34 PROCEEDINGS OF THE AMERICAN ACADEMY. 



versed. One path from A to D may be described by raising the tem- 

 perature from /q to ti at constant pressure. (Path i\.D in Figure 7.) 

 In this case the hquid does a certain amount of mechanical work 

 against external pressure and also absorbs a quantity of heat which we 

 can compute immediately when we know the specific heat at constant 



pressure. The external work during 

 this process is simply the product 

 of the constant pressure and the 

 change of volume, and may be com- 

 puted directly from the .table of 

 volume as a function of pressure 

 and temperature. Or we may pass 

 from A to D by a more circuitous 

 route, by lowering the pressure 



' isothermally at /q from A to B, 



Pressure ^j^gj^ raising the temperature at at- 



FiGURE 7. Shows tlie cycles mospheric pressure from B to C, and 

 described in finding the specific ^^^^^ increasing the pressure isother- 

 heat at constant pressure. i >. i 



mally at the final temperature (i to 



the point D. Now the advantage of this longer route is that we know 

 all the cjuantities of energy which enter the body on the way. The 

 mechanical work of compression along the isothermals from A to B 

 and from C to D we have already computed. We have also found the 

 heat of compression along the lines A-B and C-B. No work is done 

 in the expansion along the line B-C, and the heat absorbed along this 

 line is known if we know the specific heat at atmospheric pressure. 

 By comparing the inflow of energy along these different paths we are 

 in a position to compute either the quantity of heat absorbed along 

 the line A-D at constant pressure, or else the difference l)etween this 

 heat and the heat absorbed along the line B-C. This heat (or 

 else the difference of heat) may be plotted against the difference of 

 temperature between the points A and D. The same process may be 

 performed at the same pressure for a number of temperature intervals, 

 each with /q as the lower limit, giving a curve of the quantity of heat 

 absorbed at constant pressure as a function of the temperature. The 

 specific heat at any temperature is the slope of this heat curve at that 

 temperature. 



The slope was found by a method similar to that for computing 

 the thermal dilatation at constant pressure. At any temperature 

 the difference between the amount of heat actually absorbed and the 

 amoimt which would have been absorbed if the relation between heat 



