Physical Properties [CH. vi 



vapour is compressed at the temperature of the isothermal SZQXRY, the 

 substance remains a vapour until the point Z is reached. At this point 

 condensation sets in, and as the condensation proceeds the representative 

 point moves along the straight line ZXUY until, by the time the point F is 

 reached, the whole of the matter is in the liquid state. After this the 

 substance, wholly in the liquid state, moves through the series of changes 

 represented by the path YQ'N. 



It will be seen that there is an element of arbitrariness in this, for 

 instead of describing the path SZUYN the substance might equally well be 

 supposed to describe the path SR'RYN keeping at the same temperature 

 throughout; or any other path composed of two stable branches of an iso- 

 thermal joined by a line of constant pressure. In other words there is no 

 unique relation between the pressure and temperature of evaporation or 

 condensation. This is however in accordance with the known properties of 

 matter, the range ZQ in fig. 9 representing super-cooled vapour, and the range 

 YR representing super-heated liquid. 



150. It may, however, be objected that the path of the substance from 

 one state to another, given the same external conditions, must be quite 

 definite, and that we have not yet arrived at any such definiteness. 



Maxwell* and Clausiusf have both attempted to obtain definite paths for 

 a substance changing at a constant temperature. The conclusion they arrive 

 at is that the line SZXYN in fig. 9, will represent the actual isothermal 

 path from S to N, if the line ZX Y is so chosen that the areas ZQX, XR Y 

 are equal. The argument by which this conclusion is justified is as follows. 

 Imagine the substance starting from Z, and caused to pass through the cycle 

 of changes represented in fig. 9 by the path ZQXRYXZ, the first part of 

 the path ZQXY being along the curved isothermal, and the second part YXZ 

 along the straight line. Since this is a closed cycle of changes, it follows 

 from the second law of thermodynamics that 



where dQ is the total heat supplied to the substance in any small part of its 

 path in fig. 9, is the temperature measured on the thermodynamic scale, 

 and the integral is taken round the whole closed path representing the cycle. 

 Since the temperature is constant throughout the motion, this equation 



becomes I dQ = 0, so that the integral work done on the gas throughout the 



cycle is nil. This work is, however, equal to I pdv and therefore to the area, 

 measured algebraically, of the curve in fig. 9 which represents the cycle. 



* Nature, Vol. n. 1875 ; Collected Works, n. p. 425. 

 t Wied. Ann. ix. p. 337, 1880. 



