HEAT 567 >nd ni- of )lute pera- Find the ratio of the amount of work thus done to the amount of work spent in the stirring. For brevity we shall call this the work-ratio. Again, let the stress be infinitesimally increased, the thermometric body being now for the time enclosed in an impermeable envelope so that it may neither gain nor lose caloric. It will rise (or fall) 1 in temperature in virtue of the augmentation of stress. The ratio of this infinitesimal elevation of temperature to the whole absolute temperature is equal to the work-ratio multiplied into the ratio of the infinitesimal augmentation of stress to the whole stress. 38. To show how our definition of absolute temperature . is to be applied in practice take the following examples. Example 1. Any case in which- the thermometric substance is part in one condition and the remainder in another of different density, as part solid and part vapour, or part solid and part liquid, or part liquid and part steam. In this last case, as explained above ( 34), we suppose the stress to be uniform pressure in all directions. Letp be its amount, and let t be the absolute temperature corre sponding to this pressure. Let a be the ratio of the density of the rarer to that of the denser portion, p the density of the rarer por tion, and J/c the quantity of work required to generate the heat taken to convert unit mass of the substance from the lower to the higher condition (K the "latent heat" of transition from the lower to the higher condition per unit mass of the substance, and J the dynamical equivalent of the thermal unit in which K is measured). The work done by the substance in passing from the denser to the rarer condition per unit volume of the latter is p(l - a), and the amount of work required to generate the heat taken in doing so is Jp. Hence the work-ratio of our second definition is Jp/c Let now the pressure be increased by an infinitely small quantity dp, and, the substance being still in the two conditions but of uniform temperature throughout, let dt be the corresponding rise in temperature. We have by the definition ( 37) dt = p(I - a-} dp _ 1 - a^ t JpK p JpK Hence !.*_Ll t dp JpK Hence by integration (2). - <r)dp JpK (3).
- er- 39. Fig. 6 represents a thermometer constructed to
show absolute temperature on the plan of example 1, 38, ~ realized for the case of water and vapour of water as ther mometric substance. The containing vessel consists of a tube with cylindric bulb like an ordinary thermometer; but, unlike an ordinary thermometer, the tube is bent in the manner shown in the drawing. The tube may be of from 1 to 2 or 3 millims. bore, and the cylindrical part of the bulb of about ten times as much. The length of the cylindrical part of the bulb may be rather more than T i<5- of the length of the straight part of the tube. The contents, water and vapour of water, are to be put in and the glass hermetically sealed to enclose them, with the utmost precautions to obtain pure water as thoroughly freed from air as possible, after better than the best manner of instru ment makers in making cryophoruses and water hammers. The quantity of water left in at the sealing must be enough to fill the cylindrical part of the bulb and the horizontal branch of the tube. When in use the straight part of the tube must be vertical with its closed end up, and the part of it occupied by the manometric water-column must be kept at a nearly enough definite temperature by a sur- 1 In the case of fall the elevation of temperature is to be regarded as negative ; and in this case the "work-ratio " is negative also. rounding glass jacket-tube of iced water. Tins glas.-^ jacket-tube is wide enough to allow little lumps of ice to be dropped into it from its upper end, which is open. By aid of an india-rubber tube connected with its lower end, and a little movable cistern, as shown in the drawing, the level of the water in the jacket is kept from a few inches above to a quarter of an inch below that of the interior manometric column. Thus, by dropping in lumps of ice so as always to keep some unmelted ice floating in the water of the jacket, it is easy to keep the temperature of the top of the manometric water- column exactly at the freezing tem perature. As we shall see presently, the manometric water below its free surface may be at any temperature from freezing to 10 C. above freez ing without more than ~ per cent, of hydrostatic error. The temperature in the vapour-space above the liquid column may be either freezing or anything higher. It ought not to be lower than freezing, because, if it were so, vapour would condense as hoar frost on the glass, and eva poration from the top of the liquid column would either cryophoruswise (see LIQUID and THERMODYNAMICS) freeze the liquid there, or would cool it below the freezing point. 40. The chief object of keeping the top of the manometric column exactly at the freezing point is to render perfectly definite and con stant the steam pressure in the space above it. A second object of considerable importance when the bore of the tube is so small as one millimetre is to give constancy to the capillary ten sion of the surface of the water. The elevation by capillary attraction of ice-cold water in a tube of one millimetre bore is about 7 millims. The constancy of temperature pro vided by the surrounding iced water will be more than sufficient to pre vent any perceptible error due to inequality of this effect. To avoid error from capillary attraction the bore of the tube ought to be very uniform, if it is so small as one milli- . Tl" t -IT metre. If it be three millimetres or more, a very rough approach to uniformity would suffice. A third object of the iced-water jacket, and one of much more importance than the second, is to give accuracy to the hydrostatic measurement by keeping the density of the water throughout the long vertical branch definite and constant. But the density of water at the freezing point is only J^- per cent, less than the maximum density, and is the same as the density at 8 C.; and therefore when ^ per cent, is an admissible error on our thermometric pressure, the density will be nearly enough constant with any temperature from to 10 C. throughout the column. But on account of the first object mentioned above the very top of the water column must be kept with exceeding exactness at the freezing temperature. 41. In this instrument the "thermometric substance" ( 34) is the water and vapour of water in the bulb, or more properly speaking the portions of water and vapour
Fig. 6.