
bahujana pravartthana niyamam

rasathanthrathil, raasapravarthanathinte nirakk prathipravartthanangalude pravartthanangalude allengil saandrathayude uthppannathin nerittu aanupaathikamaanenna nirddeshamaanu maas aakshan niyamam. chalanathmakamaaya santhulithaavasthayile parihaarangalude perumattangal ithu vishadeekarikkukayum pravachikkukayum cheiyunnu. prathyekichum, santhulithaavasthayilulla oru rasapravarthana mishrithathinu, prathipravarthanangaludeyum uthppannangaludeyum saandrata thammilulla anupatham sthiramaanennu ithu soochippikkunnu.
niyamatthinte prarambha roopeekaranathil rund vashangal ulppedunnu 1) santhulithaavasthayil oru prathikarana mishrithatthinte gadanayekkurichulla santulita vasham, 2) praadhamika prathikaranangalude nirakk samavakyangalekkurichulla gathikosham. kaatto emm nadatthiya gaveshanathil ninnaan rund vashangalum uthbhavikkunnath. 1864num 1879num idayil guldberg peettar vaje kainettik daattayum avar nirddeshicha nirakk samavaakyavum upayogichu santulita sthiraangangal uruthirinju. raasa santhulithaavasthayil munnottum pinnotum ulla prathikaranangalude prathikarana nirakk thulyamaayirikkenda oru chalanathmaka prakriyayaan raasa santhulithaavastha ennum guldberg vaje thiricharinju. gathikorjjathe aakarshikkunna santulita sthiraankathinte aavishkaaram labhikkunnathin, nirakk samavaakyathinte aavishkaaram upayogikkanam. nirakk samavaakyangalude aavishkaaram pinneedu jacobus henricus vaan 'tii hoff swathanthramaayi veendum kandethi.
santhulithaavasthayekkurichaavuri oru prasthaavanayaan niyamam, ithu raasa santhulithaavasthayude swabhaava savisheshathayulla alavaaya santulita sthiraankathinu oru aavishkaaram nalkunnu. aadhunika rasathanthrathil ithu santhulithamaaya thermodynamics upayogichaanu uruthirinjathu. rasasheshi enna aashayathiloodeyum ithu uruthirinjedukkaam.
charithram.
rund rasathanthranjar saadhaaranayaayi oru mishrithatthinte ghadanaye santhulithaavasthaye vivarikkunnathin uthppannathinte alavumaayi bandhapetta samkhyaa moolyangalude adisthaanathil prakadippichu.
reversible kemikkal reyaakshanukalekkurichulla claude luis bertholettinte aashayangale adisthaanamaakki kaatto maximilian guldberg peettar vaje 1864-ll maas aakshan niyamam nirddeshichu. danish bhashayil eee prabandhangal, 1867-leeii pilkkala prasidheekaranam (franch bhashayil) cheythathupole, valia thothil sradhikkappedaathe pooyi, athil oru parishkaricha niyamavum aaa niyamam adisthaanamaakkiyulla pareekshanathmaka daattayum adangiyirunnu.
1877-ll vaan 'tii hoff swathanthramaayi samanamaaya nigamanagalil ethi, pakshe munkaala srishtikalekkurichu ariyillaayirunnu, ithu guldberghin vejina avarude srishtikalekkurichu kooduthal poornnavum kooduthal vikasippichathumaya vivaranam jarmman bhashayil nalkaan prerippichu. vaan' tii hoff pinneedu avarude munganana sweekarichu.
1864.
santhulithaavastha (ghadana).
avarude aadya prabandhatthil, guldberg vaje nirddeshichathu, 
eiii, bii enniva thammilulla "raasabandham" allengil "prathikaranashakthi" munbu karuthiyirunnathupole prathipravartthanangalude raasa swabhaavathe mathramalla, oru prathipravartthana mishrithatthile oro prathipravartthanathinteyum alavineyum aasrayichirikkunnu. angane bahujana pravartthana niyamam aadyam iprakaaramaanu prasthaavichathu
eee saahacharyathil oru pakara prathikaranam <kemm> {alcohol} + assid <=> {esttar} + vaattar </kemm> poleyaayirunnu. 1879-leeii prabandhatthil active maassine "pravartthanameghalayile padaarthatthinte alavu" ennu nirvachichittundu. laayaniyile sajeeva pindam saandrathaykku thulyamaanu. kharapadaarthangale sambandhichidatholam, sajeeva pindam oru sthiraankamaayi kanakkaakkappedunnu. prayogatthiloode nirnnayikkenda _ 2, a, b ennee formulakal anubhavaparamaya sthiraangangalaayi kanakkaakkappettirunnu.
santhulithaavasthayil, munnottulla prathikaranatthe nayikkunna rasashakthi vipareeta prathikaranatthe nayikkunna raasashakthiykk thulyamayirikkanam. a, b, a ', b' ennivayude prarambha sajeeva pindangale p, q, p ', q' enningane ezhuthukayum santhulithaavasthayil verpeduthiya sajeeva pindatthe soothravaakyam _ 3 aayi rekhappeduthukayum cheyyumbol eee samathvathe prathinidheekarikkunnath
a ', b' enningane parivartthanam cheyyappetta a, b ennee reactorukalude alavine formula _ 3 prathinidheekarikkunnu. eee samavaakyathe adisthaanamaakkiyulla kanakkukoottalukal randaamathe prabandhatthil report cheythittundu.
santhulithaavasthayilekkal chalanathmaka sameepanam.
1864-leeii moonnaamathe prabandham athe santulita vyavasthayude gathikolppaadanathekkurinnu. oru ghattathil verpeduthiya sajeeva pindatthe x ennu ezhuthumbol prathikaranatthinte nirakk ingane nalki
athupole a 'b'-yumayullah vipareeta prathikaranam nalkia nirakkil thudarnnu
parivartthanatthinte mothatthilulla nirakk eee nirakkukal thammilulla vyathyaasamaan, athinaal santhulithaavasthayil (ghadana maarunnath nirtthumbol) rund prathikarana nirakkukalum thulyamayirikkanam. athinaal
1867.
guldbergilum vejinte 1864 leeii pepparilum nalkiyittulla nirakk padaprayogangal verthirichariyaan kazhinjilla, athinaal avaa inipparayunna reethiyil lalithamaakki. rasashakthi prathipravartthanangalude sajeeva pindangalude uthppannathin nerittu aanupaathikamaanennu anumanikkappettu.
ithu munbathe sidhaanthathinte a, b ennee ghaathaamkangal onninanusarichu krameekarikkunnathin thulyamaanu. aanupaathikatha sthiraankathe affinity sthiraangam, k ennu vilichirunnu. oru "ideal" prathikaranatthinulla santhulithaavasthaykku lalithamaaya roopam nalki.
[a] eq, [b] eq muthalaayava. santhulithaavasthayilulla sajeeva pindangalaanu iva. p, q muthalaaya reactorukalude prarambha alavukalude adisthaanathil. ithu maarunnu
affinity kofifishyantukalude anupatham, k '/k, oru santulita sthiraankamaayi thirichariyaan kazhiyum. gathikorja vashathekku thirinjunokkumbol, prathikaranatthinte vegatha, v, raasa bandhangalude (sakthikal) koottatthinu aanupaathikamaanennu nirddeshikkappettu. athinte ettavum lalithamaaya roopathil ithu padaprayogatthil kalaashikkunnu.
ivide soothravaakyam _ 13 aanupaathikatha sthiraankamaanu. yadhaarthathil, guldberg vaje kooduthal sankeernamaaya oru padaprayogam upayogichu, athu a yum a 'umm thammilulla prathipravartthanathinu anuvadichu. kooduthal sankeernamaaya aaa padaprayogangalkku chila ekadesha kanakkukal lalithamaakkunnathiloode, nirakk samavaakyam samyojippikkaan kazhiyum, athinaal santhulithamaaya alavu soothravaakyam _ 3 kanakkakkaan kazhiyum. 1867 leeii prabandhatthile vipulamaaya kanakkukoottalukal lalithamaaya aashayathin pinthuna nalki, athaayath,
ithu bahujana pravartthana niyamatthinte oru badal prasthaavanayaan.
1879.
1872-ll boltsman vikasippicheduthathu, 1879-leeii prabandhatthil prathikarana nirakk saandrathayude uthppannathin aanupaathikamaanenna anumaanam swatantra koottiyidikalude aavruthiyude adisthaanathil sookshumadarshanaparamaayi nyayeekarikkappettu (boltsman samavaakyam). santhulithaavasthayude yadhaartha sidhaantham eathu ekapaksheeyamaaya raasa santhulithaavasthaykkum baadhakamaakkaan saamaanyavalkkarikkaamennum nirddeshikkappettu.
eksponantukal α, β muthalaayava. prathikaranatthinte stoikiyometrik gunakangalaayi avaa aadyamaayi vyakthamaayi thirichariyappedunnu.
niyamatthinte aadhunika prasthavana.
1879 leeii pepparile affinity sthiraankangalaaya k +, k− enniva ippol nirakk sthiraangangalaayi thirichariyaan kazhiyum. munnottum pinnotum ulla prathikaranangalude nirakkukal thulyamaayi krameekarichaanu santulita sthiraankamaaya k uruthirinjathu. munnottum pinnotum ulla prathikaranangalude raasabandhangal thulyamaanennum ithu ardhamaakkunnu. thathfalamaayundaakunna aavishkaaram
ghaneebhavicha dravyathil vyaapanam.
praadhamika kuthichuchaattangaludeyum kanangaludeyum vaikalyangaludeyum kwaasichemikkal edapedalukaludeyum oru koottamaayi yakov frenkel ghaneebhavicha dravyathile vyaapana prakriya prathinidheekarichu. henry iring thante samboornna prathikarana nirakkukalekkurichulla sidhaantham vyaapanathinte eee kwaasichemikkal praathinidhyathinu prayogichu. defusionulla maas aakshan niyamam phick niyamatthinte vividha nonleeniyar pathippukalilekku nayikkunnu.
ganithashaasthra paristhithishaasthrathil.
lotka-voltera samavaakyangal predator-pray sisttangalude chalanaathmakathaye vivarikkunnu. irayude mail vettayaadalinte nirakk vettakkaarum irayum kandumuttunna nirakkin aanupaathikamaanennu anumaanikkappedunnu; eee nirakk "xy" aayi vilayiruthappedunnu, ivide "x" irayude ennamaanu, "y" vettakkaarude ennamaanu. ithu bahujana pravartthana niyamatthinte oru saadhaarana udaaharanamaanu.
ganithashaasthra epidemiology.
manushyarudeyum mrugangaludeyum mattu vyakthikaludeyum janasamkhyaye rogasadhyathayullathum rogabadhithavum rogamukthavumaaya (rogaprathirodha) vibhagangalaayi vibhajikkunna ganithashaasthra epidemiology padarunna rogathinte compartmental modalinte adisthaanamaanu maas aakshan niyamam. roga chalanaathmakathayude upayogapradamaaya amoortheekaranam nalkunna epidemiology compartmental modalukalude transmission temyude hridayathilaanu maas aakshan thathwam. sarr modalinte maas aakshan formulation niyamam inipparayunna praadhamika prathikaranangalude "kwaasichemikkal" samvidaanavumaayi poruthappedunnu 
gadakangalum praadhamika prathikaranangalum cherthu ganithashaasthra epidemiology maas aakshan modalukalude niyamatthinte sambannamaaya oru samvidaanam vikasippicheduthu.
manushyarilo mrugangalilo ulla vyakthikal anuyojyamaaya laayaniyile thanmaathrakalil ninnu vyathyasthamayi ekeekrithamaayi kalarunnilla. classical saar modalinte aouttputtukalum sis allengil seyir polulla lalithamaaya saamaanyavalkkaranangalum asaadhuvaaya eee noonn-homogenity mathiyaya mikacha chila roga udaaharanangalund. eee saahacharyangalil, kooduthal sankeernamaaya compartmental modalukalo distributed reaction-defusion modalukalo upayogapradamaayekkaam.
soshyophisiksil.
saamoohikavum raashtreeyavumaaya perumaattatthinte chila vashangal vivarikkan bhauthikashaasthrathil ninnum bhauthika rasathanthrathil ninnumulla upakaranangalum ashayangalum soshyophysics upayogikkunnu. manushyar avarude koottaaya jeevithathinte chila vashangalenkilum aattangaleppole perumaarunnath enthukondaanennum engane perumaarunnuvennum vishadeekarikkaan ithu shramikkunnu. saamoohika bhauthikashaasthrathil manushyarude edapedalukalude samavaakyam srishtikkunnathinulla pradhana upakaranamaan bahujana pravartthana niyamam (aavashyamenkil saamaanyavalkkarikkappetta).