Labari game da Zagayen Injin Carnot
Domin gano yadda za a ƙara ingancin injin zafi, wani masanin kimiyya ɗan Faransa mai suna Sadi Carnot (1796-1832) ya yi nazarin injin zafi mai kyau a ka'ida a shekarar 1824. A wancan lokacin, ba a tsara dokar farko ta thermodynamics ba, kuma ba a tsara dokar ta biyu ta thermodynamics ba. Ba a tsara dokar farko ba saboda masana kimiyya ba su san cewa zafi makamashi ne ba tukuna. Bayan Joule da abokansa sun gudanar da gwaje-gwaje a shekarun 1830, masana kimiyya sun san tabbas cewa zafi makamashi ne da ake canjawa saboda bambancin zafin jiki. Don haka an tsara dokar farko ta thermodynamics bayan 1830. Sadi Carnot ya yi nazarin injin zafi mai kyau a ka'ida a shekarar 1824. Binciken da ya yi a zahiri shine don ƙara ingancin injunan tururi waɗanda ake amfani da su a wancan lokacin. Yawancin injunan tururi a wancan lokacin ba su da inganci sosai.
Ana kiran zagayowar da ke cikin injin zafi mai kyau, wanda Sadi Carnot ya ƙirƙira, ana kiranta zagayowar Carnot. Kafin a sake duba zagayowar Carnot, yana da amfani a fahimci hanyoyin da ba za a iya canzawa ba. Kowace hanyar da ke faruwa ta halitta ta canza makamashi da canja wurin makamashi yawanci ba za a iya canzawa ba. Misali, idan muka shafa hannayenmu tare, suna jin dumi. A wannan yanayin, ana samar da zafi ta hanyar aikin da muke yi. Tsarin ba zai iya canzawa ba. Zafin da aka samar ba zai iya yin aiki da kansa ta hanyar shafa hannayenmu tare ba. Manufar injin zafi shine a sake juya wannan tsari kaɗan, inda za a iya amfani da zafi don yin aiki tare da mafi girman inganci. Domin injin zafi ya sami mafi girman inganci, dole ne mu guji duk hanyoyin da ba za a iya canzawa ba. Canja wurin zafi na halitta yawanci ba za a iya canzawa ba, saboda haka ana yin ƙoƙari don hana canja wurin zafi.
Lokacin da injin ya ɗauki zafi QH a wurare masu zafi mai yawa (T)H), dole ne sinadarin aiki a cikin injin ya kasance a zafin jiki na THHaka kuma, idan injin ya cire zafi QL a wurare masu ƙarancin zafi (T)L), dole ne sinadarin aiki a cikin injin ya kasance a zafin jiki na TLDon haka kowace hanya da ta shafi canja wurin zafi dole ne ta kasance mai isothermal (zafin jiki ɗaya). Akasin haka, idan zafin sinadarin da ke aiki a cikin injin yana tsakanin TH da kuma TL, dole ne babu canja wurin zafi tsakanin na'urar da wurin da ke da zafin jiki TH (mai samar da zafi) da kuma wurin da ke da zafin jiki TL (zubar da abu). Domin kada zafi ya fita, dole ne a gudanar da aikin ta hanyar adiabatic.
Tsarin Carnot a zahiri ya ƙunshi hanyoyin isothermal guda biyu masu juyawa da kuma hanyoyin adiabatic guda biyu masu juyawa.
Hoton da ke hannun dama yana nuna zagayowar Carnot don iskar gas mai kyau. Da farko, ana sha zafi yayin faɗaɗa isothermal (a-b). A lokacin faɗaɗa isothermal, zafin iskar gas a cikin silinda yana nan a tsaye.
Na gaba, iskar gas tana faɗaɗa ta adiabatic ta yadda zafinta zai faɗi daga T H zuwa T L (b-c). T H = babban zafin jiki (Babban zafin jiki), T L = ƙaramin zafin jiki (Ƙaramin zafin jiki). A lokacin faɗaɗa adiabatic, babu wani zafi da ke shiga ko fita daga silinda. Bayan haka, ana matse iskar a isothermally (c-d). A lokacin matsewar isothermal, zafin iskar gas yana nan daram. Na gaba, ana matse iskar adiabatic (d-a). Saboda an matse ta adiabatic, zafin iskar gas yana ƙaruwa. Zafin iskar gas yana ƙaruwa don haka matsin iskar gas ma yana ƙaruwa. Duk hanyoyin da ke cikin zagayowar Carnot ana iya mayar da su.
A lokacin faɗaɗawa da matsi na isothermal, zafin iskar gas yana nan a tsaye. Manufar ita ce a guji bambance-bambancen zafin jiki. Bambancin zafin jiki na iya haifar da canja wurin zafi (tsari mai canzawa). Domin tsarin isothermal ya faru (kiyaye yanayin zafin iskar gas ɗin akai-akai), dole ne a faɗaɗa ko a matse iskar gas a hankali. A zahiri, faɗaɗawa ko matsi na iskar gas yana faruwa da sauri. Wannan ya faru ne saboda rudani (tuna batun yanayin ruwa), gogayya, danko, da sauransu. Sakamakon haka, cikakken tsarin isothermal ba zai taɓa wanzuwa ba. Madadin haka, faɗaɗawa da matsi na adiabatic suna faruwa da sauri.
Manufar ita ce hana zafi shiga ko fita daga cikin silinda. Karkacewa, danko, da sauran abubuwa suna hana cikakken faɗaɗawa da matsewa na adiabatic. Yana da mahimmanci a lura cewa injin Carnot ka'ida ce kawai; ba ya wanzuwa a rayuwarmu ta yau da kullun. Kodayake a ka'ida, injin Carnot yana ba da gudummawa sosai ga ci gaban thermodynamics. Aƙalla, za mu iya gano duk wani tsari da ba za a iya canzawa ba wanda zai iya faruwa yayin aikin kuma mu yi ƙoƙarin rage su, don haka za mu ƙara ingancin injin zafi da aka tsara.
Wani muhimmin sakamako na injin Carnot shine cewa ga cikakken injin zafi, zafin da aka karɓa (Q H ) yana daidai da zafin T H kuma zafin da aka ƙi (Q L ) yana daidai da zafin T L. Don haka, ingancin cikakken injin zafi shine:
Misali tambaya ta 1:
Injin tururi yana aiki tsakanin 500 oC da 300 oC . Kayyade ingantaccen aiki (ingancin Carnot) na injin tururi.
Tattaunawa
Dole ne a canza zafin jiki zuwa ma'aunin Kelvin.
T H (zafin jiki mai yawa) = 500 o C = 500 + 273 = 773 K
T L (ƙananan zafin jiki) = 300 o C = 300 + 273 = 573 K
Inganci ko ingancin injin zafi mai kyau wanda ke aiki tsakanin 500 oC da 300 oC shine 26%. Idan injin da muke amfani da shi a rayuwar yau da kullun yana aiki tsakanin 500 oC da 300 oC , matsakaicin ingancin da injin zai iya samu yawanci shine kusan sau 0,7 mafi kyawun inganci (18,2%).
Misali tambaya ta 2:
Injin zafi yana karɓar Joules 600 na zafi (Q) a zafin jiki na 300 oC , yana yin Joules 100 na aiki (W) kuma yana ƙin 500 J a zafin jiki na 100 oC . Kayyade ainihin inganci da ingantaccen aiki (Ingancin Carnot) na wannan injin...
Tattaunawa
Dole ne a canza zafin jiki zuwa ma'aunin Kelvin.
T H (zafin jiki mai yawa) = 300 o C ‐‐‐ 300 + 273 = 573 K
T L (ƙananan zafin jiki) = 100 o C ‐‐‐ 100 + 273 = 373 K
Q H = 600 J
Q L = 500 J
Ingancin injin:
Inganci ko ingancin injin zafi mai kyau wanda ke aiki tsakanin 300 oC da 100 oC shine 35%. Matsakaicin ingancin da injin zai iya samu yawanci shine kusan sau 0,7 mafi kyawun inganci = 0,7 x 35% = 24,5% (24,5% x 600 J = 147 J na zafi da za a iya amfani da shi don yin aiki).
Ingancin wannan injin shine kashi 17% (100 J kawai ake amfani da shi don yin aiki). Har yanzu akwai kimanin 147 J – 100 J = 47 J na zafi da za a iya amfani da shi don yin aiki. Zai yi kyau idan za a iya ƙara ingancin wannan injin don rage asarar da muke yi.
Misali tambaya ta 3:
Inji yana karɓar Joules 1000 na zafi kuma yana samar da Joules 400 na aiki a kowane zagaye. Wannan injin yana aiki tsakanin 500 oC da 200 oC . Menene ainihin inganci da ingantaccen ingancin wannan injin?
Tattaunawa
T H (zafin jiki mai yawa) = 500 o C ‐‐‐ 500 + 273 = 773 K
T L (ƙananan zafin jiki) = 200 o C ‐‐‐ 200 + 273 = 473 K
Q H = 1000 J
Q L = 400 J
Ingancin injin:
Ingancin wannan injin shine:
Ingancin aiki mai kyau, wanda aka fi sani da ingancin Carnot, shine kashi 40%. Ingancin aiki mai kyau na injin shine kashi 60%. Irin wannan injin ba ya wanzuwa. Ba zai yiwu ba ingancin injin ya wuce ingancin Carnot.
Misali tambaya ta 4:
Domin ingancin injin Carnot ya kai kashi 100% (1), menene zafin shaye-shaye (TL ) da ake buƙata?
Tattaunawa
Domin ingancin injin zafi mai kyau ya kai kashi 100% (duk zafin shigarwa za a iya amfani da shi don yin aiki), zafin shaye-shaye (TL ) dole ne ya zama = 0 Kelvin.
Kai wa yanayin zafi na 0 Kelvin ba zai yiwu ba. Wannan magana ita ce doka ta uku ta thermodynamics.
Domin kuwa babu yadda za a cimma 0 Kelvin, cikakken injin zafi ba zai iya samun inganci 100% ba. Ko da cikakken injin zafi ba zai iya samun inganci 100% ba, balle ma injinan zafi da muke amfani da su a rayuwar yau da kullum.
Tunda injin zafi ba zai iya cimma inganci 100% ba, za mu iya yanke hukuncin cewa ba zai yiwu a yi amfani da dukkan zafin shigarwa (QH ) don yin aiki ba. Dole ne a rasa ɗan zafi (QL ).
Ba zai yiwu injin zafi (yana aiki a cikin zagayowar) ya canza dukkan zafi zuwa aiki ba (Dokar thermodynamics ta biyu - bayanin Kelvin-Planck).
Rubutun da aka yi wa rubutu mai ƙarfi a sama sanarwa ce ta musamman ta dokar thermodynamics ta biyu. Ana kiransa sanarwa ta musamman saboda yana aiki ne kawai ga injunan zafi. Saboda Kelvin da Planck sun tsara shi, ana kuma kiransa bayanin Kelvin-Planck. Lura da kasancewar kalmar "zagaye" a cikin bayanin da ke sama. Zagaye tsari ne da ke faruwa akai-akai. Don haka, injin zafi yana aiki akai-akai. An ƙara kalmar "zagaye" saboda, a zahiri, ana iya mayar da duk zafi zuwa aiki idan aikin ya faru sau ɗaya kawai.
A cikin dokar farko ta thermodynamics, an yi bayanin hanyoyin thermodynamic da dama, ciki har da hanyoyin isothermal, isobaric, isochoric, da adiabatic. A cikin tsarin isothermal, ana iya canza dukkan zafi zuwa aiki (Q = W). Wannan na iya faruwa idan tsarin ya faru a mataki ɗaya kawai. Ka lura da hoton da ke ƙasa:
Wannan jadawalin yana nuna tsarin isothermal (faɗaɗawar isothermal) wanda ke faruwa a mataki ɗaya. A cikin wannan tsari, duk zafin (Q) ana mayar da shi aiki (W). Adadin aikin da aka yi = yankin da aka yi inuwa.
Domin ya zama mai amfani, injin zafi dole ne ya yi aiki akai-akai (aikin dole ne ya faru akai-akai, ba a mataki ɗaya kawai ba). Misali, injin tururi mai juyawa. Piston a cikin injin tururi mai juyawa dole ne ya motsa akai-akai zuwa dama da hagu don tayar ta iya juyawa (ana iya amfani da shi don motsa wani abu). Tayar ba za ta iya juyawa ba idan piston ya motsa kawai zuwa dama, bayan haka ya tsaya (aikin yana faruwa ne kawai a mataki ɗaya). Idan aikin ya faru akai-akai (piston yana motsawa akai-akai zuwa dama da hagu), ba zai yiwu a mayar da dukkan zafin zuwa aiki ba (bayanin Kelvin-Planck). Misali, bari mu yi la'akari da tsarin isothermal da aka nuna a cikin jadawalin da ke sama.
Jadawalin da ke hagu yana nuna faɗaɗawar isothermal (kibiya ƙasa) da matsawar isothermal (kibiya sama). Tsarin yana faruwa akai-akai ta hanyar raba yanayi (ba a samar da wani aiki ba). Jadawalin da ke dama yana nuna faɗaɗawar isothermal (kibiya ƙasa), matsawar isobaric (kibiya hagu), da kuma tsarin isochoric (kibiya sama). Daga waɗannan jadawali guda biyu, a bayyane yake cewa ga hanyoyin da ke faruwa akai-akai (zagaye), akwai asarar zafi koyaushe. Wannan ya yi daidai da bayanin Kelvin-Planck na baya.
