﻿272 Prof. 0. W. Richardson on the Electron 



pressure and temperature p. 2 ' and 6' respectively, the work 

 being NR0' and the absorption of heat 7s(w 2 ' +R6')*. 



NR 



Next compress adiabatically to 6. The work is z (6 — 6'), 



the heat absorbed being nil. During this step the pres- 



/0'\y/l-y 



sure is changed from p 2 to p 2 ' I -^ \ . Next expand at 



constant temperature 6 to the pressure p 2 °, which is the 

 equilibrium pressure at the potential screen around the 

 conductor B. [We have assumed, for the sake of definite- 

 ness, that eY 2 '>eV 2 .] The work done and heat absorbed in 



this step are each equal to — NR01og^ I -^ ) . Now 



condense into B at 6 andp 2 °- The work is — NR# and the 

 heat absorbed is — X(w 2 + e(V 2 ' — V 2 ) + R0). Finally, pass 

 through the junction to A. The work here is nil, and the 

 absorption of heat is N1V. The system is now in the state 

 in which we found it, and the cycle of operations is reversible 

 at every point. 



The balance of work done during the cycle is 



«*''<:(^'-™>«^(|.r'- 



The heat communicated to the source is 



NiR^iogg'^) 771 " 7 4 z. 2 -^ 1 + ,(v 1 -y/+ v 2 '_y 2 )_P4. 



The ratio of these is equal, by the second law of thermo- 

 dynamics, to — ^— ; whence by virtue of the relations 



R0 log B o = R# logPi-^i-eOV-VO, 

 R<9' lo gi V = Rl9' log Pi'-w/, 



R0 log pf =110 logP 2 -M? 2 -e(V 2 '-V 2 ), 

 m' hgp 2 '=W logYs'-Wt', 



-R6' log P 2 ' = K0' log Pi / + <-W4-6(V 1 / -V 2 0, 

 R0 log P 2 = R0 log P x +w 2 -w t 4 e(Y 1 -V 2 ), 



which determine the equilibrium between the electrons in 

 the different parts of the system which are at the same 



* "When the nomenclature is not quite clear from the context it will 

 "be obvious after a glance at the diagram (p. 270j r 



