in a Perfect Gas during Expansion and Condensation.. 289 



shall remain always strictly equal to the pressure of the elasti- 

 city of the gas, no external force will be introduced, and no ex- 

 ternal work will be done; and consequently the total energy 

 of this gas will remain unaltered. These conditions will be 

 fulfilled if the gas is contained in a cylinder, of which it may 

 occupy the height v, and compressed by a w r eight P placed 

 upon the (weightless) piston, which is supported at the height 

 v by the upward pressure of the gas, j» = P. So long asjo and 

 P are always equal, it does not matter whether they remain con- 

 stant, or whether they alter in any manner whatever. Let P be 

 a vessel of water allowed to run off gradually, so as to become 

 less and less, or allowed to be filled up gradually by water flow- 

 ing into it, so as to become greater and greater. Any infinite- 

 simally small variation of P either way will necessarily be in- 

 stantly followed by a corresponding change in p. If P dimi- 

 nishes, the gas will expand, and p will diminish also ; and so, 

 too, if P increases. But there will never be any, even instanta- 

 neous difference between P and p. There will be a swelling or 

 a contraction of the gas ; but while P remains as nothing but 

 the equal and opposite reaction to p, no external force will be 

 in action throughout the gas. Moreover the work done is the 

 swelling of the gas — strictly internal work, the enlargement of 

 the distance of the particles from one another. It must be con- 

 cluded that in this experiment internal forces alone have done 

 all the internal work, and, therefore, that there has been no va- 

 riation of total energy. The total energy is known to vary as 

 the temperature ; and what is concluded of the one may be im- 

 mediately transferred to the other. 



From the constant equality of the forces P and p throughout 

 the motion, it follows that the piston has risen with a uniform 

 velocity. And we may at once convert this proposition, and say 

 that whenever a weight is made to move upwards with a uniform 

 velocity, the forces which act upon it are in equilibrium, and 

 that such a raising of a weight as that is not an external work 

 done at the expense of the heat or potential energy of the gas. 



Let us now pass to another form of the experiment, and in- 

 stead of the gradual influx or efflux of water, suppose P to be 

 suddenly altered either way by the finite quantity ±?r. It is cer- 

 tain that the condensation or rarification of gas, even in a clear 

 and unobstructed chamber, takes time. It may be made by 

 proper contrivances to take considerable time. But I do not 

 suppose that the same is the case with the sudden alterations of 

 P. The change of the pressure would be felt — not perhaps to 

 the whole extent of 7r, but partially felt throughout the gas in- 

 stantaneously. If this be admitted, then we shall have, during 

 the interval of time between the alteration of P and the com- 



Phil. Mag. S. 4. Vol. 39. No. 261 . April 1870. U 



