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50 HEAT.

perature of 32 before receiving the liquid, or, if not, the vessel
should be raised to the temperature of the liquid, and introduced
empty into the calorimeter, so as to ascertain the quantity of ice
it would dissolve empty in falling from the temperature of the
liquid to 32. "When the vessel is introduced, filled with the
liquid, the quantity of ice liquefied will be the sum of the
quantities liquefied by the vessel and by the liquid which it
contains. But the quantity liquefied by the vessel being pre-
viously ascertained and subtracted, the remainder will be the
quantity dissolved by the liquid contained in the vessel.

1410. Application of the calorimeter to determine specific
heat. If equal weights of the same body, placed in the
apparatus at different temperatures, cause quantities of water
to be deposited in R which are proportional to the temperatures
through which they fall, it will follow that within such limits
the specific heat is uniform. And, if the quantity of water
deposited in R be divided by the number of degrees through
which the temperature of the body placed in the calorimeter has
fallen, the quantity of ice dissolved by the heat corresponding
to one degree will be found. This in fine being divided by the
weight of the body placed in the calorimeter expressed in
pounds, the weight of ice dissolved by the heat which would
raise 1 Ib. of the body one degree will be determined.

To express this in arithmetical symbols :

Let w=the weight of the body placed in the calorimeter,
T=its temperature,
w'=the weight of water deposited in R while the body is

reduced from T to 32,
x weight of ice dissolved by the heat which would raise

1 Ib. of the body one degree.

We shall then have

r = the weight of ice dissolved by the heat which would
(T 32)

raise w one degree ;

and therefore,

* = w x (T - 32)'

1411. Specific heat of water uniform. In applying this
method of experimenting to water, it is found that between the



CALORIMETRY. 51

freezing and boiling points its specific heat is sensibly uniform,
and that the heat necessary to raise 1 Ib. of water one degree is
that which would dissolve the 142'65th part of a Ib. of ice, so

that in the case of water we have x= .. , ...

142-OO

1412. Method of ascertaining the. specific heat of other bodies

by the calorimeter Let the specific heat of the body w be

expressed by s, that of water being the unit. Hence we shall
have,

w' 1

s ; i



142-65 '
and consequently,

_ 1 42-65 xw'

l ~ wx (T-32) ;
which gives the following

RULE.

Multiply the weight of ice dissolved by 142-65, and multiply
the weight of the body ivhich dissolves the ice by the number of
degrees of temperature it loses, and divide the former product
by the latter. The quotient will be the specific heat of the body.

1413. Method of equalization of temperatures. When two
bodies at different temperatures are mixed, or brought into
juxtaposition in such a manner that that which has the higher
* r ' jierature may transfer to that which has the lower tempe-
rature such a portion of its heat that the temperatures may be
equalized, the relation between the specific heats may be deter-
mined, provided no chemical action nor any change of state
be produced by the contact or mixture.

Let the weights of the two bodies be w and w', their tempe-
ratures T and T', and their specific heats s and s' ; and let t be
their common temperature, after the thermometric equilibrium
has been established.

It will therefore follow, that the temperature lost by w will
be T t, and the temperature gained by w' will be t T'. But
from what has been already explained, the quantity of heat lost
by w will be expressed by s x w x (T ), and the quantity of heat
gained by w' will be expressed by s' x w' x (t T'). But since
the quantity of heat lost by w is imparted to w', these two
quantities must be equal, and consequently we must have
w x s x (T f)=w' x s' x (t T') ;



52 HEAT.

and from this we infer that



that is to say, the specific heats of the two bodies are in the
inverse proportion of the products of their weights, and the
temperatures which they gain and lose.

This method of determining the relation between the specific
heats is applicable either to two liquids, or to a solid and a
liquid, provided that when they are mixed or brought together
no chemical action takes place between them, and provided the
solid be not liquefied. But if such action ensue, it is generally
attended with the development or absorption of sensible heat,
by which the common temperature would be rendered either
higher or lower than that which would result from mere ad-
mixture.

1414. Application of this method. If one of the bodies w'
be water, we shall have s'=l, and therefore



~WX(T-0 '

from which follows the

RULE.

Let the weight of a heated body immersed in water be multi-
plied by the temperature it loses, and let the weight of the water
be multiplied by the temperature it gains. The quotient ob-
tained by dividing the latter product by the former will be the
specific heat of the body.

The method of determining the specific heat of gaseous
bodies by means of the water calorimeter of Count Rumford, is
similar in principle to the preceding method. This apparatus
consists of a worm carried through a vessel of water in a
manner similar to the worm of a still. The gas bping pre-
viously weighed, prepared, and dried, is raised to 212 by passing
it through a similar worm placed in a vessel of boiling water.
It is then passed through the worm of the calorimeter and raises
the temperature of the water, its own temperature falling.
The elevation of the temperature of the water and the fall of
the temperature of the gas being observed, data are obtained
from which the specific heat of the gas is calculated.



CALORIMETRY. 53

1415. Method of cooling. Equal and similar volumes of two
bodies raised to the same temperature and allowed to cool
under precisely similar circumstances, are assumed to lose equal
quantities of heat per minute. In order to ensure the exact
fulfilment of these conditions, a multitude of precautions are
necessary which cannot be detailed here. The result, however,
is that by observing the intervals of time which are necessary
for equal volumes of the two bodies to fall one degree, we
obtain the ratio of the quantities of heat which they lose, and
this being determined for equal volumes, the quantities for
equal weights may be inferred from the specific gravities of the
bodies, and the specific heats will thus be obtained.

This was applied with considerable success by Dulong and
Petit, and also by Regnault.

1416. Results of calorimetric researches. Having thus ex-
plained the principal methods by which the specific heat of
bodies has been experimentally ascertained, we shall now state
the most important results which have been attained in this de-
partment of the physics of heat.

1417. Relation of specific heat to density. The specific
heat of bodies diminishes as their density is increased, and vice
versa. This explains the fact that mechanical compression will,
without any addition of heat, raise the temperature. If metal be
hammered it becomes hot, and it is even affirmed that iron has
been rendered incandescent in this manner.

1418. The Jire-syringe. The syringe in which compressed
air is made to inflame amadou acts on this principle. The air
compressed under the syringe acquires a greatly diminished
specific heat, and, consequently, although it has received no
heat from any external source, the same heat which before
compression only gave it the common temperature of the sur-
rounding medium, gives it, after compression, a temperature high
enough to produce the ignition of a highly inflammable sub-
stance like amadou.

1419. Specific heat of gases and vapours increase as their
density is diminished. In general, no practicable force can pre-
vent the dilatation of solids and liquids when their temperature
is elevated. This, however, is not the case with gases and
vapours, which, when heat is imparted to them, may either be
permitted to expand under a given pressure, like solids and
liquids ; or may be confined to a given volume, which they will

u 3



54 HEAT.

continue to fill in consequence of their elasticity (706), however
their temperature may be lowered, and which they will not ex-
ceed, however their temperature may be raised.

In this case, the heat imparted or abstracted is manifested by
a corresponding change of pressure of the gas or vapour instead
of dilatation or contraction.

1420. Specific heat under constant pressure and constant
volume. By the specific heat of a gas or vapour is to be under-
stood its specific heat when subject to a constant pressure, that
is to say, when it is susceptible, like solids and liquids, of dila-
tation and contraction.

Specific heat is, however, a term sometimes, though not so
properly, applied to the heat necessary to raise the gas or vapour
one degree when confined within a given volume. This last is
sometimes also called, for distinction, the relative heat.

1421. Greater under a constant pressure. The specific heat
of a gas or vapour under a given pressure is greater than under
a given volume. This difference is explained by the fact, that,
in expanding, the temperature falls, and therefore that, when
confined to a given volume, less heat is sufficient to produce a
given elevation of temperature than when confined under a
given pressure, where the dilatation diminishing the density
absorbs a portion of the heat.

For atmospheric air, oxygen and hydrogen, the ratio of the
specific heat under a given pressure is to the specific heat in a
given volume as 1-421 to 1. For carbonic acid it is 1-338 ; for
carbonic oxide, 1'428 ; for nitrous oxide, 1-343 ; and for ole-
fiant gas, 1-240.

1422. Example of the expansion of high-pressure steam.
The expansion of high-pressure steam escaping from the safety
valve forms a remarkable instance that the same quantities of
heat may give very different temperatures to a body, in different
states of density. Steam produced under a pressure of 35 at-
mospheres has the temperature of 419. When such steam
escapes into the atmosphere, it undergoes a prodigious expansion
without losing heat, and suffers a considerable fall in tem-
perature.

1423. Low temperature of superior strata of atmosphere.
The circumstance that rarefied air has an increased capacity for
heat, will explain the very low temperatures which are known
to exist in the higher regions of the atmosphere.



CALORIMETRY. 5-5

This effect becomes extremely sensible when we ascend to
any considerable height, as has been manifest in ascending high
mountains and in balloons. Upon these occasions, the cold has
sometimes become so intense, that mercury in the thermometer
has been frozen. In strata so elevated that the permanent
temperature of the air is below 32, water cannot continue in
the liquid state ; it exists there only in the form of ice or snow,
nnd we accordingly find eternal snow deposited upon those
parts of high mountains which exceed this limit of temperature.

1424. Line of perpetual snow. The level of that stratum of
air which by its rarefaction reduces the temperature to 32, is
called the line of perpetual snow, and its position in different
parts of the earth varies, the height increasing generally in ap-
proaching the equator, and falling towards the poles. The
various conditions which affect the position of this line in
different parts of the earth will be explained in a subsequent
Book. t

1425. Liquefaction of gases. The elevation of temperature
produced by the compression of gases, has supplied means of re-
ducing some of them to the liquid form.

Gases may be considered as vapours raised from liquids,
which have received, after their separation from the liquid
which produced them, a large additional supply of heat. It is
to the effects of this surplus heat that their permanent main-
tenance in the gaseous state must be ascribed. If, by any
means, they can be deprived of this surplus heat, so that no heat
shall be left in them except that which they received in the
process of vaporization, any further loss of heat would necessarily
cause them to return, in more or less quantity, to the liquid
form. But if the specific heat be so great, that notwithstanding
all the heat transmitted to the gas after taking the vaporous
form, it still has attained only the common temperature of the
atmosphere, it is clear that it can only be restored to the liquid
form, either by reducing its temperature to an immense extent,
by the application of freezing mixtures, or by first raising its
temperature by high degrees of mechanical compression, and
then allowing it to fall to the temperature of surrounding objects,
or, in fine, by combining both these methods. Thus atmo-
spheric air, at the common temperature of 50, being compressed
into a diminished volume, in the proportion of 10,000 to 3, its
temperature would be raised through an extent of 13,500 of



56 HEAT.

heat, according to Leslie's experiment. This heat being im-
mediately abstracted by the surrounding objects, its temperature
would fall to that of the medium in which it is placed. Thus,
without the application of a freezing mixture, or other means
of cooling, an immense abstraction of heat may be effected ; and
this may be continued so long as a mechanical force adequate
to the further compression of the gas could be exerted. Freez-
ing mixtures may then be applied to the further reduction of
temperature.

1426. Development and absorption of heat by chemical com-
bination. When different liquids are mixed, or when solids are
dissolved in liquids, chemical phenomena are generally developed,
in consequence of which the specific heat of the mixture differs
from that which it would have if the constituents were merely
interfused without any change in their thermal qualities. Like
the other qualities of the constituents, their specific heats are
in this case modified ; and the compound is generally found to
have a less specific heat, than that which would be inferred
from the specific heats of its components. When the chemical
combination is thus, as it is almost universally, attended by a
diminution in the specific heat of the compound as compared
with that which would be computed from the specific heats of
its components, it is also found that the volume of the mixture
is less than the sum of the volumes of its compounds, and that
the temperature of the mixture is higher than the common tem-
perature of the liquids mixed.

Thus, for example, if a pint of water and a pint of ,'ulphuric
acid, both of the temperature of 57, be mixed, the mixture will
rise to the temperature of 212, and the volume of the mixture
will be considerably less than a quart. The chemical attraction
of the particles, therefore, in this and like cases, produces con-
densation, and, in fact, the same effect ensues as would be pro-
duced by compression. The elevation of temperature may be
explained in exactly the same manner, as when bodies are
compressed by mechanical force. The specific heat of the
mixture being less than that which is due to its component
parts, and the absolute quantity of heat contained in it not
being diminished, that quantity will raise it to a much higher
temperature than that which it would have had, if the specific
heats remained unaltered.

1427. Specific heats of simple gases equal under the same



CALORIMETRY. 57

pressure. Under equal pressures the simple gases have the
same specific heat. This uniformity, however, does not prevail
among the compound gases, as will appear by the tables of specific
heat of the gases.

1428. Formula for the variation of specific heat consequent
on change of pressure. The law according to which the same
gas varies its specific heat with the change of pressure or
density is, according to Poisson, expressed by the formula



where P expresses the pressure in inches of mercury, s' the
specific heat under the mean pressure of 30 inches, and k the
constant number, which expresses the ratio of the specific heat
under a given pressure to the specific heat under a given
volume, which, in the case of common air and the simple gases,
is 1-421, as has been already explained, and as will appear by
the tables.

1429. Relation between specific heat and atomic weight.
On comparing together the numbers expressing the specific heat
of the simple bodies, with those which express their atomic
weights or chemical equivalents, Dulong and Petit observed that
the one increased in almost the exact proportion in which the
other diminished, so that by multiplying them together, a
product very nearly constant was obtained.

From this it would follow, upon the atomic hypothesis, that
the specific heats of the atoms of all the simple bodies are equal.
For in equal weights, the number of constituent atoms will be
great in proportion as the individual weights of these atoms are
small. The number of atoms, therefore, in equal weights, being
inversely proportional to the weights of the atoms, and the
specific heats being also inversely proportional to the weights
of the atoms, it follows that the specific heats of equal weights
are in the proportion of the number of atoms contained in those
weights, and that, consequently, the specific heats of the com-
ponent atoms must be equal.

This, therefore, is a quality in which the atoms of all simple
bodies, however they may differ in other respects, agree, that
their temperatures are equally affected by the same quantity of
heat.

That this law is not rigorously exact, however, is proved by



.38



HEAT.



the fact, that the specific heat of the same body is different at
different temperatures and in different states.

It has resulted from the researches of Regnault, that the re-
lation between the specific heat and atomic weights, observed
by Dulong and Petit in the simple bodies, also prevails among
compound bodies ; and that, in general, in all compound bodies
of the same atomic composition and having similar chemical
constituents, the specific heat is in the inverse ratio of the
atomic weight : this law, however, being subject to the same
qualification which has been already mentioned for the simple
bodies.

The numerical results which manifest the prevalence of this
law will be seen in the tables of specific heat.

1430. Tables of specific heat. The following series of tables
supply, in a summary form, the results of the most recent ex-
perimental researches respecting the specific heat of bodies,
and the relation between these, and their chemical constitution.



Table of specific Heats of simple and compound Bodies deter-
mined by M. Regnault.



Names of Substances.


Specific Heats.


Atomic Weights
(Oijgen=100.)


Products.


Preliminary Results.
Brass - - - - -


0-09391






Glass


0-19763






Water - - - - -


1-0080






Turpentine, spirit of -


0-42593






Simple bodies, pure.
Iron - - - - -


0-11379


339-21


38-597


Zinc - - - - -


0-0<-555


403-23


38526




0-09515


395-70


37-849


Cadmium -


0-05669


696-77


39502


Silver


0-057H1


675-80


38-527


Arsenic -


0-08140


470-04


38*261


Lead


0-03140


1294-50


40*647


Bismuth - - - -


0-03084


1330-37


45-0:t4


Antimony - - - -
Tin, Indian - ...


0-05077
0-05623


806-45
735-29


40 !I44
41-345


Nickel - - -


0-10863


369-68


40-160


Cobalt -


0-10696


368-99


39-468


Platinum, rolled ...


003243
0*05927


1233-50
665*90


39-993
39*468


Gold


0-H3244


1243-01


40328


Sulphur -


(i-20259


201-17


40-754


Selenium -


00837


494-58


4 1 -403


Tellurium ....


0-05155


801 76


41-549


Iodine .....


0-05412


7811*75


42-703


Mercury ....


0-03332


1265-82


42-149


Simple bodies, less pure.
Uranium .....


0-06190


677-84


41-960


Tungsten -


0-03636


1I8H-00


43002


Molybdenum .....

Nickel, carburetted -


0*07*218
011192


598-52
369-68


43-163
41376



CALORIMETRY.



Names of Substances.


Specific Heats.


Atomic Weights.
(Oi>gen=lUO.)


Products.


Nickel, more carburetted -


0-11631


3R9-68


42-999


Cobalt, carburetted ....


0-11714


368-99


43-217


Steel (Hausmann) - . . .


0-11848


339-21


40-172


pure metal -


12728


339-21




Cast iron (white) -


0-12983


339-21


44-0 8


Carbon - -


0-24111


15288


36-873


Phosphorus .....


0-1887


196-14


37-124


Iridium (impure) ....


0-03(i83


1233-50


45-4-28


Manganese, very carburetted


0-14411


345-89


49-848


Metallic alloys.
1 Lead 1 tin - -


0-04073


1014*9


41-34


2 -


0-r4506


9*1-7


41-53


1 antimony ....


0-03880


1050-5


40-76


Bismuth. 1 tin - ...


004' 00


103-2-8


41-31


2


0-04504


933-7


4i-OS


., 2 1 antimony


0-04621


901-8


41-67


2 1 2 zinc
Lead, 2 ,, 1 bismuth ...


0-OS657
0-C4476


735-6
1 023-9


41-61

45-83


2 2 -


0-0608-2


1088-2


66-00


Mercury, 1 -


007294


1000-5


72-97


2


Of'591


912-1


60-12


Head -


0-03827


1280-1


48-90


Oxides, RO.








Protoxide of lead in powder ...


0-05118


1394-5


71-34


cast ...


05089


1394-5


70-94


Oxide of mercury -


0-05179


1365-8


70-74


Protoxide of manganese ...


0-15701


445-9


70-01


Oxide of copper -
of nickel -


0-142H1
0- 1 6234


495-7


70-39
76-21


,, calcined at the forge


15885


469-6


74-60


Mean ....






72- (!3


Magnesia .....


024394


25R-4


63-03


Oxide of zinc


0-12480


503-2


62-77


Oxides, R2 O 3 .








Peroxide of iron (iron oligist)


0-16695


978-4


163-35


slightly calcined -


0- 1 75(i9


978-4


171-90


doubly calcined -


0-17167


978-4


168-00


strongly calcined -








twice


0-1H8I4


978-4


164-44


Acid, arsenious ....


0-1-^786


1240-1


158-56


Oxide of chromium - - - -


0-17960


100.-V6


180-01


of bismuth -


0-06053


2960-7


179-22


of antimony -


0-09009


1912-9


172-34


Mean ....


m




169-73


Alumina ( Corimion) - -


V 1 9762 "


642-4


1-26-87


(sapphire) ....


0-21732


642-4


139-61


Oxides, RO 2 .








Acid, stannic -


o-ro326


935-3


87-23


titanic (artificial)


0-17164


50H-7


86-45


(rutile)


0-17032


503-7


85-79


antimouious ....


0-09535


1006-5


8C-49
95-92


Oxides, RO 3 .








Acid, tungstic
molybdic ....


0-07983
0-13240


1483-2
898-5


118-38
118-96


silicic


19132


577-5


Hi-18


boracic .....


023743


436-0


103-52


Oxides.








Oxide of magnetic iron ...


0-16780


1417-6


237-87


Sulphurels, RS.








Proto-siilphun-t of iron ...
Sulphuret of nickel -


0-13570
1*813


540-4
570-8


73-33
73-15



D 6



CO



HEAT.



Names of Substances.


Specific Heats.


Atomic Weights.
(Onj-Ken = 100.)


Products.


Sulphuret of cobalt -
of zinc ....
of lead - ...
,, of mercury ...
Proto-sulphuret of tin


0-12512
0-12303
0-050*6
0-OM17
0-08365


570-0
604-4
'.495-6
1467-0
936-5


71-34
74-35
76-00
75-06
78-34


Mean -


-


-


74-51


Sulphureti, R 2 S' 2 .
Sulphuret of antimony
., of bismuth ...


0-08403
0-06002


2210-4
3261-2


186-21
195-90








191'OG


Sulphurets, RS 2 .
Bi-sulphuret of iron -
of tin -
Sulphuret of molybdenum -


f- 13009
0-11^32
0-12334


74 1-6
1137-7
1001-0


96-45
136-66
123-46


Mean ...


-


.


129-56


Sulphurets, R 2 S.
Sulphuret of copper -
of silver ....


0-12118
0-07460


992-0
1553-0


120-21
115-86


Sulphurets.
Pyrites, magnetic - ...


C-16023






Chhrates, R^Cl 2 .
Chlorate of sodium -
of potassium ...
of mercury - - - -
,, of copper -
of silver ....


0-21401
0-17295
0-05205
0-I3S27
0-09109


733-5

5974-2
1234-0
1794-2


156-97
161-19
154-80
156-83
163-42


Mean ....




-


158-64


Chlorates, RCR
Chlorate of barium -

of calcium ....
of magnesium ...
of lead -
Pro-chlorate of mercury ...
,, of zinc - - - -
of tin -


0-08957
CI1990
164 20
0-19460
0-06641
0-06889
0-136I8
0-10:61


1299-5
989-9
698-6
601-0
1737-1
1708-4
845-8
1177-9


116-44

118-70
114-72
1 18-54
115-35
117-68
115-2!
119-59


Mean ....
Chlorate of manganese ...


0-14255


78S-5 "


117-03
112-51


Chlorides volatile, RC1 4 .
Chloride of tin -
of titanium -



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