BRIDGMAN. — THERMODYNAMIC PROPERTIES OF LIQUIDS. 33 



between the work received and the heat given out. It was computed 

 in this way and is given in a set of diagrams (Folder 5) for the four 

 regular temperature intervals. 



Specific Heat at Constant Pressure. — Other thermodynamic 

 quantities of a simple nature which are usually thought of as char- 

 acteristic of a liquid are its two specific heats. They also may be 

 found by thermodynamic computation from the data given, but the 

 accuracy is not so great as the accuracy of the other quantities. 

 There are two methods of attack open to us here, but both of them 

 must assume as known the specific heats at atmospheric pressure 

 as a function of temperature. In general, it may be shown that the 

 characteristic equation of a substance is not sufficient in itself to 

 determine the specific heats; we must know in addition the specific 

 heats along some line not an isothermal. Unfortunately, the specific 

 heat of very few of the liquids with Avhich we are concerned is known 

 with accuracy as a function of temperature at atmospheric pressure. 

 The results of different observers are often in essential disagreement. 

 But the characteristic equation can give us the change of specific heats 

 along an isothermal. These are the results which will be tabulated 

 in this paper, therefore, leaving for other experimenters the more 

 accurate determination of the specific heats at atmospheric pressure. 

 These future results may then be combined with the difterences given 

 here to determine the specific heat at any pressure. 



The first method for calculating the specific heat at constant pres- 

 sure is the method used in the paper on water. It makes use of the 



, fdCp\ fdh\ 



formula ( -7^ ) = — r ( ^2 ) • Evidently in order to obtain the 



total change of specific heat at any pressure M^e must perform an 

 integration. The weakness of the method is that it invokes the use 

 of a second derivative, which cannot be determined with great ac- 

 curacy from measurements of volume. The method would be open to 

 greater error if applied to these twelve liquids than in the case of 

 water, because the dilatation varies more and more irregularly than 

 for water. 



The second method uses a cyclic process to determine the amount 

 of heat absorbed in passing from one temperature to another at any 

 constant pressure. Let us imagine a liquid in the condition repre- 

 sented by the point A on the diagram (see Figure 7). The liquid 

 is now to be carried to the neighboring point D at the same pressure 

 but at a higher temperature. The total change of internal energy 

 when we arrive at D is independent of the path which we have tra- 



