Single Electrode Heat Effects I. Peltier Entropies of Gas Electrodes in Carbonate Paste Electrolytes

S t a n d a r d Pet t ie r entropies for the react ions O2 + CO2 + 2 e --> C O s 2CO2 + 2 e --> CO + C O 3 in mol ten carbonate pas te e lectrolytes at 10O0~ have been de te rmined f rom thermogalvanic measurements . The resul ts are --217 and --118 J /mole~ respect ively. No dependence on e lec t ro ly te composit ion is observed. The r e vers ib le pa r t of the Pe l t i e r en t ropy for the oxygen electrode react ion is es t i ma ted f rom the rmodynamic da ta and reasonable agreement wi th the exl~erimenta l resul ts is found. I t is concluded tha t the main contr ibut ion to the Pe l t i e r en t ropy arises f rom the t rans i t ion f rom gaseous to l iquid state, whereas the t ransfe r entropies of the ionic species are of minor impor tance . In power -p roduc ing e lec t rochemical cells, hea t is l i be ra t ed f rom the e lec t rode react ions and the i r r e vers ib le losses. In most cells work ing on sol idor l iqu id s ta te reactants , the en t ropy of react ion wil l in pract ice be of minor impor tance compared to the contr ibut ions f rom ohmic resis tance and e lect rode polar izat ion. However , if the e lect rode react ions have a net consumpt ion or product ion of gaseous components, the en t ropy change wil l be considerable, due to the t rans i t ion of state, and has to be t aken into account. On the basis of the over -a l l heat evolved in a single cell dur ing load, the t empe ra tu r e d i s t r ibut ion in fuel cell ba t te r ies has been t rea ted (1-3), but so far l i t t le a t tent ion has been pa id to the s ingle e lect rode heat balance and t empe ra tu r e gradients inside single cells caused by nonsymmet r i ca l hea t evolut ion at cathode and anode. The heat evolved at a revers ib le e lec t rode is det e rmined b y the Pe l t i e r en t ropy of the e lec t rode re action, which m a y be found from thermogalvanic measurements . Previously , the Pe l t i e r entropies of high t e m p e r a t u r e gas electrodes in ionic conducting oxides l ike ZrO2 (4) and ThO2 (5) have been invest igated, and we have repor ted some p re l im ina ry resul ts for carbonate e lectrolytes (6), wh ich sti l l left some uncer t a in ty about the dependence on t e m p e r a ture and carbonate composition. In this paper , the Pe l t i e r entropies of the Oz + CO2 and the CO + ,CO2 e lec t rode are determined. In par t II of this paper , the hea t evolved at the e lect rode dur ing the i r r evers ib le passage of cur ren t is re la ted to the Pe l t i e r entropies and some effects of the t emp e r a t u r e g rad ien t s created are discussed. Theory For the thermogalvanic cell involving a mix tu re of mol ten carbonates P t ( T ) IO2 + CO21Me2COaIO2 + CO2[Pt(T + AT) [A] wi th the e lect rode react ion 1/2 O2 + CO2 + 2 e --> C O s [1] the Pe l t i e r en t ropy ASp(O2, CO2) may be de te rmined f rom the the rmogalvan ic force ATGF by the equaKey w o r d s : t h e r m o c e l l , P e l t i e r en t ropy , m o l t e n ca rbona te , g a s electrodes. t ion (7) ~TGF 2 F ASp (02, CO2) = ASp~ CO2) AT + R In p(O2) I/2p (CO2) [2] where the standard Peltier entropy is given by A S p ~ C O 2 ) = [ S o ( C O 3 ) _ I/2So(O2) A S o ( C O 2 ) 2 S o ( e ) ] + A S [ 3 ] The first t e rm in Eq. [3] is the revers ib le en t ropy of A reaction, whereas AS 1 is the e n t ropy of t ransfe r corresponding to the homogeneous par t of the t he rmogalvanic force, i.e., the t he rma l diffusion poten t ia l A in the e lec t ro ly te and the e lect rode leads. 2 AS is composed of the t ransfe r entropies of the species car ry ing the cur ren t according to A A aS _-t ( C O a ) S ( C O a ) A A 2 t ( M e + ) S ( M e +) -2 S ( e ) [4] These excess entropies of t ransfe r ar ise f rom the fact tha t t r anspor ted par t ic les are not average par t ic les but a selected ensemble, thus car ry ing an excess entropy, the t rans fe r en t ropy (8). Compared to the equi l ib r ium te rm in Eq. [3], involving a t rans i t ion f rom gaseous to l iquid state, the t ransfe r t e rm [4] is expected to be of secondary impor tance . For the cell P t ( T ) ICO + CO2]Me2CO3[CO + CO2]Pt(T + aT) [B] having the e lect rode react ion 2CO2 + 2 e --> CO + C O 3 [5] we obtain the expressions A 1 T h e e n t r o p y of t r a n s f e r S is r e l a t e d to the t r a n s p o r t e d e n t r o p y A S* u s e d i n R e f . (7) by the equa t ion S = S* S. I t is no t ed t h a t s ince the s ing le e l ec t rode po ten t i a l is no t a m e a s u r a b l e quan t i ty , t he n u m e r i c a l s e p a r a t i o n of the t h e r m a l e m f into con t r ibu t ions f r o m the h o m o g e n e o u s and h e t e r o g e n e o u s t r a n s f e r p roces se s can only be p e r f o r m e d on the bas is of a convent ion .