/ P V 517
C = *359 ( ) ^' 23} f r carbonic acid,
/ t> \' 501
C = -0497 ( ) / 1<233 for olefiant gas.
Example. Let it be required to find the whole amount of
heat due to convection and radiation united which leaves a
square foot of surface of dry chalk in one minute, the tem-
perature being 5oC, while that of the surrounding enclosure
is 1 4C ; the enclosure being filled with hydrogen of the
pressure of 760 millimetres. By reference to Art. 235
we find the whole expression for loss of heat in this case
V= R + C = 8-613 a'(^- 1)4-^288 233 ;
or, since = 14, f + = 50, a = 1-0077, we nave
K = 8-613 X i-oo77 14 (i-oo77 36 - i) + -i288(^)' 38 36 1 - 233
It ought however to be borne in mind that all these for-
mulae are to a great extent empirical, representing the ex-
periments made, and useful in so far as they enable us to
calculate approximately the loss of heat due to radiation
and convection in any case in which all the particulars are
288. In order to arrive at a complete knpwledge of the
laws which regulate the distribution of heat through space,
we must be able to measure the amount of heat which a
body absorbs, or parts with, when its temperature is changed
to a given extent, and also when it changes its state. To
do this it is necessary to adopt some unit of heat, and we
shall use in this work as our thermal unit the quantity of
heat necessary to raise one kilogramme of water from o
In the present chapter we shall treat of the amount of
heat which a body absorbs, or gives out, when its temperature
288 SPECIFIC HEAT.
rises or falls to a given extent. This is called specific heat,
and we define the specific heat of a given substance to be
the quantity of heat necessary to raise one kilogramme of
the substance iC in terms of that necessary to raise one
kilogramme of ice-cold water iC reckoned as unity. Thus,
if a kilogramme of any substance required as much heat to
raise it from 100 to ioiC as would raise three-tenths of
a kilogramme of water from o to iC, then we should say
that the specific heat of this substance at this temperature
METHODS OF MEASURING SPECIFIC HEAT.
289. I. Method by mixture. Three different methods
of measuring the specific heat of substances have been pro-
posed. They are known as (i) the method by mixture,
(2) the method by fusing ice, and (3) the method by cooling.
In the first of these, or the method of mixtures, the ex-
periment is made in the following manner. Take a known
weight of the substance of which the specific heat is desired,
and heat it to a known temperature, then mix it rapidly with
a known weight of water at an inferior temperature (say at
o c C), and notice the temperature of the mixture. If we are
at liberty to suppose that none of the heat has been otherwise
disposed of, we have at once all the means of determining
the specific heat of the substance in question. Thus, let
x denote the unknown specific heat of the substance, and
let m be its mass, and / its temperature ; also let M be the
mass of water at oC with which it is mixed, and let be
the temperature of the mixture. Then the quantity of heat
lost by the substance will be mx(t &), while that gained by
the water will be MO. Since the whole quantity of heat
remains the same, the one of these expressions must equal
the other. Hence mx(t 0) = MQ, from which x may be
SPECIFIC HEAT. 289
easily found. As an example of this method, supposing
that 3 kilogrs. of mercury at iooC have been mixed with
i kilogr. of ice-cold water, and that the temperature of the
mixture is 9C, what is the specific heat of mercury ? Here
we have m = 3, = 9, / = 100 9 = 91 : hence
3^x91=9; .-. * = .-?- = . 03 3 nearly:
so that the specific heat of mercury is only ^th of that of
In this process it is assumed that the specific heat of
mercury is constant between 100 and 9C, or rather it is
the mean specific heat between this range that is determined
by the experiment.
A serious objection. to this method consists in. the un-
avoidable loss of heat which is likewise incapable of accurate
measurement. For in the example given above the heat of
the mercury is not all confined to the mixture, but part of it
is spent :
1. In warming the vessel which contains the mixture,
2. In warming the agitator and thermometer,
3. In dissipation from the sides of the vessel ;
and unless we have the means of estimating exactly the loss
of heat from all these sources we shall not be able to obtain
a good result.
290. II. Method by fusion of ice. The second
method of measuring specific heat is by the fusion of ice.
In this method we have an inner vessel A (Fig. 68) which
contains the substance on which the experiment is made.
This vessel is placed in the interior of a larger vessel B, the
space between them being filled with melting ice. The
vessel B) again, is in the interior of a still larger vessel C,
the space between them being, again, filled as before with
Since the exterior of the vessel B is at the temperature
o c C, we may imagine that the ice in this vessel will only
melt through means of the hot substance which is placed
in A. If therefore we know not
only the weight but the tempera-
ture of the substance in A, and
also the quantity of ice which has
been converted into water in con-
sequence of this hot substance
parting with its heat, we have the
means of finding the specific heat
of the substance in A. A stop-
cock connected with B serves to
carry off the water formed through
melting of the ice, and hence, by
weighing this water, we know ap-
proximately the quantity of ice melted in B, and if we know
the quantity of heat necessary to convert ice into water we
can find the heat given out by the
substance in A. The chief objection
to this instrument is that we cannot
measure accurately the amount of
water produced, since a certain amount
remains adhering to the ice.
Professor R. Bunsen (Phil. Mag.
March, 1871) has devised a modifi-
cation of the ice calorimeter for the
purpose of measuring the specific
-0 heat of substances which can only be
procured in small quantities.
It consists of an inner glass vessel
a fused into a larger cylindrical ves-
sel b as in Fig. 69. From the vessel b
proceeds the tube c, to the termination of which the iron
collar d is fastened. The inner vessel a is filled from a
SPECIFIC HEAT. 2$I
to p., as also the outer vessel b from /3 to X, with water from
which all the air has been removed by boiling ; the re-
mainder of the vessel b up to the level y is filled with boiled
Before using the instrument it is necessary to obtain a
cylinder of ice in the vessel b so as completely to surround
the vessel a, and for this purpose the whole apparatus is
placed in a large vessel and surrounded with pure snow.
When this operation is complete the scale-tube s, fitted
accurately into the cork with fine sealing-wax, is then passed
through the mercury in the collar d and made fast in the
mouth of the tube c so that it (the scale-tube) becomes filled
Our object being to ascertain the amount of heat which
a small body gives up when cooled from its ordinary tem-
perature to oC, let this body be dropped into the water
contained in the vessel a, which is then closed with a cork
at 6 to prevent change of air. It is clear that all the heat
which this body gives up is employed to melt ice. For the
weight of the body is so small compared with that of the
ice-cold water into which it is plunged, that the temperature
of the latter never reaches 4C, the heated water will there-
fore be specifically heavier than that above it and will remain
at the bottom. Thus none of its heat will be carried away
by convection, and we may neglect that carried away by the
conducting power of the water above it, this being very
small. In fine, all the heat will go to melt ice in the vessel
b ; this melting will again cause a diminution of volume, and
this in its turn will be indicated by the motion of the
mercurial column in the scale tube s.
As the experimental difficulties in using this calorimeter
are considerable, the writer of this volume has suggested a
modification of it which appears to answer well. In this the
inner vessel a is still retained and used with water, but instead
292 SPECIFIC HEAT.
of being fused into an outer vessel that is filled with ice
it is fused into a large thermometer bulb after the manner
of Favre and Silbermann, so that while the inside of a
contains water its outside is in contact with the mercury
of the thermometer. The whole bulb is then enclosed in a
copper envelope which surrounds without touching it, and
this envelope is kept at the temperature of oC by being
surrounded by melting ice. The temperature of the large
thermometer is recorded on a very open scale, so that a very
small rise can easily be measured.
The experiment is conducted in the following manner :
The substance the specific heat of which we wish to deter-
mine is dropped as before into the water of the tube a, which
is ice-cold to begin with. The heat is then rapidly com-
municated first to the water and from it to the mercury of
the thermometer which surrounds the tube, and the rise of
this thermometer is recorded on the stem.
A slight correction has to be made for the heat which is
given out during the progress of the experiment by the (now)
heated thermometer to the copper sphere which surrounds it,
but this is easily obtained, and thus the instrument gives us
a ready and accurate method of determining the relative
specific heats of such substances as can only be procured in
- small quantity.
291. III. Method by cooling. The third means of
estimating specific heat is by the method of cooling. If
two substances be exposed to the same cooling influence
it is manifest that the one which has the smallest specific
heat will cool fastest. Thus, suppose that we have two
thermometers with blackened bulbs of precisely the same
size, the one being filled with mercury and the other with
water ; further, let these instruments both cool from a com-
mon temperature under precisely the same circumstances.
It will be found that the mercurial thermometer will cool
SPECIFIC HEAT. 393
more than twice as fast as the water one. For although
the weight of the mercury is more than thirteen times that
of the water, yet the specific heat of mercury is only one
thirtieth of that of water, and hence, while the same amount
of heat leaves both instruments in one minute, yet this heat
will produce on the water thermometer only thirteen thirtieths
of that diminution of temperature which it produces on the
mercurial one. The idea of measuring the specific heat of
bodies first originated with Black, who was also the dis-
coverer of latent heat ; and many numerous and important
experiments have since been made on this subject by a
number of observers.
SPECIFIC HEAT OF SOLIDS.
292. Some of the latest experiments in this branch of
the subject have been made by Regnault, who used the
method of cooling. In these experiments the substance was
reduced to a fine powder and enclosed along with a delicate
thermometer in a vessel which was exposed to the cooling
influence. Although every precaution was used, the result
of this process was not satisfactory ; one objection was that
the heat was not conducted sufficiently fast from the powder
to the sides of the vessel which contained it. Another is
that the specific heat of the same substance in the solid
state depends to some extent on the mechanical treatment
which it has received. Regnault has also investigated the
specific heat of various solid substances by the method of
293. Rise of specific heat of solids with tempera-
ture. It was first shewn by the experiments of Dulong and
Petit that the specific heat of a solid is greater at a high tem-
perature than at a low one. The following table embodies
the results of these experiments.
Mean Specific Heat.
Between oand IOOC. Between o and 300 C.
It will be noticed that for all the substances in the above
table the specific heat is greater at high temperatures, with
the exception of platinum, for which the specific heat
remains the same between the limits of the experiment.
Probably the reason of this is that the highest temperature
of experiment was very much below the melting-point of this
metal, and it has been found by Regnault that the variation
of specific heat with temperature is much more rapid when
the substance approaches its melting-point. M. Pouillet, by
means of the method of mixtures, has obtained the specific
heat of platinum at still higher temperatures. His results
are as follows
Mean Specific Heat of Platinum.
Between o and iooC 0-0335
o , 300 0-0343
o . 500 0-0352
o 700 0-0360
o . looo 0-0373
O , I2OO 0-0382
The constancy of the specific heat of platinum renders
this metal serviceable as a pyrometer, and a piece of pla-
tinum may be used for estimating the temperature of a
furnace. When it has attained the temperature of the
furnace it is taken out and plunged into a known quantity
of ice-cold water. By means of the rise of temperature
SPECIFIC HEAT. 295
produced it is easy to calculate approximately the tempera-
ture of the platinum, and hence of the furnace.
294. Circumstances which influence the specific
heat of solids. The specific heat of a solid has been
found to depend on the mode of aggregation of its mole-
cules and on the nature of the mechanical action to which
it has been subjected. In general whatever augments the
density diminishes the specific heat, and whatever diminishes the
density augments the specific heat ; and it is perhaps owing to
expansion that the specific heat of a body increases with its
temperature. The more carbon is divided the greater is its
specific heat. The following table exhibits the specific heat,
in their different stages of aggregation, of carbonate of lime,
sulphur, and carbon.
Carbonate of Lime.
Iceland spar 0-2085
White marble 0-2158
Recently melted 0-1844
Melted less than 2 months 0-1803
Melted less than 2 years ... 0-1764
Natural crystals 0-1776
Animal charcoal 0-2608
Wood charcoal 0-2415
Coke o. 2008
SPECIFIC HEAT OF LIQUIDS.
295. Regnault has determined the specific heat of a num-
ber of liquids by the following method. The liquid under
experiment is contained in a reservoir R (Fig. 70) which is
immersed in the middle of a bath, and by agitating the water
of this bath a definite temperature is communicated to the
2^6 SPECIFIC HEAT.
liquid in R. By opening the stop-cock at r, and bringing to
bear at the same time an atmospheric pressure upon the
liquid, it is driven through the tubes at r into a vessel con-
tained in the calorimeter C. Having entered the calori-
meter, and having disposed of its surplus heat, the tempera-
ture of the water of the calorimeter is observed by means of
the thermometer T 7 , and this affords the means of estimating
the specific heat of the liquid. The calorimeter is defended
by means of a screen P from the heat of R.
Generally speaking a substance when liquid has a greater
specific heat than when solid, a fact which was discovered by
Irvine. Thus the specific heat of ice is only one-half that of
296. Variation with temperature of the specific
heat of liquids. The specific heat of liquids increases in
SPECIFIC HEAT. 397
general with the temperature, and at a rate exceeding that of
solids. Thus bromine has between 6 and ioC the mean
specific heat 0-10513, while between 13 and 58 it has the
mean specific heat 0*11294.
The specific heat of water at various temperatures has
been especially studied by Regnault, who has obtained the
Mean Specific Heat of Water.
From o to 4OC 1-0013
o , 80 1-0035
1 20 1-0067
200 I- 0160
230 ... 1.0204
It was formerly thought that the specific heat of water
was greater than that of any other liquid, but from a recent
research of Messrs. Duprd and Page (Trans. R. S. 1869)
there is reason to think that the specific heat of a mixture of
alcohol and water in which there is 20 per cent, of alcohol is
as high as 105, that of water being 100.
SPECIFIC HEAT OF GASES.
297. In this branch of our subject there are two sets of
determinations to be made. We must find, in the first place,
the specific heat of gas under constant pressure ; and in the
second place, the specific heat of gas under constant volume.
In a future part of this work it will be shewn how these two
are connected together.
Many experimentalists have been engaged in these deter-
minations. Before the time of Regnault one of the most
exact researches was that of Delaroche and Berard, which
298 SPECIFIC HEAT.
was crowned by the Academy of Sciences. These experi-
mentalists produced a current of gas of uniform velocity
which was first heated to iooC by being passed through
tubes enveloped in boiling water, and was then cooled in its
passage through a calorimeter, to which it abandoned its
excess of heat. It ought likewise to be mentioned that
Joule made an accurate determination of the specific heat
After many years' trials Regnault finally adopted a modi-
fication of the method of Delaroche and Berard.
His apparatus was constructed so as to fulfil the following
1. To obtain a gaseous current of constant velocity, which
velocity might also be regulated at will.
2. By means of a bath to give a determinate temperature
to the gaseous current.
3. To construct a calorimeter in which the gas would
entirely dispose of its excess of heat.
In order to obtain a gaseous current of constant velocity
the following arrangement was adopted. The gas, after being
dried and purified, was forced into a large reservoir R
(Fig. 71) of 35 litres capacity. A manometer attached to
the reservoir at m indicated the pressure of the gas. The
reservoir was surrounded by a large mass of water agitated
by means of an annular plate a. The gas would thus take the
temperature of this water this temperature being denoted
by the thermometer T. Suppose, in the first place, that the
reservoir is filled with gas, and that the stop-cock / is shut.
Opening now the stop-cock at / this gas will escape through
the tube shewn in the figure, passing spirally through an
arrangement at S, by which a certain high temperature is
given to it, then parting with this excess of heat to a calori-
meter at C, and ultimately escaping (say) into the air. At
the end of the experiment suppose that the stop-cock at / is
once more shut. Knowing the pressure and temperature of
the gas in R at the beginning and end of the experiment, if
the chemical constitution of the gas be known, and if it obeys
Boyle's law, the weight of gas passed through the calorimeter
will be known. If Boyle's law do not hold, it is yet possible,
though with more difficulty, to ascertain the weight of gas
used, but into the details of the method of doing so we will
not enter. The weight of gas consumed during the experi-
ment is thus known, but in order to obtain a definite result
something more is necessary ; the velocity of the current of
gas through the apparatus ought to be constant throughout
the experiment. It is clear that without some special ar-
rangement this current will not be constant, because the
excess of pressure in the reservoir R will be greater at the
commencement of the experiment than at the end of it, when
a quantity of this gas has been used. There is, however, an
arrangement r by means of which the opening through which
300 SPECIFIC HEAT.
the gas escapes from the reservoir into the apparatus may
be enlarged or contracted at pleasure. A manometer to the
right of r, having one of its limbs open to the atmosphere,
indicates the excess of pressure of the gas in the tube, and if
the screw at r is turned in such a manner that throughout
the whole experiment the excess of pressure denoted by this
manometer is constant, then will the velocity of the current
be constant also. Agitators a, a" are attached to the source
of heat arid the calorimeter, and it was ascertained by Reg-
nault that the gas in passing through S really attained the
temperature (indicated by T') of the fluid (oil) in S. It was
further ascertained that the gas lost none, or extremely little,
of its heat in passing between S and the calorimeter, and
that in passing through the vessel of the calorimeter, which
was arranged in a spiral form so as to present as much sur-
face as possible to the surrounding water, the gas issued with
a temperature the same as that of the water of the calori-
meter indicated by the thermometer T". Finally it was
ascertained that the pressure of the gas was as nearly as
possible the same before its entrance into the calorimeter and
after its exit therefrom.
To simplify matters we may suppose the pressure of the
outward air constant throughout the experiment.
In this experiment therefore a known weight of gas
having a known temperature (that of the bath) was made
to pass with a constant velocity and at a constant pressure
through the calorimeter, where it was reduced in tem-
perature to that of the water of the calorimeter. The
specific heat of a gas under constant pressure was thus
^29 8. Results of Regnault's experiments. The fol-
lowing facts were determined by these experiments :
i . The specific heat of a given weight of a gas which is
approximately perfect^ and which therefore follows the gaseous
laws previously indicated (Art. 148), does not vary with the
temperature of the gas.
2 . The specific heat of a GIVEN WEIGHT of such a gas does not
vary with the pressure or density of the gas, and hence the
specific heat of a GIVEN VOLUME of such a gas varies as its
3. The specific heats of equal volumes of the simple andincon-
densible gases are equal, but this equality does not hold for gases
easily condensed, such as chlorine and bromine. It holds, how-
ever, for compound gases which are formed without condensation,
such as hydrochloric acid and nitric oxide.
4. These laws do not hold for condensible gases the specific
heat of carbonic acid gas, for instance, increases with the tem-
299. The following table is derived from Regnault's
Specific Heat of Gases and Vapours under Constant Pressure.
Gas or Vapour.
Bisulphide of carbon
Chloride of arsenic . .
Gas or Vapour.
Chloride of silicon
Perchloride of titanium . .
Perchloride of tin
Alcohol . . .
Chloride of ethyl
Bromide of ethyl . .
Sulphide of ethyl
Cyanide of ethyl
Oil of turpentine
Terchloride of phosphorus .
In the first column of this table the common volume is
that occupied by one kilogramme of air, while in the second
column the common weight is one kilogramme. Also the
specific heat of one kilogramme of liquid water is taken
as the unit, so that the heat required to raise a kilogramme
of atmospheric air one degree under constant pressure is