50 Prof. H. L. Callendar on the Thermodynamical 



By the second law of thermodynamics, 



(cm/jp) e =-0(dvid6) P (2) 



Whence, 



d¥ = dE + d(pv) = dK + vdp 



= idHld0)pdd+ (dR/dp) 6 dp + vdp 



= Sdd-{6(dv/d0) p -v)dp. ... (3) 



When a fluid is flowing steadily along a tube through a 

 porous plug or throttling aperture without external loss or 

 gain of heat, as in the experiment of Joule and Thomson, the 

 function, F = E-j-_/#7, will remain constant provided that the 

 kinetic energy of flow is the same on either side of the plug. 

 It is convenient to have a name for this function, which 

 I have called the Total Heat, employing the expression used 

 by Regnault for the same quantity in the case of a saturated 

 vapour. Expansion through a porous plug is frequently 

 spoken of as ij free " or " unresisted " expansion, but this 

 term appears to be inappropriate, since the external work 

 done is d(pv) and not zero, as in Joule's original experiment. 

 It is often said to be " adiabatic " in the sense that no heat 

 is supplied to the fluid from external sources. But this may 

 lead to some confusion, as the process is not isentropic. 

 I have found the term " Adiathermal " more convenient, as 

 implying that there is no heat-transmission, and that the 

 total heat remains constant (dF — 0) . 



Applying the condition c/F = 0, we have by (3) above the 

 well known relation, 



$Q=S(d6/dp) F =:6(dvldd) p -v. ... (I) 



This equation gives the " cooling effect " in adiathermal 

 expansion under the condition of constant total heat, which 

 is the quantity measured in the porous-plug experiment. It 

 is convenient to employ the single letter Q for the cooling 

 effect (dd/dp)?, and to measure it in degrees of temperature 

 centigrade per atmosphere (^> = 10 6 c.G.s. = 75 cms. Hg. at 

 0° 0. and lat. 45°), in which case S should also be measured 

 in terms of a unit 10 6 ergs. The sign of Q is positive when 

 a fall of temperature accompanies a fall of pressure, as in the 

 case of air and C0 2 . It is negative, a heating effect, in the 

 case of hydrogen at ordinary temperatures. 



It is important to observe that the vanishing of the cooling- 

 effect is not in itself a sufficient criterion of the ideal gaseous 

 state, pv — R&. The condition 6{dvjd0)p = v would evidently 

 be satisfied by any fluid possessing the characteristic equation 



