255 



III. " On the Thermal Effect of drawing out a Film of Liquid." 

 By Professor WILLIAM THOMSON, F.R.S., &c., being ex- 

 tract of two Letters to J. P. JOULE, LL.D., F.R.S., dated 

 February 2 and 3, 1858. Received April 30, 1858. 



A very novel application of Carnot's cycle has just occurred to 

 me in consequence of looking this morning into Waterston's paper 

 on Capillary Attraction, in the January Number of the Philosophical 

 Magazine. Let T be the contractile force of the surface (by which 

 in Dr. Thomas Young's theory the resultant effect of cohesion on 

 a liquid mass of varying form is represented), so that, if EL be the 

 atmospheric pressure, the pressure of air within a bubble of the 



4T 



liquid of radius r, shall be + H. Then if a bubble be blown 



from the end of a tube (as in blowing soap-bubbles), the work spent, 

 per unit of augmentation of the area of one side of the film, will be 

 equal to 2T. 



Now since liquids stand to different heights in capillary tubes at 

 different temperatures, and generally to less heights at the higher 

 temperatures, T must vary, and in general decrease, as the tempe- 

 rature rises, for one and the same liquid. If T and T' denote the 

 values of the capillary tension at temperatures t and t' of our abso- 

 lute scale, we shall have 2(T T') of mechanical work gained, in 

 allowing a bubble on the end of a tube to collapse so as to lose a 

 unit of area at the temperature t and blowing it up again to its 

 original dimensions after having raised its temperature to t'. If $ t 

 be infinitely small, and be denoted by C, the gain of work may be 

 expressed by 



and by using Carnot's principle as modified for the Dynamical 

 Theory, in the usual manner, we find that there must be an absorp- 

 tion of heat at the high temperature, and an evolution of heat at the 

 low temperature ; amounting to quantities differing from one an- 



other by 



1 -2dT 



and each infinitely nearly equal to the mechanical equivalent of this 



VOL. IX. T 



