Calling the specific heat of the liquid C, its final temperature f*,
and n the number of divisions by which the mercurial column bo has
advanced, we have

M<:(T - e) = na, from which c = na

M(T f)

The boards represented round the apparatus are hinged so as to form a
.box, which is lined with eider down or wadding to prevent any loss of
heat. It is closed at the top by a board, which is provided with a suitable
case, also lined, which fits over the tubulures rtfand a. A small magnifying
glass which slides along the latter enables the divisions on scale to be

435. Examples. I. What weight of ice at zero must be mixed with 9
pounds of water at 20 in order to cool it to 5?

436] Steam Engines. 375

Let M be the weight of ice necessary ; in passing from the state of ice
to that of water at zero, it will absorb 80 M thermal units ; and in order to
raise it from zero to 5, 5M thermal units will be needed. Hence the total

heat which it absorbs is 8oM + 5M ^=85M. On the other hand, the heat
given up by the water in cooling from 20 to 5 is 9 x (20-5) = 135,

85 M = 135 ; from which M = 1-588 pounds.

II. What weight of steam at 100 is necessary to raise the temperature
of 208 pounds of water from 14 to 32?

Let p be the weight of the steam. The latent heat of steam is 540, and
consequently p pounds of steam in condensing into water give up a
quantity of heat, 540^, and form/ pounds of water at 100. But the tem-
perature of the mixture is 32, and therefore / gives up a further quantity
of heat/(ioo-32) = 68/, for in this case c is unity. The 208 pounds of
water in being heated from 14 to 32 absorb 208(32 14) = 3744 units.

68^ = 3744; from which/ = 6' 1 58 pounds.



436. Steam engines. Steam engines are machines in which the elastic
force of aqueous vapour is used as motive power. In the ordinary engines
the alternate expansion and condensation of steam imparts to a piston an
alternating rectilinear motion, which is changed into a circular motion by
means of various mechanical arrangements.

Every steam engine consists essentially of two distinct parts : the ap-
paratus in which the vapour is produced, and the engine proper. We
shall first describe the former.


On Heat.


437. Steam boiler. The boiler is the apparatus in which steam is
generated. Fig. 325 represents a side view, and fig. 326 a cross section
of a cylindrical boiler, such as are used for fixed engines ; those of loco-
motives and of steam vessels are very different.

It is a long wrought-iron cylinder, PQ, with curved ends, beneath
which there are two smaller cylinders, BB, of the same material, and

Fig. 325-

communicating with the boiler by two tubes. Only one of these cylinders
is represented in the figure. They are called heaters, and are quite full
of water, while the boiler is only about half full.

In order to multiply the heating surface, and utilise all the heat carried
off by the products of combustion, the latter are made to circulate through
brick conduits which surround the sides of the heaters and of the boiler.
These conduits, which are called flues, divide the furnace into two
horizontal compartments, FF and BCD (fig. 326). The upper compart-
ment is moreover divided into three distinct flues, D, C, D, by two vertical
divisions, which are not represented in the drawing, and which correspond
to the two sides of the boiler. The flame and the products of com-
bustion, which first sweep below the heaters from back to front, return in
the opposite direction by the central flues C ; then, dividing, they pass
by the lateral flues into the chimney K, where they are lost in the at-


Steam Engines.


Explanation of Figures 325 and 326.

E. Float of the safety whistle, s.
FF. Furnace.

F. Float, to show the level of the water in the boiler. It consists of a
rectangular piece of stone partially immersed in water, as seen through
the space which is represented as left open. The stone, which is sus-
pended at one end of a lever, is kept poised by the loss of weight which
it sustains by immersion in the water, and

by a weight, a, at the other end of the
lever. As long as the water is at the
desired height, the lever which sustains the
float remains horizontal ; but it sinks
when there is too little water, and rises
in the contrary direction when there is
too much. Guided by these indications,
the stoker can regulate the supply of

K. Chimney, which has usually a
great height so as to increase the draught.

S. Safety valve, described under
Papin's digester (347).

T. Man-hole, an aperture by which
the boiler can be repaired and cleansed
This is self-closing, and consists of a
cover fitting against the inside edges. It-
is kept in position by a screw, which also Fig 326
presses it strongly against the sides. Thus

the greater the internal pressure, the more firmly is the cover pressed
against the sides, and the more completely does it close.

a. Counterpoise of the float.

m. Tube which leads the steam to the tube c of the valve chest.

n. Tube for the admission of feed water for the boiler.

s. Safety whistle so called because it gives a whistle when there is
not enough water in the boiler ; a circumstance which might produce an
accident. As long as the level of the water is not too low in the boiler,
the steam does not pass into the whistle ; but if the level sinks below a
certain point, a small float, E, which closes the bottom of the whistle
sinks, and the steam escapes ; in so doing it grazes against the edge of a
thin metal plate, which it sets in vibration, and produces a sharp and
loud sound. This steam whistle is the sound frequently heard upon
railways ; it is used as a signal in locomotives.

438. Double action, or Watt's engine. In the double acting steam
engine, the steam acts alternately above and below the piston. It is also
known as Waffs engine, from its illustrious inventor.

We shall first give a general idea of this engine, and shall then describe
each part separately. On the left of the fig. 327 is the cylinder which


On Heat.


receives the steam from the boiler. A 'part of its side is represented
as being left open, and a piston, P, can be seen which is moved alter-
nately up and down by the pressure of the steam above or below the
piston. By the piston rod A this motion is transmitted to a huge iron
lever, L, called the beam, which is supported by four iron columns. The

Fig. 327.

beam transmits its motion to a connecting rod, I, working on a crank,
K, to which it imparts a continuous rotatory motion. The crank is fixed
to a horizontal shaft, which turns with it, and, by means of wheels or
endless bands, this shaft sets in motion various machines, such as
spinning frames, saw mills, lathes, etc.

On the left of the cylinder is a valve chest, where, by a mechanism
which will presently be described, the steam passes alternately above
and below the piston. Now, after its action on either face of the piston,
it must disappear, for otherwise a pressure would be exerted in two
opposite directions, and the piston would remain at rest. To effect this
the steam, after it has acted on one side of the piston, passes into a vessel,
O, called the condenser, into which cold water is injected. It is almost
completely condensed there, and consequently the pressure ceases in

-438] Double-acting Steam Engine. 3/9

that part of the cylinder which is in communication with the condenser,
and as there is now pressure on only one face of the piston, it either rises
or sinks.

The use of the condenser depends upon Watt's law of vapours (337),
that when two vessels communicating with each other, and containing
saturated vapour, are at different temperatures, the tension is the same
in both vessels, and is that corresponding to the temperature of the colder

The injected water is rapidly heated by the condensation of the steam,
and must be constantly renewed. This is effected by means of two
pumps ; one M, is called the air pump, and pumps, from the condenser,
the heated water which it contains, and also the air which was dis-
solved in the water of the boiler, and which passes with the steam into
the cylinder and condenser ; the other, R, is called the cold water
pump, and forces cold water from a well, or from a river, into the con-

A third pump, O, which is called the feed pump, utilises the heated
water by forcing it from the condenser into the boiler.

Double acting steam engine.

A. Piston rod connected with a parallel motion, and serving to trans-
mit to the beam the upward and downward motion of the piston.

B. Rod fixed to the cylinder, or elsewhere, and supporting the guiding
arm or radius rod, C.

C. Double guiding arm directing the parallel motion.

DDDE. Rods forming at the end of the beam a parallel motion, to
which is fixed the piston rod, and the object of which is to guide the
motion of this rod in a straight line.

F. Rod of the air pump, which removes from the condenser the air and
heated water which it contains.

G. Rod of the feed pump, which forces into the boiler through the
tube S the heated water pumped from the condenser.

H. Rod of the cold water pump, which supplies the cold water neces-
sary for condensation.

I. Connecting rod, which transmits the motion of the beam to the

K. Crank, which imparts the motion of the rod to the horizontal

L. Seam, which moves on an axle in its middle, and transmits the
motion of the piston to the connecting rod I.

M. Cylinder of the air pump, in connection with the condenser O.

N. Reservoir for the heated water pumped by the air pump from the

O. Condenser into which cold water is injected to condense the steam
after it has acted on the piston.

P. Metallic piston, moving in a cast-iron cylinder ; this piston receives
the direct pressure of the steam, and transmits the motion to all parts of
the machine,..

380 On Heat. [438-

Q. Feeding force pump, which sends the water into the boiler.

R. Cold water pump.

S. Pipe by which the hot water from the feed pump passes into the

T. Pipe by which cold water from the reservoir of the pump, R, passes
into the condenser.

U. Pipe by which the steam from the cylinder passes into the con-
denser after acting on the piston.

V. Large iron wheel, called the fly wheel, which, by its inertia, serves
to regulate the motion, especially when the piston is at the top or bottom
of its course, and the crank K at its dead points.

Y. Bent lever which imparts the motion of the eccentric e to the slide
valve b.

Z. Eccentric rod.

a. Aperture which communicates both with the upper and lower part
'of the cylinder, according to the position of the slide valve, and by which
steam passes into the condenser through the tube U.

b. Rod transmitting motion to the slide valve, by which steam is alter-
nately admitted above and below the piston. This will be described in
greater detail in the next article.

c. Aperture by which steam reaches the valve chest.

d. Stuffing box, in which the piston rod works without giving exit to
the steam.

e. Eccentric, fixed to the horizontal shaft, and rotating in a collar, to
which the rod Z is attached.

m. Rod which connects the rod of the slide valve b to the bent lever
Y, and to the eccentric.

The lower part of the figure does not exactly represent the usual
arrangement of the pumps. The drawing has been modified in order
more clearly to show how these parts work, and their connection with
each other.

439. Distribution of the steam. Eccentric. Fig. 328 represents
the details of the valve chest or arrangement for the distribution of
steam. The steam from the boiler passes by a pipe, c, into a cast-iron
box on the side of the cylinder. In the sides of the cylinder there are
three openings or ports, u, n, and a, of which u communicates by an
internal conduit with the upper part of the cylinder, and n with the
lower part. A slide, /, works over these three orifices. It is fixed to a
vertical rod, b, which is jointed at m to a larger rod, d, and receives an
upward and downward motion from the bent lever yoS, attached to the
eccentric rod. When the slide is at the top of its course, as shown in
the figure, the steam passes through n into the lower part of the cylinder,
while the steam cannot pass through the orifice u, for it is covered by the

But the vapour which is above the piston passes through // and through
a into the hole r, from which it enters the condenser. The, piston is then
only pressed upwards, and therefore ascends.

When the slide is at the bottom of its course, the steam enters the


Single Acting Steam Engine.


cylinder by the aperture u, and passes from the lower part of the cylinder
into the condenser by n and a. The piston consequently descends, and
this motion goes on for each displacement of the slide.

The upward and down-ward motion of the slide is effected by means
of the eccentric. This is a circular piece, E, fixed to the horizontal shaft.

Fig. 328.

A, but in such a manner that its centre does not coincide with the axis
of this shaft. The eccentric works with gentle friction in a collar, C, to
which the rod ZZ is fixed. The collar, without rotating, follows the
motion of the eccentric, and receives an alternating motion in a horizontal
direction, which it communicates to the lever Soy, and from thence to the

^ / 440. Single acting: engine. In a single acting engine the steam only
\/acts on the upper face of the piston ; a counterpoise fixed to the other
/ end of the beam makes the piston rise. These engines were first con-,
structed by Watt for pumping water from mines, and are still used for
this purpose in Cornwall, and also for the supply of water to towns. They
are preferred for these purposes from their simplicity, but for other pur-
poses they have been superseded by the double acting engine.

Fig. 329 represents a section. The beam BB is of wood, with wooden
segments at each end, to which chains are attached. One of these
chains is connected with the piston, and the other with the pump.
On the right of the cylinder A is a valve chest, C, into which steam

Online LibraryAdolphe GanotElementary treatise on physics → online text (page 39 of 94)