BRIDGMAN. — THERMODYNAMIC PROPERTIES OF LIQUIDS. 91 



part of the diagram giving on an enlarged scale the difference of the 

 work for intervals of 20°. 



The curves for the separate liquids do not require much comment. 

 The difference curves are universally positive; that is, it is always 

 true that more mechanical work is expended when a liquid is com- 

 pressed to a given pressure at a high temperature than at a lower 

 one. Beyond this, however, there do not seem to be man}^ common 

 features. The curves show irregular and apparently unrelated varia- 

 tions, but the irregularities are not so great as for the dilatation or 

 the compressibility. Of course this was to be expected, because the 

 curves are essentially integral ciu'ves. 



Three of the alcohols, methyl, ethyl, and amyl, show similar differ- 

 ence curves. Ether and isobutyl alcohol, isomers, are unlike, as we 

 have found them before. The difference curve 20°— 40° for carbon 

 bisulphide shows the effect of the abnormally high compressibility 

 at 20°, which we saw previously, and the three ethyl halogens show 

 similarities. Other variations in the difference curves are not par- 

 ticularly illuminating. 



Figure 59, combining the average results for the twelve liquids, is 

 of more interest. The similarity in general shape of all the curves is 

 perhaps the most interesting feature. The curves become nearly 

 linear at the higher pressures. This of course is not the usual rela- 

 tion between stress and work for a body like a steel spring, which 

 maintains a stiffness independent of stress. For such bodies the 

 work stored up as potential energy of strain varies as the square of 

 the stress. This is true for liquids also over a pressure range so small 

 that the compressibility may be regarded as constant, and is shown 

 in the initial stages by all the curves, which are tangent to the axis 

 at the origin. The fact that at high pressures the curves tend to 

 become linear, still remaining slightly concave upwards, means that 

 at high pressures the compressibility is becoming less, so that the 

 change of volume, and therefore the work, is less for a given increment 

 of pressure. 



If we assume tentatively that the work of compression is linear at 

 high pressures, we have a means of finding the compressibility and 

 the volume at high pressures. For; 



W 



~ — / p [-^ j dp = a -\- bp (a is negative, b positive). 



Differentiating this equation, we obtain, 



'dv\ ^ _b 

 KdpJt p 



