82 



NA riJRE 



[November i8, 1909 



EXPERIMENTS AT HIGH TEMPERATURES 



AND PRESSURES.' 

 T!\riTHIN a few miles of this lecture-room there is an 

 unexplored region — to approach it we should have to 

 move vertically downwards. It has been suggested by Mr. 

 Parsons " that it would be worth while to make a short 

 expedition in this direction, but the journey would be slow 

 and the cost high — for instance, to bore a hole twelve miles 

 deep was estimated to be a labour which would occupy 

 eighty-five years and cost 5,ooo,oooi. A well-to-do man 

 desiring to benefit his fellow creatures could not do betl'ir 

 than undertake this project, but until he comes forward 

 we must perforce be content to try to imitate in our labora- 

 tories the temperature and pressure conditions which would 

 be met with deep down in the earth. 



Information, attainable from experiments under these 

 conditions, is essential to the development of any exact 

 concept of the structure and evolution of the earth. One of 

 the most important questions in connection with the study of 

 bodies under high pressures and at various temperatures is 

 as to whether any particular body is solid or liquid under 

 specified conditions, and, if solid, whether it is amorphous, 

 glassy, or crystalline. That pressure would influence the 

 melting point of solids was clearly put forward by Clapeyron 

 ill 1834, but it was not until after the establishment of the 

 mechanical theory of heat in the " forties " of the last 

 century that the exact numerical relations could be estab- 

 lished, as was done by Prof. James Thomson in 1851, 

 when he calculated, for the first time, the amount by 

 which the temperature of fusion of ice would be reduced 

 by a given increase of pressure. The ideas underlying such 

 calculations are based on a consideration of the way in 

 which heat is converted into mechanical work in any prime 

 mover depending on a heat-supply, and were first formu- 

 lated by Carnot in 1824, before the true nature of heat was 

 understood. -Xs the matter is fully dealt with in every text- 

 buoic, I will merely remind you that Prof. James Thomson 

 was able to obtain an equation between the mechanical 

 work actually produced under stated conditions and the 

 work which, according to Carnot's principle, must be 

 developed by a reversible engine operating between fixed 

 temperature limits upon a given amount of heat. 



The general relation for a substance undergoing a change 

 of state at absolute temperature T, such change involving 

 a change of volume Av and an absorption or emission of 

 heat at constant pressure Qp, is, reserving the questixin of 

 sign. 



(//• ' Qi, 



or, in words, the change of melting point produced by 

 unit change of pressure equals the product of the absolute 

 temperature, and the ratio of the change of volume of 

 unit mass on melting to the quantity of heat absorbed or 

 emitted by unit mass in the process. 



-Now the greater number of substances when they pass 

 from the liquid to the solid state evolve heat and contract 

 in volume. An increase of volume is, of course, a positive 

 quantity, and if heat is absorbed during this increase it is 

 reckoned positive also. In the case of water, heat is 

 evolved during freezing as in other cases, but the mixture 

 of ice and water has a smaller volume than the solid ice. 

 Accordingly, the change of volume in this case is negative, 

 and the melting point falls as the pressure rises. 



The first fairly exact confirmation of the theory appears 

 to be due to De Visser,' who selected acetic acid most 

 carefully purified as a test substance, though valuable 

 experiments up to much higher pressures had been 

 previously made by many others, particularly by Dewar on 

 water,* Ferche on benzol," and Damien ' on a variety of 

 substances. 



It is necessary to work with a pure substance in order 

 to test the theory, or at all events with one the solid phase 

 of which has the same constitution as its liquid phase. If 

 the acetic acid had not been pure, the probability is that 



^ Discourse delivered at the Royal Institution on Friday, March 19, bv 

 Rinhard Threlfall, F.R.S. 

 ~ B.A. Reportc, Cambridge. 1C04, 672. 



3 RecueildcsTravauitCh miques dcs Pays Mis xili.. . eqq, lol. 

 ■1 Proc. R.S., XXX., 1880, 533. '6 W!ed. Ann., xliv., iSgt, 265. 



" C. R., cxii., 1891, 7S5. 



NO. 2090, VOL. 82] 



the frozen part would have contained more or less of the 

 impurity than the unfrozen, and consequently a state of 

 affairs not contemplated in the theory would have arisen. 

 From the experimental point of view, it is obvious that a 

 sharp melting point is a necessary condition for its accurate 

 observation. 



A quantity of acetic acid — rather more than 40 c.c. — is 

 confined by mercury in a closed apparatus based on a 

 previous design by Bunsen, which also contains air in a 

 graduated tube. When the acetic acid melts it expands, 

 and compresses the air through the intermediary of the 

 mercury, whereby the pressure can be inferred. The part 

 of the apparatus containing the acetic acid is immersed in 

 a bath which can be kept at any desired temperature. As 

 the melting progresses a pressure is set up by the ex- 

 pansion, and finally attains such a value that no further 

 melting can take place. We then have a mixture of solid 

 and liquid acetic acid in presence of each other under a 

 measured pressure and at a known temperature. The 

 quantities entering into the calculation are ascertained from 

 other experiments — notably the ratio of the change of 

 volume to heat absorbed was ingeniously ascertained by a 

 modification of Bunsen's ice calorimeter. The final result 

 was that the rale of variation of temperature of melting 

 point with increasing pressure was calculated to be 

 002421° C. per atmosphere as against 002435° ^- found 

 by experiment, a difference of 057 per cent. I have dwelt 

 on this work at some length in the hope that it may make 

 the nature of the problem clear. It is to be noted that the 

 experimental difficulties are considerable, and are enhanced 

 by the fact that we have no a priori reason to suppose 

 that the rate of change of melting point with pressure is 

 a constant quantity independent of the pressure. In fact, 

 it was shown by .Sir Joseph Thomson about 1SS6' that in 

 calculating the change of melting point we ought to take 

 into consideration " the difference between the energy due 

 to strains produced by the pressure in unit mass before and 

 after solidification." Sir Joseph Thomson's reasoning, 

 based as it is on a generalised Lagrangian method of 

 treating problems involving energy changes, is unsuited for 

 discussion in a non-mathematical address, but it is easy 

 to see that if the compressibilities of liquid and solid are 

 different, then the change of volume accompanying the 

 change of state of unit mass must itself depend on the 

 pressure, and therefore the pressure change of melting 

 point, which is proportional to the change of volume, must 

 depend on the square of the actual pressure so far as this 

 part of the effect is concerned. This anticipation was 

 re.-ilised by Damien in iSqi, who showed that the melting 

 points of substances in terms of the pressure could be 

 expressed by a formula of the kind 



t = t„ + a{p-i)-h(p-j)-. 

 K being m.p. under i atmosphere pressure. 



I think we may add that there will also be a small effect 

 depending on changes of energy in the capillary layer 

 separating the phases. 



The first adequate investigation of the change of m.p. 

 under pressure over a wide range of pressures was made 

 by Barus.- Time does not permit nip to do more than 

 exhibit the results obtained, though the apparatus employed 

 was most cleverly designed. It requires great experimental 

 knowledge and injjenuity to infer with accuracy changes of 

 volume of a few per cent, of the original volume at 

 pressures of 1500 atmospheres, nearly ten tons per square 

 inch. If we note the pressures and temperatures of melt- 

 ing, and plot the result as a curve against the pressure and 

 temperature, we obtain what is called a melting-point curve, 

 rnd this divides the field into two parts, so that on one 

 side of the curve the temperature and pressure at each 

 point have such values that the substance is solid, while 

 on the other side their values are such that the substance 

 is liquid. It is instructive, therefore, to regard the melting- 

 point curve as the line separating the region of solid from 

 the region of liquid. Along the line, and along it only, 

 i.e. at the pressures and temperatures indicated by points 

 on the line, the solid and liquid phases can exist in 

 equilibrium together. Such a diagram is called a " diagram 

 of condition." 



1 Appli;atinns of D namics to Physics and Chemistiv. 259- 

 ^ Bulletin No, g6 of the U.S.A. Geo'ogical Survey, 1S92. 



