432 Variation of Surface- Tension ivith Temperature. 



Let the liquid be maintained at constant temperature, and 

 have a volume v and surface S ; and let L be the latent heat 

 of dilatation at constant surface. 



Pat the liquid through a cycle consisting of two isome- 

 trics v, v + dv, and two lines of constant surface S, S + r/S. 



Since the cycle is reversible and the temperature is con- 

 stant, the heat absorbed is zero. 



Therefore 



dl _ dL _ . 

 do " rfS 



Therefore / is independent of v, and so is b since l—bt. 



Thus the latent heat of extension is proportional to the 

 absolute temperature. This agrees with a hypothesis of 

 Clausius (Phil. Mag. 1862, vol. xxiv.). 



It has been shown that T can be expressed in the form 



f{v)-bt. 



We shall show that it can also be written cf>(p)—bt. 



For let the pressure of the liquid remain constant while the 

 surface, volume, and temperature vary. 



Then 



K being the specific heat at constant pressure and I having 

 the same meaning as before, for the latent heat of extension 

 at constant temperature and volume is also the latent heat of 

 extension at constant pressure (and temperature). 

 The external work done on the liquid is 



dW=Td$-pf t dt, 



p being regarded as constant in forming — . 

 Therefore, 



dR + dW = CK-p^f\dt-h(l + T)d^. 



Since this is a perfect differential, 



— (Z + T) = -j^-l K — p — ) = 0, except for a very thin film. 



Now l = bt. 



Therefore T = <j>(p)-bt. 



