PROCEEDINGS 



OF THE 



Camfrnirg* ^^tksop^kal Stftbtg, 



The expansion of a gas into a vacuum and the determination 

 of the specific heat at constant pressure for gases. By G. F. C. 

 Searle, M. A., F.R.S., University Lecturer in Experimental Physics, 

 Cambridge. 



[Bead 29 January 1906.] 



§ 1. The expansion of a gas into a vacuum. 



In an important thermodynamical experiment, first made by 

 Gay Lussac, gas is forced into a receiver till a high pressure is 

 reached and then the pressure is allowed to fall by opening a 

 communication between the receiver and an exhausted vessel. 

 The experiment was repeated, with modifications, by Joule, who 

 found that, when thermal equilibrium between the parts of the 

 gas had been re-established by means of the water in which the 

 apparatus was immersed, the temperature of this water was not 

 sensibly changed by the expansion. When the change of tempe- 

 rature of the water is accurately zero, it follows that the internal 

 energy of a gramme of the gas depends only upon its temperature 

 and not upon its volume. But it may be useful to consider a case 

 in which this ideal experimental result would not be obtained, and 

 to show how the change of temperature of the gas, when the 

 vessels are impermeable to heat, may be calculated for a gas 

 obeying Van der Waals' equation 



P+fy(v-b) = m (i). 



Here, and throughout this communication, the symbol t denotes 

 the absolute temperature. 



If U be the internal energy and cf) the entropy of one gramme 

 of gas, and if the heat taken in by the gas be measured in ergs, 

 we have, for isothermal expansion, 



d U = td<f> — pdv, (t constant), 



VOL. Mil. PT. V. 17 



