386 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



decreasing. The rise of temperature for 500 kgm. was found by actual 

 experiment by Richards 3* to be 1°.2, agreeing essentially with above. 

 The fact that this rise of temperature is less at high pressures might at 

 first sight seem surprising, since the work done by the external pres- 

 sure during a given pressure increase is increasing nearly proportionally 



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PRE55URE,K6M./CM'XIQ' 



Figure 14. The rate of change of internal energy with pressure along an 

 isothermal in gm. cal. for a quantity of mercurj^ occupying 1 cm.' at 0° and 

 atmospheric pressure. Notice that the sign of the derivative is negative. 



to the pressure and the specific heats are nearly constant. It must be, 

 therefore, that most of the work done by external pressure goes toward 

 increasing the internal energy of the liquid, very little being left over 

 to increase the temperature. That this is true is seen at once from the 

 thermodynamic formula 



\ dp J4> 



which shows that the internal energy is increasing along an adiabatic, 

 and at a rate very nearly proportional to the pressure. The internal 

 energy decreases along an isothermal, however, as may be inferred fi-om 

 the value of the derivative given by 



3* Richards, loc. cit. (1903), p. 40. 



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dp)^' 



