244 P N E II M A TICS column ; and the third column contains the corresponding mean coefficients between 60 and 100 C. Iso therms. Pressure in Metres 1 17 _60 of Mercury. CO 8 - 100. 40 0033 0029 100 0033 0028 180 0031 0027 260 0030 0025 320 0028 0024 The temperature effect upon the coefficient of expan sion, as shown by these numbers, is approximately that indicated above, viz., that at constant pressure the co efficient of expansion is inversely as the absolute tempera ture. A glance down each column shows at once the marked effect of pressure. In this steady decrease of the coefficient of expansion with increase of pressure, hydrogen stands alone amongst the substances discussed by Amagat. His conclusions are given in these words : 1. The coefficient of expansion of gases increases with the pres sure to a maximum, after which it decreases indefinitely. 2. This maximum occurs at the pressure for which at constant temperature the product^;; is a minimum, that is, the pressure at which the gas follows for the instant Boyle s law. 3. With increasing temperature this maximum becomes less and less sensible, finally disappearing with the minimum characteristic of the compressibility curve. Thus, as hydrogen does not show this minimum characteristic, its coefficient of expansion has no maximum value. Possibly at lower temperatures hydrogen may, however, possess these characteristics. It thus appears that the simple gaseous laws established by Boyle and Charles are most nearly fulfilled by those gases which are difficult to liquefy, and are better fulfilled by all the higher the temperature is. When a gas is near its point of liquefaction the density increases more rapidly than the pressure, or in other words the volume diminishes more quickly than Boyle s law requires. When the point of liquefaction is actually reached, the slightest increase of pressure condenses the whole of the gas into a liquid ; and in this state the alteration of volume is very small even for a large increase of pressure. The transition from the gaseous to the liquid state is conveniently studied by the help of isothermal lines, which may be generally defined as curves showing the relation between two mutually dependent variables for given con stant temperatures. Such variables are the pressure and volume of a mass of gas. Let the numbers representing the volumes be measured from a chosen origin along a horizontal axis, and the numbers representing the pressures similarly along a vertical axis passing through the same origin. If we consider a mass of gas at a given tempera ture, for any volume that can be named there will be a definite pressure corresponding, and vice versa. Hence the point whose coordinates are the corresponding volume and pressure is completely determined if either coordinate is given. The temperature always being kept constant, let now the volume change continuously. The pressure will also alter according to a definite law ; and the point whose coordinates are at any instant the corresponding volume and pressure will trace out a curve. This curve is an isothermal curve, or simply an isotherm. If Boyle s law were fulfilled, the equation to the isotherm for any given temperature would be of the form pv = constant. The isotherm would be a rectangular hyperbola, whose asymptotes are the coordinate axes. For any gas not near its point of liquefaction the isotherm will not deviate greatly from the hyperbolic form. Let now the pressure be kept constant, and the gas raised someAvhat in temperature. The volume of course increases, and the corresponding point on the diagram moves off the original isotherm. Through this point in its neAv position we can draw a second isotherm corresponding to the new temperature. And thus the whole field may be mapped out by a series of isotherms, each one of Avhich corresponds to a definite temperature. The higher the temperature the farther does the isotherm lie from the origin. Such a mapped out diagram or chart shoAvs at a glance the rela tions between the volume, pressure, and temperature of a given mass of gas, so that if any two of these are given the third can be found at once. So long as the substance is in the gaseous form, the Iso- isotherm remains approximately hyperbolic ; but at the therms pressure at which liquefaction takes place a marked change foi j wat occurs in the form of the curve. For greater definiteness stance consider the case of a gramme of steam at 100 C. and at a pressure somewhat beloAv one atmosphere. As the pres sure is increased, the volume diminishes appreciably faster than Boyle s laAv requires, but still in such a Avay as to give an approximately hyperbolic form to the isotherm. When the pressure reaches one atmosphere, however, any further increase is accompanied by the liquefaction of the whole ; that is, the volume suddenly diminishes from 16 47 5 cubic centimetres to 1 cubic centimetre. Between these extremes of volume, the isotherm is a straight line parallel to the horizontal axis. The pressure remains constant until the Avhole of the gas is liquefied. In other words, the pressure of a yas in presence of its liquid does not alter provided the temperature is kept constant. This is a partial statement of the more general lav that the tempera ture of the liquid surface alone determines the maximum pressure Avhich its vapour or gas in contact therewith can exert (see HEAT). After the whole has been liquefied, any increase of pressure is accompanied by a very minute diminution of volume. Hence the isotherm rises abruptly from the point whose coordinates are 1 cubic centimetre and 1 atmosphere, becoming nearly but not quite vertical. Thus, the isotherm for water-substance at 100 consists of three parts : an approximately hyperbolic portion for pressures less than one atmosphere, the substance being then Avholly gaseous ; a horizontal portion, corresponding to the state in which the substance is partly liquid partly gaseous ; and a nearly vertical portion for pressures higher than one atmosphere, the substance being then wholly liquid. If Ave trace out the isotherm for some higher temperature, say 150 C., we obtain the same general characteristics. The straight line portion, hoAvever, is not so long, for tAvo reasons : the steam must be reduced to a smaller volume before liquefaction begins ; and the volume of the liquid Avhen condensed is greater. The pressure corresponding to the transition state is in this case 4 7 atmospheres, and the range of volumes is from 384 4 cubic centimetres in the gaseous state to 1 038 cubic centimetres in the liquid state. It thus appears that the positions of the two points of abrupt change on an isotherm draAV nearer the higher the temperature, coming together finally when the temperature has reached a certain critical value. In other Avords, at and above a certain temperature a liquid and its vapour cannot co-exist. This temperature for water-substance is very high, someAvhere about the point of fusion of zinc, and is therefore difficult to measure. Dr Andrews, hoAvever, in his classical researches on car- And > bonic acid gas, 1 to which AVC OAVC most of what is said esu above, has discussed the Avhole subject in a very complete boni j manner. This substance, at a temperature of 13 l C., gas. begins to liquefy at a pressure of 47 atmospheres. During the process of liquefaction there is a perfectly visible
1 I ltU. Tran>,., 1869.