The Efficiency of Ideal Thermomagnetic Engine

Transcription

1 he fficiecy of Iea heoagetic gie A.G. Kviiaze М.D. Zviaaze.A. aov G.G. Kiaze L.A. Zataaze I. avahishvii biisi tate ivesity havchavaze Ave. biisi 8 Geogia. Aoiashvii Istitute of Physics 6 aaashvii t. biisi 77 Geogia zviaazeichae@yahoo.co Abstact he atice cotais cacuatio of the efficiecy of the iea theoagetic egie whose woig boy is feoagetic has bee suggeste. uggeste etho beig appicabe to ay heat egie opeatig o the basis of stuctua phase tasitios i soi boies. Key wos: heat egie feoagetic stuctua phase tasitio

2 . Itouctio Recety i coectio with the eve-iceasig wo-wie eegetic cisis a geat attetio has bee pai to heat egies opeatig at ow-potetia eegy. Aog the ae the egies opeatig at usig the stuctua phase tasitios i soi boies: atesite-austeite feoeectic-ieectic feoagetic-paaagetic. he pesete wo gives the cacuatio of the efficiecy of the iea theoagetic egie the woig boy of which is a feoagetic ateia.. asic physics of a wo of the theoagetic egie As it is we ow the agetic oet ocate i ohoogeeous agetic fi is acte ot oy by the pecessioa foce popotioa to the vecto pouct [ ] but aso by the foce F cause by the ihoogeeity of agetic fie is the gaiet opeato. Fo the feoagetic ateia of the fia iesios F foce is equa to the su of foces actig o iffeet sectios of the sape. It is assue that this foce is popotioa to the fu agetic oet. esies it is assue that the gaiets of agetic fie ae such that we ca egect the agetostictive effects a hece ot tae ito accout the chages of the shape a the voue of sape. I just this foce F oes the wo a theefoe to achieve the high vaues of this foce the agetic fies with a high gaiet a the feoagetic ateias with a age agetic oet shou be chose. he oai stuctue of feoagetic ateia is sigificaty eteie by the eagetizig fie that epes o the shape of sape []. wo cases ae ow whe eagetizig fie is equa to zeo a the sape is i the sige-oai state. he sape ae of uiaxia feoagetic ateia is a paae-sie ifiite pate with paes paae to the agetizatio vecto a a ifiite cyie with axis paae to the agetizatio vecto. esies as the iite iesios of the egio whee the extea agetic fie is ceate i oe the esutat foce at the iput a at the output be axiu it is ecessay to chage sigificaty the agetic popeties of sape withi the age of agetic fie. hese popeties ae chage ost stogy at the phase tasitios of the seco oe feoagetic-paaagetic i the viciity of uie tepeatue []. hough the epeece i the viciity of has a athe copicate fo it is ipotat that a shap chage of agetic oet taes pace i the aow tepeatue ba Δ. hus if the tepeatue of sape at the iput is < c Δ the agetic oet is of oe the axiu agetic oet of sape. If we heat the sape up to the tepeatue > Δ whe it passes the agetic fie the its agetic oet is p ef whe it eaves the agetic fie whee p is the agetic oet of paaagetic ateia ef is the cetai efficiet agetic fie at the output i the egio of stog ihoogeeity of the fie. Obviousy. I the geea case epes i a copicate way o the tepeatue a o the chaacte of otio that eteies. he esutat foce epes o the iffeece - a just ef p p ef

3 this iffeece eteies the chaacte of otio of sape i.e. the syste with feebac is obtaie the popeties of which epe sigificaty o the etho of heatig the sape. As it was aeay etioe ue to the sa chaacteistic iesios of the egios of agetic fie i the case of ovig sape a etaie stuy of the pocesses of heat tasfe fo the heate to the sape is ecessay. he pocesses of heat tasfe ae ess iite i coectio with the ess stict equieets fo the cooig egios. he pocesses of heat tasfe becoe oe ipotat taig ito accout the cycic opeatio of the egie. I this case the oy way to act o the syste fo the outsie is a thea cotact. As it is ow [] the pocess of heat tasfe is evesibe at egectig the agetostictive effects; theefoe to obtai the sigificat iffeece i the quatity of heat geeate by the heate a tasfee to the cooe it is ecessay to chage the coitios of heat tasfe. I this case the oy etho of chagig these coitios is to heat a to coo the sape i iffeet agetic fies.. acuatio of the efficiecy of iea theoagetic egie Let us eote the quatity of heat ecessay fo heatig the sape fo to i hoogeeous agetic fie by a by the quatity of heat tasfee by this sape to the cooe at cooig fo to i the agetic fie equa to zeo. he the iffeece is equa to the wo oe by the agetic fie a the vaue is the efficiecy. η hus the efficiecy epes sigificaty o the egie esig of the cofiguatio of extea agetic fie o the coitios i.e. whee the heatig is state a at which fies it is esiabe to cay out the heatig i such sectios of the agetic fie whee it has the axiu vaue a is hoogeeous etc. o estiate the efficiecy of i ost iteestig tepeatue egio << << we ca ae use of the ieaize patte assuig that the feoagetic sape is heate uifoy i hoogeeous agetic fie a thus is cooe i the absece of agetic fie. aig ito accout the evesibiity of thea cotact a egectig the agetostictive a agetocaoic effects as we as the thea expasio a ca be easiy expesse by the chage of itea eegy of the sape. Iee ue the popose coitios whee a ae the itea eegies of feoagetic ateia i the agetic fie at the coespoig tepeatues. ece the heat tasfee fo the sape to the cooe is. Itea eegy of feoagetic cysta ca be pesete i the fo of the su 4

4 whee is the itea eegy of agetic subsyste of feoagetic ateia a is the itea eegy of the cysta attice ot epeig o the agetic fie owig to the fact that the agetostictive effects ae egecte. o estiate the itea eegy of the agetic subsyste we ca use the sipest fo of aitoia μ z 5 whee the exchage itega is cosiee to be iffeet fo zeo oy fo the eaest eh eighbos μ is the oh ageto a is the spi opeato fo the -th ato. c eow the aow egio of phase tasitio the itea eegy of feoagetic ateia ca be a of the eegy of ago gas pesete as a su of the eegy of gou state. he eegy of gou state. 6 fo agetic subsyste with aitoia 5 is 7 μ N whee the esity of agetic oet of the gou state is eteie by the axiu vaue of the spi of sepaate ato a by the esity of atos N ~ v is the voue of eeetay ce pe oe agetic ato a v ~ whee a v a is the attice costat. I expessio 7 the suatio ove is ae oy ove the eaest eighbos of the agetic ato ocate at the oigi of cooiates a z whee z is the ube of the eaest e eighbos a ~ ξ is the exchage itega a is the iesioess paaete ξ fo a typica feoagetic ateias is of the oe of ξ ~.. 4. Accoig to the oe of agitue ~. ago eegy with the wave vecto fo the syste with aitoia 5 is cos μ 8 a i the og-wave appoxiatio fo the cysta with cubic syety we have: a α. 9 μ; α 4

5 5 hus the itea eegy of ago gas is equa to / exp. he fo the itea eegy of feoagetic ateia i paaagetic state at >> we have z μ besies the eatio betwee the esity of agetic oet a the aveage vaue of spi z is of the sae chaacte as i case of the gou state i.e. N μ. Fo this easo at >> because of the ifiitesia of we ca assue that ~ ~ thus the heat absobe by the feoagetic ateia at heatig fo to i the agetic fie is equa to / exp. he heat tasfee to the cooe at cooig the sape fo to i the agetic fie equa to zeo is absoutey the sae / exp 4 hece the wo pefoe by the syste is / exp 5 a the efficiecy of accoig to 5 is / exp / exp / exp η. 6 he iffeece i itea eegy of uit voue of cysta attice ca be expesse by the iffeece i eegy of phoo gas of uit voue o by specific heat capacity of the attice

6 6 / exp / exp. 7 hus the efficiecy equas to / exp η. 8 It shou be ote that o the basis of the appoxiatios ae above expessio 8 is the efficiecy of the iea theefoe the estiatio 8 ca be cosiee as a ough appoxiatio fo the efficiecy of ea. Acowegeets: his wo is suppote by the hota Rustavei Natioa ciece Fouatio Gat GNF 7/7. he authos ae gatefu to. Nioaze fo hep with pocessig atices RFRN... osovsi agetiz. agetic popeties of ia- paa- feo- atifeo- a feoagetic ateias i Russia.. Naua 97 pages.. L.D. Laau..Lifshitz tatistica Physics pat i Russia.. Naua pages.