which signifies that the loss of acetylene by leakage under the same conditions of pressure, &c., will be only 0.663 times that of the loss of coal-gas. In practice, however, the pressures at which the gases are usually sent through mains are not identical, being greater in the case of acetylene than in that of coal-gas. Formula (1) therefore requires correction whenever the pressures are different, and calling the pressure at which the acetylene exists in the main p, and the corresponding pressure of the coal-gas p', the relative losses by leakage are--
(2) (_v_/_v'_) = (0.40 / 0.91)^(1/2) x (_p_/_p'_)^(1/2)
_v_ = 0.663_v'_ x (_p_/_p'_)^(1/2)
It will be evident that whenever the value of the fraction (_p_/_p'_)^(1/2), is less than 1.5, i.e., whenever the pressure of the acetylene does not exceed double that of the coal-gas present in pipes of given porosity or unsoundness, the loss of acetylene will be less than that of coal-gas. This is important, especially in the case of large village acetylene installations, where after a time it would be impossible to avoid some imperfect joints, fractured pipes, &c., throughout the extensive distributing mains. The same loss of gas by leakage would represent a far higher pecuniary value with acetylene than with coal-gas, because the former must always be more costly per unit of volume than the latter. Hence it is important to recognise that the rate of leakage, coeteris paribus, is less with acetylene, and it is also important to observe the economical advantage, at least in terms of gas or calcium carbide, of sending the acetylene into the mains at as low a pressure as is compatible with the length of those mains and the character of the consumers' burners. As follows from what will be said in Chapter VII., a high initial pressure makes for economy in the prime cost of, and in the expense of laying, the mains, by enabling the diameter of those mains to be diminished; but the purchase and erection of the distributing system are capital expenses, while a constant expenditure upon carbide to meet loss by leakage falls upon revenue.
The critical temperature of acetylene, i.e., the temperature below which an abrupt change from the gaseous to the liquid state takes place if the pressure is sufficiently high, is 37° C., and the critical pressure, i.e., the pressure under which that change takes place at that temperature, is nearly 68 atmospheres. Below the critical temperature, a lower pressure than this effects liquefaction of the gas, i.e., at 13.5° C. a pressure of 32.77 atmospheres, at 0° C., 21.53 atmospheres (Ansdell, cf. Chapter XI.). These data are of comparatively little practical importance, owing to the fact that, as explained in Chapter XI., liquefied acetylene cannot be safely utilised.
The mean coefficient of expansion of gaseous acetylene between 0° C. and 100° C., is, under constant pressure, 0.003738; under constant volume, 0.003724. This means that, if the pressure is constant, 0.003738 represents the increase in volume of a given mass of gaseous acetylene when its temperature is raised one degree (C.), divided by the volume of the same mass at 0° C. The coefficients of expansion of air are: under constant pressure, 0.003671; under constant volume, 0.003665; and those of the simple gases (nitrogen, hydrogen, oxygen) are very nearly the same. Strictly speaking the table given in Chapter XIV., for facilitating the correction of the volume of gas measured over water, is not quite correct for acetylene, owing to the difference in the coefficients of expansion of acetylene and the simple gases for which the table was drawn up, but practically no appreciable error can ensue from its use. It is, however, for the correction of volumes of gases measured at different temperatures to one (normal) temperature, and, broadly, for determining the change of volume which a given mass of the gas will undergo with change of temperature, that the coefficient of expansion of a gas becomes an important factor industrially.
Ansdell has found the density of liquid acetylene to range from 0.460 at -7° C. to 0.364 at +35.8° C., being 0.451 at 0° C. Taking the volume of the liquid at -7° as unity, it becomes 1.264 at 35.8", and thence Ansdell infers that the mean coefficient of expansion per degree is 0.00489° for the total range of pressure." Assuming that the liquid was under the same pressure at the two temperatures, the coefficient of expansion per degree Centigrade would be 0.00605, which agrees more nearly with the figure 0.007 which is quoted, by Fouché As mentioned before, data referring to liquid (i.e., liquefied) acetylene are of no practical importance, because the substance is too dangerous to use. They are, however, interesting in so far as they indicate the differences in properties between acetylene converted into the liquid state by great pressure, and acetylene dissolved in acetone under less pressure; which differences make the solution fit for employment. It may be observed that as the solution of acetylene in acetone is a liquid, the acetylene must exist therein as a liquid; it is, in fact, liquid acetylene in a state of dilution, the diluent being an exothermic and comparatively stable body. The specific heat of acetylene is given by M. A. Morel at 0.310, though he has not stated by whom the value was determined. For the purpose of a calculation in Chapter III. the specific heat at constant pressure was assumed to be 0.25, which, in the absence of precise information, appears somewhat more probable as an approximation to the truth. The ratio (k or C_p/C_v ) of the specific heat at constant pressure to that at constant volume has been found by Maneuvrier and Fournier to be 1.26; but they did not measure the specific heat itself. [Footnote: The ratio 1.26 k or (C_p/C_v) has been given in many text-books as the value of the specific heat of acetylene, whereas this value should obviously be only about one-fourth or one-fifth of 1.26.
By employing the ordinary gas laws it is possible approximately to calculate the specific heat of acetylene from Maneuvrier and Fournier's ratio. Taking the molecular weight of acetylene as 26, we have
26 C_p - 26 C_v = 2 cal.,
and