ENRGY AD IFOO The ow of energy in uma soceties s regulaed by tiny rco of e ngy at s sed for e ow f infrmatin. Enrgy an 1in are also related a a mu deepe level
S
Cii ss Kee s
per"te Ras sai a cturies ater sciece as in prase ne eai. Te pr t ic te Rs reerre as pitica ut tat is a sa etai Sciece es t eitate t ie precise e t eryay rs suc as rk" per a irti" a in te prcess t trasr preria truts int scetic truts. Ty e k tat it takes eery t tai kee a tat it taks irti t ars ry. Rarc t te eati tee nery a iratin es ack ay yars ut e era precise et ena quaticati iratin an ny it aue E Sas aus 1948 pape Te Mateatica Try uicati." t as e k ta ay yaic easurin itruent pace in a t us ra pr i rr t actuate its eci. Fr eape a ter cec t ectica circui ue se p t caue te eecti a pintr Te ect is rciprca ereas te tery istruetati s y ery is e t tain iratin rece aacs i iati tery s iatin is ee r trasrati eey n ti artice e sa purue t ie tut. eas au y are part te eucati eer cientit Sic t ccp eer is icusse in eti eeer in ti issue e a rea ta iscussi Te uaentas iratin try are es knn We a eree e at e t n unaeta ias inrati ere e take up t iter acti ery an irati eas aut aut praiit praiit a a cenra e in a ter klee n er irati try praiites are
trte as a uerica eci a tate knee s kee aut a partcuar questin ca e rersete y te asie a certain praity (ete p) t te arius cceiae asers t te questi pete kee aut a questi is te aiity t asi a r praiity (p = ) t a cceiae aers sae e A prn (crrecty) ais uit priity = 1) t a prticuar aser iusy as i e t ear aut tat qusti By ri tat kee ca e tus ece i a prity istiuti (a se praiities asi t te set piiiies) e can ene iratin as ayi ta caus a ajustet i a praiity assiet Nuerus rkrs ae strate ta San asure uncertaity c e cae etrpy asurs uc is epecte e are aut a questin e a at is k k i t praiities ctriutn t e tery anns iratin as s e eistece a easure iatin ta is epee te as use erate te inratn Te inatin ctent a esae is accri iarian te r a es t ep n eter te esae is se ts a aes y ipresi a particuar ape a carrier ae r y se r crprapy ce tis inariac s uerst i eces an eieer task t ei g a cuicatis cae n itrui aspec cuicatin ter is in te seratin ta te rit a particuar cuicatiscnne esin ies in e te actua esae is se u in e te ce cu ae st a te er esa i i ae en ske t ce A teter ta accuratey nicats nicats 1 ts e c
T make thigs mpat e let the smbl X represet ur klege abut I ur eaple X stas fr all the thigs e k abut the rulette hee iluig ur eperiee it the asi er, the past histr f the heel a the atis f the isreputablelkig pers staig ear the table) This klege, X leas t a assigmet f pbabilities t the aius pssible a sers ssigig p = t a e a ser is the same as saig, That aser s impssible ssigig p = 1 t a a ser is the same as saig, That aser s ertai less X is f a er speial ature e shall en up assigig iter meiate ues beteen a 1 t all the pssible resuts ha's measure s repesete sblial b X t emphasie that the uertait r e trp epes bth the ell
ENTROPY IN COMMUNICAIONS was formulated mathematically y Claude E. Shannon in 9 Shannon's entropy S is de· nd in terms of a welldened quetion Q and knowledge ) about Q In Shannon's fomula the symbol epeents an arbi tary ale fato, and the sign � means to "um over, r imply add up for eah posible answe to the question Q the prod the probabiliy asigned to tha answe and the natural lgarihm of he probability Shannon went on o de ne the information in a meage as the dierene between two entropies, ne taintie: one that is asoiated with knowl edge before a mesage and te other tha i asoiated wih knowledge ater a me sage; in mbol, = SQ ) - SQ )
5' - ENROPY IN HERMODYAMICS wa dened by Rudolf lausis in in terms f a "anfomaion ha lways aom anies onvesion etwee thermal and ehaial enegy Aoding t asi fomla hen a system hanges frm tat desribed y o anthe state desried y ' the entopy hange S S i a lated by diiding eah ineen f e ersile he addition Q y th abslute tempeatre whih the he additio us and addin he oients ve he hange f sat ste '; the intega io sign syizes his themaia peratin. I a b hown ht Shannons fntin n lasius' fntin ae he s
(fl
ee questi a the klege
X [see uper iusrion on hs pge J
The athematial eitin f ha nn's etp has the terestig prpe t that if e rretl assigns p 1 t e f the asers a therefre) p t al the thers, s If u k the right aser, u hae uertait) On the ther ha, if all the prbabilities are equal, is a maimum If ur i fmati is s sight tht u ust as sig equal prbabilities, u are as u etai as pssible abut the aser) In the preeig isussi e use the klege X abut a questi t e e the etrp egaig the uer tait f the aser Cersel, e ul hae use t ee X b saig that a X that maimies X is a state f maimum igrae abut ma h es t kn e aser fm ather is as igrat abut as he a pssibl be The state f geater igrae s t t k Hee e a use the ha frma ism t esibe X quatitatiel Other ise X is a qualitatie ept Fr a gie questi stat) it is f urse pssible t hae ieet states f klege ha ee the i frati i a message i the fllig a message prdues a e X e X leas t a e assigmet f prbabilities a thus a e alue f T btai a measure f the ifrma tin ha ppse that the ifr ati be ee b the ieree beteen the t uertaities i sm bls, I X X' The fratin tet f a essage, the, s a measure f the hage in the bseer's klege frm klege befe the message t klege X' after the message) essage that tells u hat u alrea k prues n hage either i kege X reais the same) r i prbabilit assigment a therefre es ifrmati ha's measure is an enti It as esge t ll a spei nee: t prie a useful measure f hat is transmitte a mmuiatins han ne t has als bee shn t be the nl futin that satises erta basi re quireets f ifrmati ther I the eas sie ha put frar his easure thusas f papers hae bee ritten n the subjet a n e as fun a replaement futin, r een a nee fr e O the tar, man a ternatie eriatis hae been fun We lue that the hann entrp measure s funaetal i frati sene, just as te Pthagean thee s funamental eetr rin
ha's ept f etp shul be a useful startig pint fr easig abut frmati presses n general et ha f use hebeenr use befre ha In 1864 Rulf Clausius itrue the ter i his bk Abhdlungen er die me chnsche Weheorie t represet a tasfmati that alas ampa nies a nersi betee theral a mehaial eerg If a phsial sstem hages frm a state esrbe b X a partiular mbiati f pressure, emperature, mpsiti an ageti el, fr eample) t ather state e e b X' a ieret mbiatin f pressure, temperature, mpsiti a magneti el), the arig t the Clausius eitin, the etp hage is aluate b iiig eah iremet f eat aiti b the abslute tem peature at hih the heat aitin urs a aig the qutets see ower isrion on hs pge J Eept fr the fat that ha's etrp a Clausi us' etrp are repesete b the same smbl a the same ame, there ap pears at rst sight nthig t iiate that the t futis ae i fat the same futi What's i a ae? I the ase f ha 's measue the amig as t a ietal I 196 e f us Tribus) aske han hat he a thught abut hen he ha all re his famus easure han eple M greatest en as hat t all t thught f alling t ifrati, but the r as er use, s ee t al t uertait' When isusse t ith Jhn Neuman, e ha a bet ter iea Vn Neuman tl me, Yu shul al it etrp, fr t eass I the rst plae u ueraint fu tin has been use in statistial eha s une that ae, s t area has a ae n the se plae, a e mptat, n ne ks hat entrp reall s, s a ebate u ill aas hae the aatage' The pit behi Neua's jest is seus Clausius' eitin f entrp as e lttle iet phsa appeal It a be erie it satisfatr mathe atial igr an a be shn t hae nterestng an useful prpertes, par tiular n egineein, but a ret aestheti sense t has nt been satis fatr fr eeratns f stuents i ple psial aruents ea ne t be ee in the retness f st quan tties phss uruning Clausus' entrp thee as alas been an etra ste
The aearane of Shannon's ma sure, wth the same name and the sam untonal esentaton as th earle easure n statstal therodnamis, aoused great nterst among theortial hssts One of the bestknown ontibutos to the subsquent disussion was Lon Blloun, who teated the two entroies as the same in a sers of paes and n the book Science d nfo mion Theoy The oof that the are nded the same (and not mere analogues has ben deat wth xtensvl elsewhere an wl not be treated here
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of inforation s detrmined heb unit th hoie of the abitrar sae fator K in Shannon's nto fomua If K s made qual to the atio /ln 2 (where th exression n 2 rsnts the natura" loarithm of 2 thn S is said to be measured in bits" of nfoma ion ommon themodnmi oie or K s k where is the nuber of moeuls n the sstem onsded and s 138 X 10- oule dere Kelvn, a quantt kown as Boltmanns on stant Wth that hoie for K the entro of statstal mehans is x pssed n unts of oules e dgre The smlest themodnami sstm to wh w an al Shannons qua ton s a singe moeue that has an qual robabt of bng in ethr of two stats, for xaml an lmntar agnet In this ase both and equal 1/2, and hee S quals +k n 2 Th emoval of that uh unertaint oresonds to one bit of nfomtio Tefoe a bit is equal to k n 2, or ap oximatel 10- oule e dgre K Tis is an motant gure, the salest thrmodami en hange that an b assoiatd wih a masuement ied ng bt of nrmaion In lassi thmodams t has long ben kown tat te nto o mixing, r moua weit of mix tu, is a funion of th fationa om osition bvious the frational on ntration of a prtiua molua se es presnts the robabilt of ik ng out a oeule of that ses in a ando samng of the mixture What os the at of ixing signif f we use the no of xing as a masue of nfomaion? Imagine that we mix haf a oeua wigt of eah of two sotoes The esuting nto hange woud be ok n 2, where o (vogados numb, 6 10) s the nume o molues oeua wigt Nurial tis hane is about six oues r dge K, or 6 X 10 bis t t numbr rrsns t numbe of
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AXWLLS ON, a hypohel beg oked by Jame lek xwell a poble oator o the eod law o hemodm, wa umed o opere a mll rp doo eparag two veel ull o ar a a urm emperure t By opeg ad log the tapdoor o a to allow oly he we moleule o p rom to B d oly the lowe oe to p om B o he demo ould, whou expedtue o ork, e the tempeure o B ad lower th o tt odon to the eod lw o thermodyam. he demon w lly "exoed i 9 by eon Brillou, who poed out h he demon were to dey he moleule, he wold have to illume hem ome way, uig a ee epy ha would more hn ompete r ay dereae n eropy uh a beg ould ee Whout he pu eergy repreeted by the illumnao, he demo lk ue mo o he he eergy the moleule
esons ha would have o be made f a peson wee to sor he sotopes one at a me Just as he eno of nformaon has eanng onl n relaton o a welldene queston so the enrop of her odnam analss has meanng onl n relaon to a welldened ssem In our presen understandng of phsa sene ha sstem s ene b quan um heor The queston s: In wha quantum state s ths sstem" The an swer s In some satstal ombnaton of sates dene b he quanume hanal soluons of the wave equaton" n fat these solutons dene he poss bltes we alluded to n sussng nforaton an unerant The pob abltes enoe our knowledge abou he oupan of the possble quanum saes (possble that s for a gven state of knowledge) of an nherent onne eononet beween he enrop of Clausus and he ntuve noon of nformaton preeded Shannon's work b man ears n fa he nformatontheo aroah o hermonams s almost as old as hermodnams tself Clausus' 864 ook eresents he earles omlete ormulaon of lassal (nonsatstal) hermonams B 8 James Clerk
Maxwell ha nodued the role of n formaon b poposng h faous de mon see Maxwell Demon" b W Ehrenbeg; CIII IC No vembe 967] He suggesed hat a demon of mnue sze ough o be able o oerae a small rapdoor saratng wo vessels permng fas moleuls to move n one reon and slow ones n he other hereb reang a derene n emeature an pressure between the two vessels [see iustrtion on pe ceding pge] Maxwell's emon beame an nelltual thon n the sde of thermod namsts fo almos a entur The hal enge to he seond law of hemod nams was hs: Is he prnle of the nrease of entrop n all sontaneous proesses nvald where ntllgene nervenes Fro Maxwell's me on man leadpondered the rlaton ng beween observaton and nformaton on he one han and he seond law of hermodnas on he other For ex amle n 9 J D Van der Waals speulated on he elaton between en ro hange and he proess of rasonng fom ause o ee In 99 Leo Szlard ommened on he ntmate onneton between enrop hange and nformaon In 9 N Lews wrote: an n entop means loss of nfor
aon; othng more" Untl Shannon ame on the sene however here was no measure of nformaton so that the dsussons ould not be quanttatve What Shannon added was the reog nton hat nformaton tslf ould be gven a numeral masure If an of the earl hrmodnamsts had hosn to do so he ould have dnd nforma on to be onsstent wth thermodnam ento ft all the enro of mxng" was wll known n one of hose mn ould have hosn to dne nformaton as the number of dsons requrd to unsort" a mxtur The Shannon masure would hav followed Shannon who had no diret ntrst n thermodnams ndndntl develoed a masur of nformaton For ratal rasons he hose to requre the measure to t rtan logal rtera of onsstn and addtvt In rtro set a logan an how that wth hese rtera Shannon was bound to ro due a measure that would b onssten wth thermodnam entro On t s eognzed that the two subets de ve from ommon onsdratons t s straghtfowad o dve one from the oher The Shannon formulaton s somewha more gneral sne t s entrel a mathematal heor and s alable
ENRGY (JOULES)
INORMATION CONTEN (BITS)
ENERG PR INFORMATION (JOULES PER BIT)
TYPE ONE PAGE (ELETRI TYPEWRITER)
30.000
21000
1
TEEOPY ONE PAGE (TELEPHONE FASIMLE)
20000
21.000
5400
21000
3
500
21000
07
120.000
22,400
TRANSM T 3000 HARAERS OF DATA
14000
21000
7
READ ONE AGE OMUER OUUT (ENERGY OF LLUMNATION)
13000
50,400
3
SORT 3,000-ENRY BNARY FE (OMPUTER SYSEM)
2000
31000
06
PRNT ONE AGE OF OMUTER OUPUT (60 NES x 120 HARAERS)
500
50400
.03
ACTIVIY
CHARATER REORD ATIVITIES:
READ ONE PAGE (ENERGY OF ILLUMNATON) OPY ONE PAGE (XEROGRAPH OPY) DGTAL REORD AVTIES: KEYUN 40 OLLERITH ARDS
RAIOS OF ENERGY O INFORMAON or various inoma tion-preparation inormationproessing and inormationdistribu tion ativities involing symbols are presented in this table he energy values used are those typially involved in poering the mehanisms employed or these ativities and in most ases are
5
aurate only to about an order o magnitude For harater reords inormaton ontent is assumed to be about seven "bits pe ara ter he energy/inormation ratio or inomation systems based on harater eords and digitally enoded eords varies rom a e joules per bit don to a e hundredths o a joule per bit
to all kinds of nertaint. The thermo dnami theor is less general sine it is bond to or real wold" environment of atoms, moleules and energ. Bril oin tried to emhasie this distintion seaking of fee information" for the stra Shannon qantit and bond information" for the qantit when it desibed hsiall eal sitations (and ths themodnamis s we shall see in onsideing ratial informationroessing ativities, the onl real distin tion is that natral hsial sitations in volve mh larger amonts of information than we aear able to ontrol in or hmanoriented information sstems. There is no onit between abstrat Shannon information and thermodnami information, as long as the qestions we ask are hsiall eal qestions interesting aliation of informa An tion theor to themodnamis is
rvided b rilins exorising" of axwels demon. s we mentioned aove, the demon ed to aarent ther modnami aradoxes. Brilloin ointed ot that if the demon were to see the moleles, he wold have to illminate them in some seial wa. Sine the blakbod adiation in a gas vessel is the same in all diretions, withot a toh the demon wold have no wa of distinguishing the loation of individa gas moleules. It takes seial infomation to harness the eneg of the moleules, and this infomation is above and beond the norma themodnami infomation that serves to distingish the sstem itself from its srodings. Without the deartre from eqilibrim reeseted the torh, Maxwells demon aks the information on whih to at. Unlike the demon, we o not ive inside a gas vessel in eqilibrim at a niform temerate. Sose for a mo ment that we did. Imagine that the earth is ontained in a totall absorbing lak box" at a niform temerate of 90 degrees K. (6 degees Fahrenheit, a easonale estimate of the eal earths average sfae temeratre. We wold e as heless as Maxwells demon withot a toh. In site of the large energ x and the modeate averae srfae temeratre, an earth at eqilibrim in an ambient envionment wold be inhositabe to ife. No information ould be oessed; no eneg would be avaible in the themodnami sense. The atal ase is of ourse dierent The eath is at of a snearthsae" sstem that s qite ot of eqilibrim. The sun las the same ole fo us that the toh did for Maxwells demon. B oviding a deatre fom equilibim
it beomes a soe o information and sefl eneg. In onsidering the man se of en eg and information, we mst ake into aont the adiation balane of the earths surfae. The eah eeives 16 X 105 megawatthors of energ fom the sn eah ear in the fom of sola eletro magneti radiation, and it eradiates this energ iniall as blakbod adia tion. Ths the eart aroximatel balanes its eneg dget. Mans se of en erg on the earths surfae atall on stittes internal transations with eneg uxes that are thermodnamal avail able, that is, usale before the eneg is thermall degaded to the aveage sfae temeatre or hemiall degraded b dision to the environment. Taking ommonl aeted average values fo the temeatres of the sn and the earth, the 16 X 105 meawatthos of energ adiated to oute sae aries with it the aabiit fo an ento derease, o negento x," of 3 X 10 joles e degee K e ear, o 10 its e seond. Of ourse, this negentro ux derive fom the energ x fom the sn to the eath to dee sae. B stoing the ener g and negentro in vaios sstems (fossi fuels, akes, lods, green lants and so forth, the eath eates subss tems that ae ot of eqilibrim with the general envionment. In addition to the solar ux, then, we have the stoed energ and negentro of the eaths esore. Onl in the ase of the otential se of deteium in fusion reatos does this stored energ exist in amounts signiantl greate than one ears solaenerg ux. Fo atial uoses we ma onsider that both the energ ux and the negentro x at the eaths srfae are de to sola roesses. On the srfae of the earth, therefore, the maximm steadstate ate at whih infomtion an be sed to aet hsial roesses is of the order of 10 bits e seond. great deal of his information is sed" n meteoologial roesses (lod fomation, thnderstorms, the es tablishment of highaltitude lake and watesheds and so on). arge additional amont is sed" fo the ife resses of lants and animals. omarativel small qantit is nde the ontol of man, et this quantit is esonsile fo mans tehnologial eshaing of his envionment. The limitation of 10 its e seond is not a stringent one. Conside the info mation ate of a television broadast Television stations boadast 30 fames er seond, eah frame ontaining sa lines. The esoltion along eah
san line allows abot 630 bits of information to be enoded. The eslting information ate is 30 X X 630, or 07 bits er seond. Suose e now onsider a totall nonredndant television boadast one in whih eah dot is n orrelated with the othe dots on the same frame and eah frame is nrelated to other frames. No hman being old ibl absob information from a television tbe at sh a rate. Even if the material being broadast were a tial inted ae (and on sh a age there is a great del of orrelation between dots it wold take a erson of resonable skills abot 60 seonds to absob the inormation fom one frame. Ths e an estimate the robable bit rate reqired to engae a hman being in inteletl ttention as being less than 104 bits er seond. With a world oulation of less thn ve billion, the entire hman ae old have its information hannels individal sevied nd satated with a bit rate of X 10, ve mh less than the 10 bits e seond available an old mxims oint ot that talk is heaer than ation. omrison of the entro balane and the eneg balane on the srfae of the erth indi ates that the maxims are indeed a reetion of or exeriene. The amliation of information is esie than the amlation of ower. The total msleowe ott of the hman ae is estimated to be abot 3 X 10 megawatthors er ea (somewhat less than one megawatthor e erson e ear. orldwide ower sge nder hman diretion is of the order of 7 X 10 megawatthors r ear, so that the eergamliation ratio r entl is abot to one. In the . the amliation is mh larger: roxi matel 0 to one. If all the therod namiall available solar energ were sed, an amliation of 0000 to one is theoretiall ossible. The ossible amliation of inform tionroessing ativities is mh greater. B eliminating the hman oerator from the hain of dataroessg d mahine ontrol over hsial sstems, an diet deendene on the ntral te of human datahandling is removed. human oerato, working with a xe set of qestions, an se a mode digitl omte to amlif his bilities b a fator well in exess of 10, erhas a fator of 10. The weak limitation on in formationroessing rtes de to adi ation to sae (10 bits er seond) wold indiate the theoretial mximm amliation to be in exess of 10"4
e possibility of added ifoatio e for of ages of fot, boldfae, talis ad ote additos to sets of ar aters e eeg is te eergy volved i poerig the eaiss typially eplyed i ese ativities ad lluiaig pages for readig Mos of the values are auate o iti about a order of agiude I e table e alulaed the illuiao fro a 60 at lap Obviousy oe a also read uder a highpoer ar lap or by the ligh o a adle he eerg per ortio ui paly varies ro a e oues per bi do a e hudeds o a oule er bi iilar ioatio is oaied i he be o age or pratal equpet oguraios use i aiviies i volvig audo represeaios ad pitorialage represeaos We have used tpial values or slideproeor l luiaio, radio ad televiso reeiver poer ad telephoe etraloe po er Clearly he values vary i iividual isaes Addioal ueraties arse fro our estiates of iorao oet Audioitesity odulaio, pitoral gray sale ad olor ositute ultilevel odig teiques For ultilevel odig te iforaio aaiy of a ael is relaed to the sigalooise
ararisis as ell s o he freque adidth Fro a pratial poi of vie hoeve, te ale overstaes forao ote; he ul badidh is ever used i audio ativiies ad e typial ioial reord has a geat deal o reduda he values are hu aurae o less ha a order o agi ude, but tey are oeheess sugges ive A exee ase of reduda at teds a 3illieer pitorial iage of a page of pit Assug a resoluto o 00 lie pais per illieter, about o ilio bits are used to represet appoxiately 3,000 haraers Most o he ioraio s reduda ad is used to ovey te ite spaes, he detals of e arae fot ad oter aeria a ay e of o portae to the es sage Eve a fouleter ord ould tae up a llio its a ghresolui pho torap At te other extree a siple, oedudat olevel audo od a be used to represet he sae our lette ord oly 2 bits tehology has as oe of foaio its prese oers e est use of
eergy ad pysial srutures to o ve iforato as eeded for ua puposes, tou udue reduday
E + PoV To
� j Nj
E + Po To S To
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HREE EQUAIONS show the derivation of the onept of therodynai inoration he top equaton s based on assia therodynas: So is the nertainty when energy ( ), voue V and the nube of oes of various heia speies (N) are unreogni able beause they are distributed in an environent at a tepeature o a pressure o and hea potentias f o he idde equaton s deived fro the top one on the basis of the reation = So S here is inforation and S is the unertanty about the syste fored with energy voue V and oposition Nj and the syste is now disernible fro the environent hese equatons ere derved by Robert B Evans, now at the er gia Institute of ehnoogy, in 99 He shoed that a new quantity obtained by utipyng the idde equation by is the ost genera easure of disequiibriu or potentia ork Evans has naed this new quantity "essegy (for the essentia aspet of energy )
ad yet ih veraity, style ad as As a part of tat oe te oit poesses of eergy o ad ioratio o are of speial iterest e are led a to te osideratio of he eodyai fuis of a physal sys te hat is ivolved i iforatio proessig I he disussio hat follos e shall ae use o deas reetly developed by Robert Evas, o at e eorgia Isiute o eholo, ho has devoed a deade e uraveli o he uesio he oraioheory treae of heodyais aries he oept o equilibru A e oes thougt shoud serve o ove oe hat the oepts isiuishable ro the evroe ad Out of equilibriu are the sae Our abiliy to reoge a syse depeds the a tha it dies fro its eviroet herodyai orao is oeptualy he sae as egree o deparure o equilibi u I eah o hese quatites is ea sured i su a ay as to satisy te ee eary propertes of additivty, osisey ad ootoi rease i te systes sie, te apar fro us o easure ea ill e the sae atheaial expressio, sie thy really re fe to he sae ti erdyai foratio s de ed as e dieree etee o e ropies: = reers to the etropy of a syste of give eegy, olue ad opositio s the eropy of e ae syse of eegy, volu a o positio e t is iused ito (ids tiguisable a refereed evroet I easures te loss o iora o ot beig ale to disiuis te syse fo ts suroudigs (as he a eerg elts i he ope sea e idea of usi therodyai iforatio as a geeralie easure of he availaility o eergy as rst pu forad tetatively y Evas 1965 (Alouh eat eergy, ehaial eery ad eial eegy a be oeted oe aohe, tey ae ot equally available to do or Wha all aot eiey ad is ree eery ere veted o deal it e availability of eery y 1969 Evas subied his dotoral dissertatio otaig a etirey lassial poo at a e quatiy, obtaie y ultiplyi is forula or herodyai ifoaio y a appropriae eferee e peatur, has ost uusual pperties vas has alled tis e fuo essergy, or he esseia aspet of eergy [ee iusro ef He has deo strated hat essery is a uique easure o poeial or Moreover, i ior
The ging power mn: i futu lads pull pl u? Evey year, the U .S adds more generating capacty to ts el ectrcal systems than does all the rest of the free world And t's stll not enough Helpng Amerca's utl tes meet the g rowng n eed for more power s bg busness for Colt In dustres Today were better tan ever prepared to help, through o r nw letrc Utlt Sales Dvso, fomed to oer the nd ustry essental equ pment and systems from a un fed so rce Among the produs we sup ply are Central Moloey power ad srbuton trasormers ragng from gants andl ng hun dreds o ousas of kowas to m -n ts oy nhes
hgh and hghvoltage power crcut breakers to safegua rd costly trans msson systems Hund reds of m les of welded stan less steel tub ng fro m our Tret be Dvson go nto powerhouse condensers and heat exhangers O r desel ge erators are used for base loa a d peakng power generaton and nulear power lant proecton An you'l nd ou r Farbanks Morse pum ps a Q ny compressors, too even sysems to wegh the m l l ons of tons of coal consu med by tl tes Helpng keep Amera growng has been our a m ever snce Sam Colt massprouced the poneerng revolver
that tamed t he West Our dvsons and ther plants serve not only electrc utl tes ut vrtual l every other n dustry aomotve, aerospace and transportaton, chemca and petrochemcal, constructon, securty and defense, agrclt ure and food processng Over $665mll on n sales l ast year A sonofag n of a c ompan y Col Ind ustres, Park Avenue New Yor, New York Yo rem ember us e tame frontes
I is up here, is probably n here, n ths cholaly but comprehensible addition to the Haard Books on Astronomy series. f yo're a backyard asonomer, or a beginning studen f astrophysics, the completely revised edition f this highly-praise book tells he story, in imple and direct terms, of how pysics and stronomy work together llust rated $
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Th i s Ti m e, Mak e It A G if t Th at's A C OM P L I M E N
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Designed by nversty professors o teach nd hllenge thse who njy BRAIN - TO - BRAI ACTION. WFF 'N PROOF (lgic) $8.7 5' QUERIES N THEORIES (scienc & lnguge) 875 EQUATIONS (mhe atics) 5.0 ONSETS (set her) 5 . 50 PROPAGANDA (sl stes) 650 CONFIGU RATIONS (geoetry 550 6·GAME SPECAL (the boe 3495 Postg nlded Send ch ek to:
What's the foreca st for Aegeny Ludlum Indusries ? hats the forecast for power The explosive dmand for electr power has a whole i ndustry nnng j ust to keep up . And when the poe people moe, do we. Beca use our Walinford St l produs stainlss condnsr tubs or nucar powr plants stainlss stri or many aiations indin a nw ndrround ab wrap Spi Mtas mas sophistiat ih tmperatur aloys or trbine componnts and nuar rtors. heny Lulm Stl producs rain-orinted siicon sts for nerators and trnsormrs ctria aoys for motor ontrol reostats a n a host of otr trial spiatis rnold Eninerin contributes with Sictron cores or distribution and power transormrs nd tose are j ust te hih spots Whn tomorrow happens we'll b th r waitin or it in al the iht place Lie the power marke. Wating with a tihtlynt group of companies all ith interrelate technooies and all rowth oriented Wats the forecast fo Alegheny Ludlum Industres? Wee got our wok cut out fo . . . moe power to you. Aleheny Lulum Industries Inc. Dep t. B-4 Olive Bldg. Pittsburh Pa 5 2 2 2