﻿Theory of Contact Electromotive Force. 271 



Y which differ by indefinitely small amounts from the true 

 equilibrium values at the specified temperatures. Thus in 

 general the pressure p x , the temperature 6, and the electric 

 potential V A o£ the electrons in equilibrium with A will all be 

 different from the corresponding quantities 6', pi, and V/ 

 of the electrons in equilibrium with A'. Let us suppose that 

 eVY is > eVx. Around A place a screen (wire gauze) main- 

 tained at the potential V/ and permeable to the electrons. 

 This will reduce the pressure of the electrons outside of it to 

 some definite value pi without affecting their temperature 0*, 

 and will reduce their potential to the value Y/ of the electrons 

 in equilibrium with A'. The further transference of the 

 electrons to A' will not involve any work against the elec- 

 trical forces, and may be calculated on the hypothesis that 

 the electrons are dynamically equivalent to a perfect gas f. 

 The work done during the evaporation through the potential 

 screen is pv = NB,0 and the heat absorbed is 



N(t*i + e(V/-V,)+B0)- f 



where N is the number of electrons in one gram-molecule 

 of them. 



The freed electrons are then compressed adiabatically to 

 a temperature 0', the work done in this operation being 



NR 



-z (d f — 6), where y is the ratio of the specific heats of the 



electrons at constant pressure and constant volume. The 



beat absorbed in this operation is zero, but the pressure 



/0\y/y-l 

 is changed from p x ° to p x ° 1 ^, ) . We next expand to 



the pressure pj at constant temperature 6\ The work done 



t> ' /0 \ y/y — 1 

 is — NR#' log ^— l 7p \ , and an equal amount of heat is 



absorbed. The electrons now have the same pressure, tempe- 

 rature, and potential as those in equilibrium with A', and the 

 transference has been accomplished in a strictly reversible 

 manner. They are then condensed into A', which is for the 

 time being disconnected from the other conductors, at the 

 constant pressure p{ and temperature 6' '. The work done 

 in this operation is — NR0' and the heat absorbed is 

 — N^' + Rfl'). The transference from A ; to B' involves 

 no work, but there is an amount of heat — NP'<? absorbed at 

 the junction, where P' is the Peltier effect per unit charge. 

 The electrons are then evaporated from B' at the equilibrium 



* Cf. 0. W. Richardson, Phil. Mag. [5] vol. xviii. p. 695 (LOOP), 

 t See Mow, p. 273. 



