Lissafi na Aiki da Makamashi a Tsarin Thermodynamic
Thermodynamics yana nazarin alaƙar da ke tsakanin zafi, aiki, da makamashi a cikin tsarin. A aikace—ko a cikin injunan abin hawa, tashoshin wutar lantarki, na'urorin damfara na masana'antu, ko ma firiji—ra'ayoyin aiki da makamashi suna da mahimmanci wajen nazarin ingancin tsarin, buƙatun wutar lantarki, da ikon samarwa ko shan makamashi. Wannan labarin ya tattauna yadda ake ƙididdige aiki da makamashi a cikin tsarin thermodynamic, manyan ra'ayoyin da suke buƙata, da misalan aikace-aikacensu a cikin hanyoyin asali.
1. Tsarin, iyakokin tsarin, da nau'ikan makamashi
Kafin mu yi lissafi, dole ne mu ayyana tsarin (ɓangaren da ake nazarinsa) da kuma kewayensa (a wajen tsarin). Iyakokin tsarin na iya zama na gaske (bangayen akwati) ko na tunani. Akwai rarrabuwa guda uku na gabaɗaya:
1. Tsarin rufewa: taro ba ya ketare iyakoki, amma makamashi zai iya.
2. Tsarin buɗewa (buɗaɗɗen tsarin/ƙarfin sarrafawa): nauyi da kuzari na iya ƙetare iyaka.
3. Tsarin da aka keɓe: babu musayar taro ko makamashi (wanda ya dace).
Makamashi a cikin thermodynamics yana bayyana a cikin manyan siffofi da dama:
– Makamashin ciki (U): makamashin da ke cikin ƙananan ƙwayoyin halitta ke amfani da shi saboda motsi da hulɗar ƙwayoyin halitta.
– Ƙarfin motsi (KE): mai alaƙa da saurin macroscopic na ruwa/abu, \(KE = \frac{1}{2} m V^2 \).
– Ƙarfin kuzari (PE): wanda ke da alaƙa da tsayi a cikin filin nauyi, \(PE = mgz \).
– Ƙarfin kwarara a cikin tsarin buɗewa sau da yawa yana bayyana a cikin nau'i \( pv \) (matsi yana ɗaukar takamaiman girma).
A cikin nazarin aiki, muna tantance wanne makamashi ne yake da mahimmanci. Misali, a cikin tanki mai tsayawa, sau da yawa ana yin watsi da canje-canje a cikin KE da PE. Duk da haka, a cikin injin turbine ko bututun ƙarfe, canje-canje a cikin KE na iya zama rinjaye.
2. Yi aiki a cikin thermodynamics
Aiki shine canja wurin makamashi wanda ke faruwa sakamakon tasirin da ke faruwa ta hanyar motsawa a kan iyakar tsarin. A cikin thermodynamics, yanayin alamun da aka fi amfani da su shine:
- Aiki daga tsarin yana da kyau (tsarin yana aiki).
– Shigar da aiki a cikin tsarin ba shi da kyau (muhalli yana aiki akan tsarin).
Nau'ikan aiki da aka saba amfani da su:
1. Aikin iyaka: yana faruwa ne lokacin da girman tsarin ya canza.
2. Aikin shaft: aikin injiniya ta cikin shaft, misali turbines da compressors.
3. Aikin lantarki: tsarin yana hulɗa ta hanyar wutar lantarki da ƙarfin lantarki.
4. Aikin saman da sauran siffofi (misali aikin bazara).
2.1 Iyakance aiki a cikin hanyoyin da ba su da tsari
Ga hanyoyin da ba su da tsauri ( matsi a kan iyakar tsarin an bayyana shi sosai), an bayyana aikin iyaka:
\[
W_b = \int_{V_1}^{V_2} p \, dV
\]
Darajar aiki ta dogara ne akan hanyar da tsarin yake tafiya, ba kawai yanayin farko da na ƙarshe ba. Wannan yana da mahimmanci: kodayake makamashin ciki aikin jiha ne, aiki ba haka bane.
Wasu lokuta na yau da kullun:
- Tsarin matsin lamba akai-akai (isobaric)
\[
W_b = p(V_2 – V_1)
\]
- Tsarin girma mai ɗorewa (isochoric)
Tunda \( dV = 0 \), to \( W_b = 0 \).
– Tsarin Polytropic \( pV^n = \text{constant} \)
Domin \( n \neq 1 \):
\[
W_b = \frac{p_2 V_2 – p_1 V_1}{1-n}
\]
Ga \( n = 1 \) (isotherm mai kyau na iskar gas):
\[
W_b = mRT \ln\left(\frac{V_2}{V_1}\right)
\]
Zaɓin samfurin tsari (isobaric, isothermal, adiabatic, polytropic) yana da matuƙar muhimmanci don tantance sakamakon lissafi, don haka ana buƙatar a bayyana bayanai ko zato a sarari.
3. Zafi da alaƙarsa da aiki
Zafi (Q) shine canja wurin makamashi saboda bambancin zafin jiki. A cikin wannan al'ada:
– \( Q > 0 \): zafi yana shiga tsarin.
– \( Q < 0 \): zafi yana barin tsarin.
A cikin thermodynamics, zafi da aiki nau'ikan canja wurin makamashi ne, ba "ƙarfin da aka adana ba." Ana bayyana kuzarin da aka adana ta hanyar \(U \), \(KE \), \(PE \), ko enthalpy \(H \).
4. Dokar Farko ta Thermodynamics: tushen lissafin makamashi
4.1 Tsarin rufewa
Dokar Farko ta bayyana kiyaye makamashi:
\[
\Delta E = Q - W
\]
tare da \(E = U + KE + PE \). Don haka:
\[
\Delta U + \ Delta KE + \ Delta PE = Q – W
\]
A cikin matsaloli da yawa, canje-canje a cikin \( KE \) da \( PE \) ƙanana ne don haka:
\[
\Delta U = Q – W
\]
Wannan shine tushen lissafin zafi ko aiki idan an san canjin makamashin ciki (misali daga teburin halaye ko daidaitaccen lissafin iskar gas).
4.2 Tsarin buɗewa (ƙarar sarrafawa) da daidaiton kuzarin kwarara mai ɗorewa
Don ingantaccen kwarara, shahararrun nau'ikan sune:
\[
\dot{Q} – \dot{W}_s = \dot{m}\left(h_2 – h_1 + \frac{V_2^2 – V_1^2}{2} + g(z_2 – z_1) \right)
\]
Nan:
– \( \dot{W}_s \) shine aikin shaft a kowane lokaci na raka'a.
– \(h \) shine enthalpy \( h = u + pv \), yana da matuƙar muhimmanci a cikin tsarin buɗewa saboda ya haɗa da kuzarin ciki da kuzarin kwarara.
Ana iya yin watsi da sassan \( \frac{V^2}{2} \) da \(gz \) a wasu lokutan, amma ga bututun ruwa/masu rarrabawa ko tsarin da ke da babban bambancin tsayi, dole ne a yi la'akari da waɗannan sassan.
5. Hanyoyin lissafin aiki da makamashi na gaba ɗaya
Wajen magance matsalolin thermodynamics, matakai na tsari suna taimakawa wajen guje wa kurakurai:
1. Bayyana tsarin (a rufe ko a buɗe) sannan a zana zane mai sauƙi.
2. Bayyana tsarin (isobaric, adiabatic, isothermal, polytropic, da sauransu).
3. Rubuta ma'aunin makamashi (Dokar I) bisa ga nau'in tsarin.
4. Gano adadin da aka yi watsi da shi (misali \( \Delta KE \approx 0 \)).
5. Yi amfani da alaƙar kadarori: teburin tururi, iskar gas mai kyau, ko lissafin yanayi.
6. Lissafa aikin daga integral \( \int p\,dV \) ko daga lissafin kuzarin kwarara.
7. Duba raka'o'i da alamomi (mai kyau/mara kyau bisa ga al'ada).
Kuskuren da aka saba gani shine a haɗa ma'anar aikin iyaka a cikin tsarin rufewa da aikin axis a cikin tsarin budewa, kuma a manta cewa aiki ya dogara da hanyar.
6. Misalan ra'ayoyin amfani a cikin na'urorin thermodynamic
6.1 Injin turbin
Turbines suna canza kuzarin ruwa zuwa aikin shaft. Don kwararar ruwa mai ɗorewa, sau da yawa ana ɗauka cewa adiabatic ne (\( \dot{Q} \approx 0 \)) kuma canjin tsayi ƙarami ne:
\[
\dot{W}_s \approx \dot{m}(h_1 – h_2)
\]
Idan saurin fita ya fi girma, to dole ne a haɗa canjin kuzarin motsi don hasashen wutar ya zama daidai.
6.2 Matsawa
Matsewar na'urar kwampreso tana buƙatar aikin shaft don ƙara matsin lamba. A ƙarƙashin yanayin adiabatic mai kyau, takamaiman aiki yana da alaƙa da ƙaruwar enthalpy:
\[
w_s \kimanin h_2 – h_1
\]
A zahiri, akwai asara don haka ana amfani da ingancin isentropic don danganta yanayi masu kyau da na gaske.
6.3 Silinda-piston (tsarin rufewa)
A fannin faɗaɗa iskar gas a cikin piston, ana ƙididdige aikin iyaka daga yankin da ke ƙarƙashin lanƙwasa \( p \)-\( V \). Idan tsarin yana da sauri kuma ba mai canzawa ba, matsin lamba na iya zama ba iri ɗaya ba don haka hanyar haɗin kai mai sauƙi tana buƙatar taka tsantsan ko amfani da matsin lamba na waje.
7. Ma'anar jiki: aiki, kuzari, da inganci
Lissafin aiki da makamashi ba wai kawai yana samar da lambobi ba ne, har ma yana ba da fahimtar yadda ake canja wurin makamashi da kuma inda asara ke faruwa. Dangane da inganci:
- Injin zafi niyya ga mafi girman aikin fitarwa daga zafin shigarwa.
– Tsarin sanyaya yana nufin wani takamaiman canja wurin zafi tare da ƙaramin aiki.
– A tsarin masana'antu, ingantawa galibi yana mai da hankali kan rage aikin matsewa, dawo da zafi na sharar gida, ko rage rashin iya jurewa.
Duk da cewa Dokar Farko ta tabbatar da cewa makamashi ba ya "ɓacewa," ingancin makamashi na iya raguwa saboda rashin juyawa - wanda aka ƙara yin nazari ta amfani da Dokar Biyu da kuma manufar entropy . A matsayin tushe, duk da haka, ƙwarewa ga Dokar Farko da lissafin aiki da makamashi muhimmin mataki ne na farko.
Kammalawa
Lissafin aiki da makamashi a cikin tsarin thermodynamic yana farawa da ma'anar tsarin, gano siffofin makamashi masu dacewa, da kuma amfani da Dokar Thermodynamics ta Farko . Ga tsarin rufewa, babban abin da aka fi mayar da hankali a kai shine canje-canje a cikin makamashin ciki da aikin iyaka \( \int p \,dV \). Ga tsarin buɗewa, enthalpy shine mabuɗin, kuma ana yin nazarin ta amfani da daidaitattun kuzarin kwarara mai ƙarfi waɗanda suka haɗa da aikin shaft da canje-canje masu yuwuwa a cikin kuzarin motsi da yuwuwar. Tare da tsarin tsari da fahimtar hanyoyin aiwatarwa, ana iya amfani da waɗannan lissafin don tantancewa da tsara nau'ikan na'urorin makamashi iri-iri daidai.
Idan kuna so, zan iya ƙara cikakkun misalan lambobi (misali faɗaɗa iskar gas ta polytropic ko ƙarfin turbine tare da bayanan enthalpy) don sanya labarin ya fi dacewa.
