and that heat could not be a material substance, but must be
something of the nature of motion.” Unfortunately Rumford’s
argument was not quite conclusive. The supporters of the
caloric theory appear, whether consciously or unconsciously,
to have used the phrase “capacity for heat” in two entirely
distinct senses without any clear definition of the difference.
The phrase “capacity for heat” might very naturally denote
the total quantity of heat contained in a body, which we have
no means of measuring, but it was generally used to signify the
quantity of heat required to raise the temperature of a body
one degree, which is quite a different thing, and has no necessary
relation to the total heat. In proving that the powder and the
solid metal required the same quantity of heat to raise the
temperature of equal masses of either one degree, Rumford
did not prove that they contained equal quantities of heat,
which was the real point at issue in this instance. The metal
tin actually changes into powder below a certain temperature,
and in so doing evolves a measurable quantity of heat. A
mixture of the gases oxygen and hydrogen, in the proportions
in which they combine to form water, evolves when burnt
sufficient heat to raise more than thirty times its weight of water
from the freezing to the boiling point; and the mixture of gases
may, in this sense, be said to contain so much more heat than
the water, although its capacity for heat in the ordinary sense
is only about half that of the water produced. To complete
the refutation of the calorists’ explanation of the heat produced
by friction, it would have been necessary for Rumford to show
that the powder when reconverted into the same state as the
solid metal did not absorb a quantity of heat equivalent to that
evolved in the grinding; in other words that the heat produced
by friction was not simply that due to the change of state of
the metal from solid to powder.
Shortly afterwards, in 1799, Davy[1] described an experiment in which he melted ice by rubbing two blocks together. This experiment afforded a very direct refutation of the calorists’ view, because it was a well-known fact that ice required to have a quantity of heat added to it to convert it into water, so that the water produced by the friction contained more heat than the ice. In stating as the conclusion to be drawn from this experiment that “friction consequently does not diminish the capacity of bodies for heat,” Davy apparently uses the phrase capacity for heat in the sense of total heat contained in a body, because in a later section of the same essay he definitely gives the phrase this meaning, and uses the term “capability of temperature” to denote what we now term capacity for heat.
The delay in the overthrow of the caloric theory, and in the acceptance of the view that heat is a mode of motion, was no doubt partly due to some fundamental confusion of ideas in the use of the term “capacity for heat” and similar phrases. A still greater obstacle lay in the comparative vagueness of the motion or vibration theory. Davy speaks of heat as being “repulsive motion,” and distinguishes it from light, which is “projective motion”; though heat is certainly not a substance—according to Davy in the essay under discussion—and may not even be treated as an imponderable fluid, light as certainly is a material substance, and is capable of forming chemical compounds with ordinary matter, such as oxygen gas, which is not a simple substance, but a compound, termed phosoxygen, of light and oxygen. Accepting the conclusions of Davy and Rumford that heat is not a material substance but a mode of motion, there still remains the question, what definite conception is to be attached to a quantity of heat? What do we mean by a quantity of vibratory motion, how is the quantity of motion to be estimated, and why should it remain invariable in many transformations? The idea that heat was a “mode of motion” was applicable as a qualitative explanation of many of the effects of heat, but it lacked the quantitative precision of a scientific statement, and could not be applied to the calculation and prediction of definite results. The state of science at the time of Rumford’s and Davy’s experiments did not admit of a more exact generalization. The way was paved in the first instance by a more complete study of the laws of gases, to which Laplace, Dalton, Gay-Lussac, Dulong and many others contributed both on the experimental and theoretical side. Although the development proceeded simultaneously along many parallel lines, it is interesting and instructive to take the investigation of the properties of gases, and to endeavour to trace the steps by which the true theory was finally attained.
10. Thermal Properties of Gases.—The most characteristic property of a gaseous or elastic fluid, namely, the elasticity, or resistance to compression, was first investigated scientifically by Robert Boyle (1662), who showed that the pressure p of a given mass of gas varied inversely as the volume v, provided that the temperature remained constant. This is generally expressed by the formula pv = C, where C is a constant for any given temperature, and v is taken to represent the specific volume, or the volume of unit mass, of the gas at the given pressure and temperature. Boyle was well aware of the effect of heat in expanding a gas, but he was unable to investigate this properly as no thermometric scale had been defined at that date. According to Boyle’s law, when a mass of gas is compressed by a small amount at constant temperature, the percentage increase of pressure is equal to the percentage diminution of volume (if the compression is v/100, the increase of pressure is very nearly p/100). Adopting this law, Newton showed, by a most ingenious piece of reasoning (Principia, ii., sect. 8), that the velocity of sound in air should be equal to the velocity acquired by a body falling under gravity through a distance equal to half the height of the atmosphere, considered as being of uniform density equal to that at the surface of the earth. This gave the result 918 ft. per sec. (280 metres per sec.) for the velocity at the freezing point. Newton was aware that the actual velocity of sound was somewhat greater than this, but supposed that the difference might be due in some way to the size of the air particles, of which no account could be taken in the calculation. The first accurate measurement of the velocity of sound by the French Académie des Sciences in 1738 gave the value 332 metres per sec. as the velocity at 0° C. The true explanation of the discrepancy was not discovered till nearly 100 years later.
The law of expansion of gases with change of temperature was investigated by Dalton and Gay-Lussac (1802), who found that the volume of a gas under constant pressure increased by 1/267th part of its volume at 0° C. for each 1° C. rise in temperature. This value was generally assumed in all calculations for nearly 50 years. More exact researches, especially those of Regnault, at a later date, showed that the law was very nearly correct for all permanent gases, but that the value of the coefficient should be 1173rd. According to this law the volume of a gas at any temperature t° C. should be proportional to 273 + t, i.e. to the temperature reckoned from a zero 273° below that of the Centigrade scale, which was called the absolute zero of the gas thermometer. If T = 273 + t, denotes the temperature measured from this zero, the law of expansion of a gas may be combined with Boyle’s law in the simple formula
| pv = RT | (1) |
which is generally taken as the expression of the gaseous laws. If equal volumes of different gases are taken at the same temperature and pressure, it follows that the constant R is the same for all gases. If equal masses are taken, the value of the constant R for different gases varies inversely as the molecular weight or as the density relative to hydrogen.
Dalton also investigated the laws of vapours, and of mixtures of gases and vapours. He found that condensible vapours approximately followed Boyle’s law when compressed, until the condensation pressure was reached, at which the vapour liquefied without further increase of pressure. He found that when a liquid was introduced into a closed space, and allowed to evaporate until the space was saturated with the vapour and evaporation ceased, the increase of pressure in the space was equal to the condensation pressure of the vapour, and did not depend on the volume of the space or the presence of any other gas or vapour
- ↑ In an essay on “Heat, Light, and Combinations of Light,” republished in Sir H. Davy’s Collected Works, ii. (London, 1836).
