540 Royal Society .— 



Professor Thomson has obligingly furnished me with the fol- 

 lowing investigation : — 



On the Alterations of Temperature accompanying Changes of 

 Pressure in Fluids. 



Let a mass of fluid, given at a temperature t and under a pres- 

 sure p, be subjected to the following cycle of four operations in 

 order. 



(1) The fluid being protected against gain or loss of heat, let 

 the pressure on it be increased from p to p + zs. 



(2) Let heat be added, and the jjrcssure of the fluid maintained 

 constant at^ + ro, till its temperature rises by dt. 



(3) The fluid being again protected against gain or loss of heat, 

 let its pressure be reduced from p + vT to p. 



(4) Let heat be abstracted, and the pressure maintained at 

 2J, till the temperature sinks to f again. 



At the end of this cycle of ojjerations, the fluid is again in the 

 same physical condition as it was at the beginning, but, as is shown 

 by the following considerations, a certain transformation of heat 

 into work or the reverse has been effected by means of it. 



In two of these four operations the fluid increases in bulk, and 

 in the other two it contracts to an equal extent. If the pressure 

 wei'e uniform during them all, tlierc would be neither gain nor loss 

 of work ; but inasmucli as the pressure is greater by ■nr during 

 operation (2) than during operation (4), and rises during (1) by 

 the same amount as it falls during (3), there will, on the whole, be 

 an amount of work equal to ■m dv, done by the fluid in expanding, 

 over and above that which is spent on it by pressure from without 

 while it is contracting, if dv denote a certain augmentation of 

 volume which, when •nr and dt are infinitely small, is infinitely 

 nearly equal to the expansion of the fluid during operation (2), or 

 its contraction during operation (4). Hence, considering the bulk 

 of the fluid primitively oj)cratcd on as unity, if we take 



dv 

 dt='' 



to denote an average coefficient of expansion of the fluid under 

 constant pressure of from p) to ^ + w, or simply its coefficient of 

 expansion at temperature t and pressure p, when we regard cr as 

 infinitely small, we have an amount of work equal to 



■u: e dt 

 gained from the cycle. The case of a fluid such as water below 

 39°' 1 Fahr., which contracts under constant pressure, with an ele- 

 vation of temperature, is of course included by admitting negative 

 values for e, and making the corresponding changes in statement. 



Rendu Annuel, Si. Petersburg, 1356). He finds by his metliod of twisting and 

 transverse oscillations that the decrease of elasticity for steel and copper is '000471 

 and '000478. Very careful experiments recently made by Prof. Thomson, indicate 

 a slight increase of expansibility by heat in wires placed under tension. — August 1. 

 J. P. J. 



