Thomson (Lord Kelvin) from Regnault's tables of the properties of steam, assuming the gaseous laws, did not vary exactly as J/T.
If we also assume that they are constant with respect to temperature (which does not necessarily follow from the characteristic equation, but is generally assumed, and appears from Regnault's experiments to be approximately the case for simple gases), the expressions for the change of energy or total heat from 00 to 0 may be written E - Eo = s(0 - 0 0), F - Fo = S(0-00).
Soc. Ed., 1854) to represent Regnault's experiments on the deviations of CO 2 from.
The method differed from Regnault's inasmuch as the flask was exhausted to an almost complete vacuum,a performance rendered possible by the high efficiency of the modern air-pump. The actual experiment necessitates the most elaborate precautions, for which reference must be made to Morley's original papers in the Smithsonian Contributions to Knowledge (1895), or to M.
Soc. 43, p. 361) an important correction which had been overlooked by previous experimenters with Regnault's method, viz.
Mag., 1868, 35, p. 161, and the full account, which serves as an excellent example of the extraordinary care and ingenuity of Regnault's work, is given in the Memoires de l'academie des sciences, 1868, xxxvii.
In diameter, and, using Regnault's apparatus, found, that the velocity could be represented by 33 3(1 +C/P), where P is the mean excess of pressure above the normal.
Bosscha From An Independent Reduction Of Regnault'S Experiments Is Probably Within The Limits Of Accuracy Between Ioo° And Zoo° C., So Far As The Mean Rate Of Variation Is Concerned, But The Absolute Values Require Reduction.
These Experiments, Which Have Been Extended By Barnes Over The Whole Range O° To 100°, Agree Very Well With Rowland And Griffiths In The Rate Of Variation At 20° C., But Show A Rather Flat Minimum Of Specific Heat In The Neighbourhood Of 38° To 40° C. At Higher Points The Rate Of Variation Is Very Similar To That Of Regnault'S Curve, But Taking The Specific Heat At 20° As The Standard Of Reference, The Actual Values Are Nearly 0.56% Less Than Regnault'S.
Above 60° C. Regnault'S Formula Is Adopted, The Absolute Values Being Simply Diminished By A Constant Quantity O O056 To Allow For The Probable Errors Of His Thermometry.
Many Authors, Adopting Regnault'S Formula, Have Selected O° C. As The Standard Temperature, But This Cannot Be Practically Realized In The Case Of Water, And His Formula Is Certainly Erroneous At Low Temperatures.
1.40, Rankine found S = .385, a value which he used, in default of a better, in calculating some of the properties of steam, although he observed that it was much larger than the coefficient .305 in Regnault's formula for the variation of the total heat.
S = 475, greatly increased the apparent discrepancy between Regnault's and Rankine's formulae for the total heat.
Assuming an equation of the form log (p/760) =a log (0/373), their results give a = S/R =4.305, or S=0.474, which agrees very perfectly with Regnault's value.
1889), who has devoted minute attention to the reduction of Regnault's observations, assuming S/s =1.400 as the theoretical ratio of specific heats of all vapours on his " aether-pressure theory," has calculated the properties of steam on the assumption S=0.384.
He endeavours to support this value by reference to sixteen of Regnault's observations on the total heat of steam at atmospheric pressure with only 19° to 28° of superheat.
A similar objection applies, though with less force, to Regnault's main experiments between 125° and 225° C., giving the value S =0.475, in which the superheat (on which the value of S depends) is only one-sixteenth of the total heat measured.
Perry (Steam Engine, p. 580), assuming a characteristic equation similar to Zeuner's (which makes v a linear function of the temperature at constant pressure, and S independent of the pressure), calculates S as a function of the temperature to satisfy Regnault's formula (10) for the total heat.
This method is logically consistent, and gives values ranging from 0.305 at o° to 0.345 at Ioo° C. and 0.464 at 210° C., but the difference from Regnault's S = 0.475 cannot easily be explained.
If the steam at A were dry and saturated, we should have, assuming Regnault's formula (to), H A -H D = 305 (0'-O), whence, if S = .475, we have zL = .3 0 5 (0 '- 0)-.
It is evident that this is a very delicate method of determining the wetness z, but, since with dry saturated steam at low pressures this formula always gives negative values of the wetness, it is clear that Regnault's numerical coefficients must be wrong.
If we assume Regnault's formula (10) for the total heat, we have evidently the simple relation S=0.305(0'-0)/(0"-o), supposing the initial steam to be dry, or at least of the same quality as that employed by Regnault.
Whatever may be the objections to Regnault's method of measuring the specific heat of a vapour, it seems impossible to reconcile so wide a range of variation of S with his value 5=0.475 between 125° and 225° C. It is also extremely unlikely that a vapour which is so stable a chemical compound as steam should show so wide a range of variation of specific heat.
The method of deducing the specific heat from Regnault's formula for the variation of the total heat is evidently liable in a greater degree to the objections which have been urged against his method of determining the specific heat, since it makes the value of the specific heat depend on small differences of total heat observed under conditions of greater difficulty at various pressures.
Between 103° C. and 113 ° C. This is about 4% larger than Regnault's value, but is not really inconsistent with it, if we suppose that the specific heat at any given pressure diminishes slightly with rise of temperature, as indicated in formula (16) below.
Admitting the value S =0.497 for the specific heat at 108° C., it is clear that the form of Regnault's equation (io) must be wrong, although the numerical value of the coefficient 0.305 may approximately represent the average rate of variation over the range (loo° to 190° C.) of the experiments on which it chiefly depends.
Regnault's experiments at lower temperatures were extremely discordant, and have been shown by the work of E.
The introduction of this correction into the calculations would slightly improve the agreement with Regnault's values of the specific heat and total heat between 100° and 200° C., where they are most trustworthy, but would not materially affect the general nature of the results.
The values of H at o° and 40° agree fairly with those found by Dieterici (596.7) and Griffiths (613.2) respectively, but differ considerably from Regnault's values 606.5 and 618.7.
The rate of increase of the total heat, instead of being constant for saturated steam as in Regnault's formula, is given by the equation dH/d0 =S(1 - Qdp/d0).
The mean value, 0.313 of dH/d0, between loo° and 200° agrees fairly well with Regnault's coefficient 0.305, but it is clear that considerable errors in calculating the wetness of steam or the amount of cylinder condensation would result from assuming this important coefficient to be constant.
Regnault's formula for the total heat is here again seen to be inadmissible, as it would make the latent heat of steam vanish at about 870° C. instead of at 365° C. It should be observed, however, that the assumptions made in deducing the above formulae apply only for moderate pressures, and that the formulae cannot be employed up to the critical point owing to the uncertainty of the variation of the specific heats and the cooling effect Q at high pressures beyond the experimental range.
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.
103, p. 185, 1858) to represent the vapour-pressure of a solution, and was verified by Regnault's experiments on solutions of H 2 SO 4 in water, in which case a constant, the heat of dilution, is added to the latent heat.
A formula of the same type was given by Athenase Dupre (Theorie de chaleur, p. 96, Paris, 1869), on the assumption that the latent heat was a linear function of the temperature, taking the instance of Regnault's formula (io) for steam.
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.
The values of the saturation-pressure given in the last column are calculated by formula (25), which agrees with Regnault's observations better than his own empirical formulae.