If by the help of this equation we eliminate the constant The question is now whether, for any given temperature t, the quantity() or. its reciprocal (), which expresses 0 0 the specific weight of the steam at temperature to, can be determined with sufficient certainty. The ordinary values given for the specific weight of steam refer not to saturated but to highly superheated steam. They agree very well, as is known, with the theoretical values which may be deduced from the well-known law as to the relation between the volume of a compound gas, and those of the gases which compose it. Thus e.g. Gay-Lussac found for the specific weight of steam the experimental value 0-6235; whilst the theoretical value obtained by assuming two units of hydrogen and one unit of oxygen to form, by combining, 2 units of steam, is This value of the specific weight we cannot in general apply to saturated steam, since the table in the last section, d (ps), indicates too large a which gives the values of dt divergence from the law of Mariotte and Gay-Lussac. the other hand the table shews that the divergences are smaller as the temperature is lower; hence, the error will be insignificant if we assume that at freezing temperature saturated steam follows exactly the law of Mariotte and GayLussac, and accordingly take 0-622 as the specific heat at that temperature. In strict accuracy we must go yet further and put the temperature, at which the specific weight of saturated steam has its theoretical value, still lower than freezing point. But, as it would be somewhat questionable to use equation (37), which is only empirical, at such low temperatures, we shall content ourselves with the above assumption. Thus giving to to the value 0, and at the same time putting (~)= = 0·622 and therefore (5) tain from equation (43) 1 = 0 0.622 we ob (44). From this equation, using the values for m, n, and k given in (37a), the quantity, and therefore the quantity s, may be calculated for each temperature. The foregoing equation may be thrown into a more convenient form by putting and by giving to the constants M, N, and a the following values, calculated from those of m, n, and k: M=1663; N=0·05527; a=1007164...(45a). To give some idea of the working of this formula, we give in the following table certain values of, and of its re ciprocal which for the sake of brevity we shall denote by the letter d, already used to designate specific weight. The result that saturated steam diverges, so widely as the above formulæ and tables indicate, from the law of Mariotte and Gay-Lussac, which had been previously applied to it without reserve, met at first, as mentioned in another place, with the strongest opposition, even from very competent judges. The author believes however that it is now generally accepted as correct. It has also received an experimental verification by the experiments of Fairbairn and Tate*, published in 1860. The results of their experiments are compared in the following table, on the one hand with the results previously obtained by assuming the specific weight to be 0.622 at all temperatures, and on the other hand with the values calculated by equation (45). This table shews that the values given by experiment agree much better with those calculated by the author's equation than with the values previously obtained; and that the ex * Proc. Royal Soc. 1850, and Phil. Mag., Series Iv. Vol. xxi. perimental values are in general yet further removed from those previously obtained than are the values derived from the author's formula. § 10. Determination of the Mechanical Equivalent of Heat from the behaviour of Saturated Steam. Since we have determined the absolute values of s, without assuming the mechanical equivalent of heat to be known, we may now apply these values, by means of equation (17), to determine the mechanical equivalent itself. For this purpose we may give that equation the following form: The coefficient of so in this equation may be calculated for different temperatures by means of Regnault's tables. For example, to calculate its values for 100°, we have given for dp dt the value 27.20, the pressure being reckoned in millimetres of mercury. To reduce this to the measure here employed, viz. kilogrammes per square metre, we must multiply by the weight of a column of mercury at temperature 0°, 1 square metre in area and 1 millimetre in height, that is by the weight of 1 cubic decimetre of mercury at 0°. As Regnault gives this weight at 13:596 kilogrammes, the multiplication gives us the number 369 8. The values of (a+t) and of r at 100° are 373 and 536·5 respectively. Hence we have We have now to determine the quantity (so), or, since σ is known, the quantity s for steam at 100°. The method formerly pursued, i.e. to use for saturated steam the same specific weight, which for superheated steam had been found by experiment or deduced theoretically from the condensation of water, led to the result, that a kilogram of steam at 100° should have a volume of 1·696 cubic metres. From the foregoing however it appears that this value must be considerably too large, and must therefore give too large a value for the mechanical equivalent of heat. Taking the specific heat as calculated by equation (45), which for 100° is 0·645, we obtain for s the value 1638. Applying this value of s we get from equation (47) This method therefore gives for the mechanical equivalent of heat a value which agrees in a very satisfactory manner with the value found by Joule from the friction of water, and with that deduced in Chapter II. from the behaviour of gases; both of which are about equal to 424. This agreement may serve as a verification of the author's theory as to the density of saturated steam. § 11. Complete Differential Equation for Q in the case of a body composed both of liquid and vapour. In § 1 of this chapter we expressed the two first differential coefficients of Q, for a body consisting both of liquid and vapour, by equations (7) and (8), as follows: Hence we may form the complete differential equation of the first order for Q, as follows: dQ= pdm+m (H-C) + MC dT........(49). [ ·Mc] a dQ= = pdm + [m (d/ - - f) T +MC dT. .(50). |