22Zamonaviy ta'limda matematika, fizika va raqamli texnologiyalarning dolzarb muammolari va yutuqlari
Toshkent viloyati Chirchiq davlat pedagogika instituti
TERMODINAMIKA KURSIDA STATISTIK G'OYALARNI
SHAKLLANTIRISH
J. M. Abdullayev
Navoiy davlat pedagogika instituti, Navoiy, O'zbekiston
Termodinamikaning rivojlanishi statistik fizikaning rivojlanishi bilan bog'langanligini asosiy termodinamika kattaliklarning statistik talqinini tahlil etish orqali ko'rish mumkin. Shu o'rinda termodinmikaning ikkinchi qonuni statistk talqinini qaraylik.
Ma'lumki, gazlar kinetik nazariyasi nuqtai nazardan entropiyani tizim tartibsizligi o'lchovi sifatida qarash mumkin. Agar qaralayotgan tizimdan o'zgarmas bosimda issiqlik ajralib chiqsa entropiyaning kamayishi tizim tartiblanishi ortishi kuzatiladi. Bu holatni gazsimon moddaning qattiq holatga o'tishida yaqqol ko'rinadi. Gaz molekulalari tartibsiz harakatlanishi tajribalarda isbotlangan bunday gaz issiqlik chiqarish va uning molekulalari ma'lum bir holatni egallash mumkin. Ma'lum vaqt oralig'ida bu molekula shu holat atrofida tebranib turadi, lekin vaqt o'tishi bilan molekula suyuqlik ichida siljiydi. Shunday qilib suyuqlik ichida molekulalarning kichik hajmlarda tebranishi va bir vaqtning o'zida hajm bo'ylab siljish kuzatiladi. Haroratning yanada pasayishi suyuqlik entropiyasining ham kamayishiga issiqlik molekulalarining issiqlik harakati intensivligi pasayishiga olib keladi. Natijada suyuqlikning qotishi, tartibsizlikning va entropiyaning kamayishi, tartibsiz harakat kamayishi kuzatiladi. Bu holda molekulalar o'rtacha muvozanat holati atrofida tebranadi.
Gazlar kinetik nazariyasida sistemaning berilgan holatidagi entropiyasi va holatning termodinamik entropiyasi orasida funksianal bog'lanish mavjudligi isbotlangan. Buni tahlil etish uchun gaz holatidagi termodinmik sistemani qaraylik. Bunda gaz holatini makroskopik yoki mikroskopik parametrlar orqali ya'ni, gaz holatini bosim va haraorat orqali yoki alohida zarraning tezligi va koordinatasi orqali ifodalash mumkin.
Bu holda termodinamik parametrning bitta qiymatiga zarralarning turli tezliklari va koordinatalari erishish mumkinligini yoki boshqacha aytganda sistemaning bitta mikroholatiga bir qancha mikroholatlar to'g'ri kelishini hisobga olish kerak. Shuning uchun ham statistic fizikada har bir mikroholat shu holatni yuzga keltiruvchi mikroholatlar soni W(x) bilan xarakterlanadai va bu kattalik qaralayotgan makroholatlarning termodinamik ehtimoliyati deyiladi.
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Academic Research, Uzbekistan
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Zamonaviy ta'limda matematika, fizika va raqamli texnologiyalarning dolzarb muammolari va yutuqlari
Toshkent viloyati Chirchiq davlat pedagogika instituti
Agar sistemada termodinamik holatning o'z-o'zidan o'zgarishi kuzatilsa yangi holatda mikroholatlar soni ko'p ekanligini, ya'ni bu holatning termodinamik ehtimoliyati katta ekanligini ko'rsatadi. Bu esa o'z navbatida entropiyaning ortishiga ham olib keladi. Bolsman tomonidan sistemaning termodinamik ehtimoliyati va entropiya orasidagi quyidgi funksional bog'lanish mavjudligi aniqlangan:
5 = klnW(x) = klnN bu yerda, k —Bolsman doimiysi, W(x) —termodinamik ehtimollik, N —bitta makroholatga to'g'ri keluvchi mikroholatlar soni.
Bu ifodadan ko'rinadiki izolyatsalyangan sistemaning entropiyasi shu holat
ehtimolyatining logarifimiga to'g'ri mutanosib ekan. O'z navbatida tabiatdagi barcha
jarayonlar kam ehtimolli holatdan ehtimolligi katta holatga o'tishini hisoblasak
izolyatsiyalangan sistemaning entropiyasi ortib borish kerakligi ko'rinadi. Shunday
qilib, termodinamikaning ikkinchi qonunining statistik va fenomenologik ta'riflari
orasidagi umumiylik va farqlarni ko'rsatish mumkin: har ikkala ta'rif bo'yicha ham
entropiyaning ortishi tasdiqlansada statistik talqin bo'yicha entropiya ortishi bilan
kechadigan jarayonlar eng katta ehtimoliyatga ega jarayon, fenomenologik talqinda
esa bu jarayon mumkin bo'lgan yagona jarayon deb qaraladi[1].
Umuman olganda ko'p sonly zarralardan iborat oddiy sistemalarda eng katta
ehtimolli holat kutilishi aniq bo'lgan holat bilan mos tushadi. Buni muvozanat
holatdagi gazning ma'lum bir hajmida bosim o'zgarishini kuzatish orqali tahlil etish
mumkin. Bu hajmda bosmning o'z-o'zidan ortishini ehtimoliyatini qaraylik.
Issiqlik harakati tufayli qaralayotgan hajmdagi molekulalar soni biror o'rtacha N
qiymat atrofida fluktuatsiyalanadi. Bunga mos holda harorat, bosm, ichki energiya va
boshqa kattaliklar ham biror o'rtacha qiymat atrofida fluktuatsiyalanishi kuzatiladi.
Nazariy hisoblashlar fluktuatsiya qaralayotgan hajmdagi zarralar sonining kvadrat
i
ildiziga teskari proporsional ekanligini ko'rsatadi: S = Bu ifodani bosim uchun
AP 1 AP
qarasak, — = va N ^ da — « 0, ya'ni termodinamikaning ikkinchi qonuniga
ko'ra berilgan hajmda bosimning o'z-o'zidan ortishi mumkin emas.
Qaralayotgan hajmdagi zarralar soni ham, siyraklashgan bo'lsa fluktuatsiya
AP
chekli qiymatga ega bo'ladi. Masalan, N=100 ga teng bo'lsa, — = 0,1(10%).
Bu yerda termodinamikaning ikkinchi qonuni buziladi chunki bunday sistema uchun harorat, issiqlik miqdori entropiya tushunchalari o'z ma'nosini yuqotadi. Shunday qilib, termodinamikaning ikkinchi qonuni entropiyaning ortish qonuni (dS > 0) yoki sistemaning yuqori ehtimoliyatli holatga o'tish qonuni (AW(x) > 0) sifatida talqin etish mumkin ekan.
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Zamonaviv ta'limda matematika, fizika va raqamli texnologivalarning dolzarb muammolari va vutuqlari
Toshkent viloyati Chirchiq davlat pedagogika instituti
Shu o'rinda sistema ustida bajarilishi mumkin bo'lgan maksimal foydali ish ish eksergiyaning fizik talqinini qaraylik. Harorti Tt bo'lgan ishchi jism (gaz)ning T0 harortli muhitda bajarilishi mumkin bo'lgan ishi
T
Lmax = lQi = Qi(1-:0)
T1
T
ga teng. Ko'rinib turibdiki — qancha kichik bo'lsa, Q1 — issiqlik miqdorining
T1
bajargan ishi shuncha katta bo'ladi. Ikkinchi tomondan L = Qt — Q2 va Q2 = TAS ekanligini hisobga olsak, sistema ish qobilyatining kamayish entropiyasining o'zgarishi orqali ifodalash mumkin:
dL = T0dS
ya'ni entropiyaning oshishi eksergiyaning kamayishiga olib keladi[2].
Yuqorida qaralgan termodinamik parametrlarning statistik talqini pedagogika oily oily o'quv yurtlarida bo'lajak fizika o'qituvchilarini tayyorlash jarayonida molekulyar fizika va termodinamika hamda statistik fizika va termodinamika kurslarida tahlil etilishi ushbu fanlarni o'zlashtirishda muhim omil bo'lib xizmat qiladi. Shu bilan birgalikda ta'lim jarayonida termodinamik makroskopik va mikroskopik parametrlarning statistik mohiyatini taqqoslash ta'limning izchilligini ta'minlaydi.
REFERENCES
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Zamonaviv ta'limda matematika, fizika va raqamli texnologiyalarning dolzarb muammolari va vutuqlari
Toshkent viloyati Chirchiq davlat pedagogika instituti
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