Hugh Longbourne Callendar

“ In common language a vapour is a gaseous or elastic fluid, which emanates or evaporates from the surface of a solid or liquid at temperatures below its boiling-point. A volatile liquid or solid is one which evaporates rapidly at ordinary temperatures. ”

“ The values of the coefficients given by Bertrand, for instance, in the formula for steam, correspond to the values S=·576 and L=573 at 0° C, which are impossible, and the values of p given by his formula (e.g. 763 mm. at 100° C.) do not agree sufficiently with experiment to be of much practical value. The true application of the formula is to low pressures, at which it is very accurate. The close agreement found under these conditions is a very strong confirmation of the correctness of the assumption that a vapour at low pressures does really behave as an ideal gas of constant specific heat. ”

“ The saturation-pressure invariably increases rapidly with rise of temperature, according to a regular law which has been the subject of many elaborate investigations. When the vapour-pressure of a liquid becomes equal to the external pressure, bubbles of vapour are freely formed in the interior of the liquid by the familiar process of boiling or ebullition. ”

“ But in order to deduce the values of c by the Joule-Thomson method, it is necessary to assume an empirical formula, and the type c=c0 (θ0/θ) n is chosen as being the simplest. The justification of this assumption lies in the fact that the values of c found in this manner/ when substituted in equation (25) for the saturation-pressure, give correct results for p within the probable limits of error of Regnault’s experiments. ”

“ In all cases, if the temperature is given, there is a corresponding equilibrium or saturation pressure of the vapour, and vice versa, in accordance with Dalton's law. It was shown, however, by Cagniard de la Tour (Ann. Chirn. Phys., 1822, 1823) that the temperature and pressure of the liquid could not be raised indefinitely in this manner. By heating liquids in strong glass bulbs with manometers attached, he found that at a certain temperature the meniscus or curved surface separating the liquid from the vapour disappeared, and the bulb became filled with an apparently uniform substance. ”

“ This relation gives a linear formula for the variation of the total heat, a result which agrees in form with that found by Regnault for steam, and implies that the coefficient of t in his formula should be equal to the specific heat S of steam. Rankine's equation follows directly from the first law of thermodynamics, and may be proved as follows: The heat absorbed in any transformation is the change of intrinsic energy plus the external work done. To find the total heat H of a vapour, we have H=K-{-p (v-b) , where the intrinsic energy E is measured from the selected zero θ0 of total heat. ”

“ It is probable that osmotic pressure is not really of the same nature as gas-pressure, but depends on equilibrium of vapour-pressure. The vapour-molecules of the solvent are free to pass through the semi-permeable membrane, and will continue to condense in the solution until the hydrostatic pressure is so raised as to produce equality of vapour-pressure. ”

“ Since the specific heat of the liquid increases rapidly at high temperatures, while dH/dO diminishes, it is clear that the latent heat must diminish more and more rapidly as the critical point, is approached. ”

“ This relation cannot be directly integrated, so as to obtain the equation for the saturation-pressure, unless L and v−w are known as functions of θ. Since it is much easier to measure p than either L or v, the relation has generally been employed for deducing either L or v from observations of p. For instance, it is usual to calculate the specific volumes of saturated steam by assuming Regnault's formulae for p and L. The values so found are necessarily erroneous if formula (10) for the total heat is wrong. ”

“ It is obvious, however, that the assumption = constant is not sufficiently accurate in many cases. The rate of variation of the latent heat at low pressures is equal to , where is the specific heat of the liquid. Under these conditions both and may be regarded as approximately constant, so that is a linear function of the temperature. ”

“ Many attempts have been made to construct formulae representing the deviations of vapours from the ideal state up to the critical point. One of the most complete is that proposed by R. J. E. Clausius, which may be written
but such formulae are much too complicated to be of any practical use, and are too empirical in their nature to permit of the direct physical interpretation of the constants they contain. ”

“ Assuming dH/dθ=0·305 for saturated steam, he found that S was nearly independent of the pressure at constant temperature, but that it varied with the temperature from 0·387 at 100° C. to 0·665 at 160° C. Writing Q for the Joule-Thomson “cooling effect,” dθ/dp, or the slope BC/AC of the line of constant total heat, he found that Q was nearly independent of the pressure at constant temperature, a result which agrees with that of Joule and Thomson for air and CO2 ”