Labarin da ya shafi Amfani da Dokar Farko ta Thermodynamics ga wasu hanyoyin Thermodynamics
A baya, mun tattauna Dokar Farko ta Thermodynamics kuma mun yi nazarin aikin da wani tsari ya yi. A wannan karon, za mu bincika wasu aikace-aikacen Dokar Farko ta Thermodynamics a cikin matakai huɗu na thermodynamic. Waɗannan matakai huɗu sune isothermal, isochoric, isobaric, da adiabatic. Waɗannan kalmomi sun samo asali ne daga Girkanci.
Tsarin Isothermal (zafin jiki mai ɗorewa)
Da farko, bari mu sake duba yadda aka yi amfani da dokar farko ta thermodynamics ga tsarin isothermal. A cikin tsarin isothermal, zafin tsarin yana nan a tsaye. Tsarin da muke nazari a ka'ida shine iskar gas mai kyau. Zafin iskar gas mai kyau yana daidai gwargwado kai tsaye da kuzarin ciki na iskar gas mai kyau (U = 3/2 nRT). Tunda T ya kasance mai daidaito, U kuma yana nan a tsaye. Saboda haka, idan aka yi amfani da shi ga tsarin isothermal, lissafin dokar farko ta thermodynamics zai zama:
Daga waɗannan sakamakon za a iya kammalawa cewa a cikin tsarin isothermal (zafin da ba ya canzawa), ana amfani da zafi (Q) da aka ƙara wa tsarin don yin aiki (W).
An nuna canje-canje a cikin matsin lamba da girma na tsarin a cikin tsarin isothermal a cikin jadawalin da ke ƙasa:
Da farko girman tsarin = V1 (ƙaramin girma) da matsin lamba na tsarin = P1 (matsin lamba mai yawa). Domin kiyaye yanayin zafin tsarin ya kasance daidai, bayan an ƙara zafi a cikin tsarin, tsarin yana faɗaɗa kuma yana aiki akan muhalli. Bayan tsarin ya yi aiki akan muhalli, girman tsarin yana canzawa zuwa V2 (ƙarfin tsarin yana ƙaruwa) kuma matsin lambar tsarin yana canzawa zuwa P2 (matsin tsarin yana raguwa). Jadawalin yana lanƙwasa saboda matsin tsarin baya canzawa akai-akai yayin aikin. Adadin aikin da tsarin yayi = yankin da aka yi inuwa.
Tsarin Adiabatic
A cikin tsarin adiabatic, babu wani zafi da aka ƙara ko aka bar shi a cikin tsarin (Q = 0). Tsarin adiabatic na iya faruwa a cikin tsarin rufewa, mai tsari mai tsari. Ga tsarin rufewa mai tsari, yawanci babu zafi da ke gudana cikin tsarin ko barin shi yadda ya ga dama. Tsarin adiabatic kuma na iya faruwa a cikin tsarin rufewa, wanda ba shi da tsari.
A wannan yanayin, dole ne a aiwatar da tsarin da sauri don kada zafi ya sami lokacin shiga ko fita daga tsarin. Idan aka yi amfani da shi ga tsarin adiabatic, lissafin Dokar Farko ta Thermodynamics ya canza zuwa wannan tsari:
Idan tsarin ya matse da sauri (ana yin aiki akan tsarin), to aikin yana da kyau. Saboda W yana da kyau, to U yana da kyau (makamashi a cikin tsarin yana ƙaruwa). Akasin haka, idan tsarin ya faɗaɗa ko ya faɗaɗa da sauri (tsarin yana aiki), to W yana da kyau. Domin W yana da kyau, to U yana da kyau (makamashi a cikin tsarin yana raguwa). Makamashi a cikin tsarin (iskar gas mai kyau) yana daidai da zafin jiki kai tsaye (U = 3/2 nRT), saboda haka idan makamashi a cikin tsarin ya ƙaru to zafin tsarin ma yana ƙaruwa. Akasin haka, idan makamashi a cikin tsarin ya ragu to zafin tsarin yana raguwa.
An nuna canje-canje a cikin matsin lamba da girma na tsarin a cikin tsarin adiabatic a cikin jadawalin da ke ƙasa:
Idan tsarin ya matse da sauri (ana yin aiki akan tsarin), to aikin yana da kyau. Saboda W yana da kyau, to U yana da kyau (makamashi a cikin tsarin yana ƙaruwa). Akasin haka, idan tsarin ya faɗaɗa ko ya faɗaɗa da sauri (tsarin yana aiki), to W yana da kyau. Domin W yana da kyau, to U yana da kyau (makamashi a cikin tsarin yana raguwa). Makamashi a cikin tsarin (iskar gas mai kyau) yana daidai da zafin jiki kai tsaye (U = 3/2 nRT), saboda haka idan makamashi a cikin tsarin ya ƙaru to zafin tsarin ma yana ƙaruwa. Akasin haka, idan makamashi a cikin tsarin ya ragu to zafin tsarin yana raguwa.
An nuna canje-canje a cikin matsin lamba da girma na tsarin a cikin tsarin adiabatic a cikin jadawalin da ke ƙasa:
Layin adiabatic a cikin wannan jadawalin (layi 1-2) ya fi layi na isothermal (layi 1-3). Wannan bambancin tsayi yana nuna cewa ga irin wannan ƙaruwar girma, matsin tsarin yana raguwa sosai a cikin tsarin adiabatic idan aka kwatanta da tsarin isothermal. Matsin tsarin yana raguwa sosai a cikin tsarin adiabatic saboda lokacin da faɗaɗa adiabatic ya faru, zafin tsarin shima yana raguwa. Zafin jiki yana daidai da matsin lamba kai tsaye, saboda haka, idan zafin tsarin ya ragu, matsin tsarin shima yana raguwa. Akasin haka, a cikin tsarin isothermal, zafin tsarin yana ci gaba da kasancewa akai-akai. Saboda haka, a cikin tsarin isothermal, zafin jiki baya shafar raguwar matsin lamba.
Misali ɗaya na tsarin da ke kusantar matsawar adiabatic yana faruwa a cikin injunan konewa na ciki, kamar injunan dizal da fetur. A cikin injin dizal, ana jan iska zuwa cikin silinda kuma ana matse ta da sauri ta amfani da piston (ana yin aiki akan iska). Tsarin matsewar adiabatic (rage girman tsarin) an kwatanta shi da lanƙwasa 2-1. Saboda iskar tana matsewa da sauri ta hanyar allura, zafin iskar yana tashi da sauri. A lokaci guda, ana fesa dizal cikin silinda ta hanyar allura, kuma cakuda yana ƙonewa nan da nan (ƙonewa yana faruwa). A cikin injin mai, ana jawo cakuda iska da mai a cikin silinda kuma ana matse shi da sauri ta amfani da piston. Saboda matsewar tana da sauri adiabatic, zafinta yana tashi da sauri. A lokaci guda, toshewar walƙiya tana haifar da walƙiya, tana haifar da ƙonewa.
Tsarin Isochoric (ƙari mai ɗorewa)
A cikin tsarin isochoric, girman tsarin yana nan a tsaye. Saboda girman tsarin yana nan a tsaye, tsarin ba zai iya yin aiki a kan muhalli ba. Haka nan, muhalli ba zai iya yin aiki a kan tsarin ba. Idan aka yi amfani da shi ga tsarin isochoric, lissafin Dokar Farko ta Thermodynamics zai zama:
Daga waɗannan sakamakon, za mu iya kammala da cewa a cikin tsarin isochoric (ƙara mai ɗorewa), ana amfani da zafi (Q) da aka ƙara wa tsarin don ƙara kuzarin ciki na tsarin.
Canje-canje a cikin matsin lamba da girma na tsarin a cikin tsarin isochoric an nuna su a cikin jadawalin da ke ƙasa:
Da farko, matsin lamba na tsarin = p 1 (ƙarancin matsin lamba). Ƙara zafi ga tsarin yana sa kuzarin ciki na tsarin ya ƙaru. Saboda kuzarin ciki na tsarin yana ƙaruwa, zafin tsarin (iskar gas mai kyau) yana ƙaruwa (U = 3/2 nRT). Zafin jiki yana daidai da matsin lamba kai tsaye. Saboda haka, idan zafin tsarin ya ƙaru, matsin lamba na tsarin yana ƙaruwa (p 2 ). Saboda girman tsarin yana dawwama, babu wani aiki da aka yi (babu yanki mai inuwa).
Kamar yadda aka faɗa a baya, a cikin tsarin isochoric, tsarin ba zai iya yin aiki a kan muhalli ba. Haka nan, muhalli ba zai iya yin aiki a kan tsarin ba. Wannan saboda a cikin tsarin isochoric, girman tsarin yana nan daram, ma'ana ba ya canzawa. Wasu nau'ikan aiki ba sa buƙatar canje-canje a cikin girma. Saboda haka, ko da girman tsarin ya kasance daidai, ana iya yin aiki a kan tsarin. Misali, fanka da baturi suna cikin akwati mai rufewa. Fanka na iya juyawa ta amfani da kuzarin da batirin ke bayarwa. A wannan yanayin, fanka, baturi, da iska a cikin akwati ana ɗaukar su a matsayin tsarin.
Idan fanka ta juya, tana aiki a kan iskar da ke cikin akwati. A lokaci guda, makamashin motsi na fanka yana canzawa zuwa makamashi a cikin iska. Ƙarfin wutar lantarki da ke cikin batirin yana raguwa ta halitta saboda an mayar da shi makamashi a cikin iska. Wannan misali ya nuna cewa a cikin tsari na isochoric (ƙarfin da ba ya canzawa), har yanzu ana iya yin aiki akan tsarin (aikin da ba ya haɗa da canjin girma).
Tsarin isobaric (matsi mai ɗorewa)
A cikin tsarin isobaric, matsin lambar tsarin yana nan a tsaye. Saboda matsin lamba ne, canje-canje a cikin makamashin ciki (delta U), zafi (Q), da aiki (W) a cikin tsarin isobaric ba sa taɓa zama sifili. Don haka, dokar farko ta thermodynamics ta kasance cikakke:
ΔU = Q - W
An nuna canje-canje a cikin matsin lamba da girma na iskar gas a cikin tsarin isobaric a cikin jadawalin da ke ƙasa:
Da farko, girman tsarin = V1 ( ƙaramin girma). Saboda matsin lamba yana ci gaba da kasancewa akai-akai, bayan an ƙara zafi a cikin tsarin, tsarin yana faɗaɗa kuma yana aiki akan muhalli. Bayan yin aiki akan muhalli, girman tsarin yana canzawa zuwa V2 (ƙarfin tsarin yana ƙaruwa). Adadin aikin (W) da tsarin yayi = yankin da aka yi inuwa.
Misali tambaya ta 1:
Lanƙwasa 1-2 a cikin zane-zane biyu da ke ƙasa suna nuna faɗaɗar iskar gas (ƙaruwar yawan iskar gas) wanda ke faruwa ta adiabatic da kuma ta isothermally. A wace hanya ce aikin da iskar gas ɗin ke yi ya fi ƙasa?
Aikin da iskar gas ke yi a cikin tsarin adiabatic ya yi ƙasa da aikin da iskar gas ke yi a cikin tsarin isothermal. Yankin da aka yi inuwa = aikin da iskar gas ke yi a lokacin tsarin faɗaɗawa (ƙara yawan iskar gas). Yankin da aka yi inuwa a cikin tsarin adiabatic ya yi ƙasa da yankin da aka yi inuwa a cikin tsarin isothermal.
Misali tambaya ta 2:
An nuna jerin hanyoyin thermodynamic a cikin zane a ƙasa. Lanƙwasa a-b da d-c = hanyoyin isochoric (ƙara mai ɗorewa). Lanƙwasa b-c da a-d = hanyoyin isobaric (matsi mai ɗorewa). A cikin tsari a-b, an ƙara Joules 600 na zafi (Q) zuwa tsarin. A cikin tsari b-c, an ƙara Joules 800 na zafi (Q) zuwa tsarin. Ƙayyade:
a) Canje-canje a cikin makamashin ciki a cikin matakai a-b
b) Canje-canje a cikin makamashin ciki a cikin tsarin a-b-c
c) Jimlar zafi da aka ƙara a cikin tsarin a-d-c
P 1 = 2 x 10 5 Pa = 2 x 10 5 N/m 2
P 2 = 4 x 10 5 Pa = 4 x 10 5 N/m 2
V 1 = lita 2 = 2 dm 3 = 2 x 10 ‐3 m 3
V 2 = lita 4 = 2 dm 3 = 4 x 10 ‐3 m 3
Tattaunawa
a) Canje-canje a cikin makamashin ciki a cikin matakai a-b
A cikin tsarin a-b, ana ƙara zafi 600 J a cikin tsarin. Tsarin a-b tsari ne na isochoric (ƙara mai ɗorewa). A cikin tsarin isochoric, ƙara zafi a cikin tsarin yana ƙara kuzarin ciki na tsarin ne kawai. Don haka, canjin makamashin ciki na tsarin bayan karɓar gudummawar zafi shine:
ΔU = Q
ΔU = 600 J
b) Canje-canje a cikin makamashin ciki a cikin tsarin a-b-c
Tsarin a-b = tsarin isochoric (ƙarfin da ba ya canzawa). A cikin tsari a-b, an ƙara zafi 600 J.
zuwa ga tsarin. Tunda girman yana nan daram, babu wani aiki da tsarin ke yi.
Tsarin b‐c = tsarin isobaric (matsi mai ɗorewa). A cikin tsarin b‐c, ana ƙara Joules 800 na zafi (Q) zuwa tsarin. A cikin tsarin isobaric, tsarin zai iya yin aiki. Adadin aikin da tsarin ke yi a cikin tsarin b‐c (tsarin isobaric) shine:
W = P (V2 - V1 ) --- matsin lamba mai ɗorewa
W = P2 ( V2 - V1 )
W = 4 x 10 5 N/m 2 (4 x 10 ‐3 m 3 ‐ 2 x 10 ‐3 m 3 )
W = 4 x 10 5 N/m 2 (2 x 10 ‐3 m 3 )
W = 8 x 10 Joules 2
W = Joule 800
Jimillar zafin da aka ƙara wa tsarin a cikin tsarin a-b-c shine:
Jimlar Q = Q ab + Q bc
Jimlar Q = 600 J + 800 J
Jimlar Q = Joule 1400
Jimillar aikin da tsarin ya yi a tsarin a-b-c shine:
Jimlar W = W ab + W bc
Jimlar W = 0 + W bc
Jimlar W = 0 + Joule 800
Jimlar W = Joule 800
Canjin makamashi a cikin tsarin a cikin tsarin a-b-c shine:
ΔU = Q - W
ΔU = 1400 J − 800 J
ΔU = 600 J
Canji a cikin makamashin ciki a cikin tsari a-b-c = 600 J
c) Jimlar zafi da aka ƙara a cikin tsarin a-d-c
Ana iya samun jimlar zafi da aka ƙara wa tsarin ta hanyar lissafin da ke ƙasa:
ΔU = Q - W
Q = ΔU + W
Jimlar zafi da aka ƙara a cikin tsarin a‐d‐c = canjin makamashin ciki a cikin tsarin a‐d‐c + jimlar aikin da aka yi a cikin tsarin a‐d‐c.
Zafi da aiki suna da hannu wajen canja wurin makamashi tsakanin tsarin da kewayensa, yayin da canje-canje a cikin makamashin ciki ke faruwa ne sakamakon canja wurin makamashi tsakanin tsarin da kewayensa. Saboda haka, canje-canje a cikin makamashin ciki ba su da alaƙa da tsarin canja wurin makamashi. Akasin haka, zafi da aiki sun dogara sosai akan tsarin. A cikin tsarin isochoric (ƙaramin ci gaba), canja wurin makamashi yana faruwa ne kawai a cikin yanayin zafi, amma ba aiki ba. A cikin tsarin isobaric (matsi mai ci gaba), canja wurin makamashi ya ƙunshi zafi da aiki. Ko da yake ba ya bambanta da tsarin, canje-canje a cikin makamashin ciki ya dogara ne akan yanayin farko da na ƙarshe na tsarin. Idan yanayin farko da na ƙarshe iri ɗaya ne, canjin makamashin ciki zai kasance iri ɗaya koyaushe, koda kuwa hanyoyin da abin ya shafa sun bambanta.
Yanayin farko da yanayin ƙarshe na tsarin a-b-c a cikin jadawalin da ke sama = yanayin farko da yanayin ƙarshe na tsarin a-d-c. Don haka, canjin makamashin ciki a cikin tsarin a-d-c = 600 J.
Jimlar aikin da aka yi (W) a cikin tsarin a-d-c = W a cikin tsarin a-d + W a cikin tsarin d-c.
Tsarin a-d tsari ne na isobaric (matsi mai ɗorewa), yayin da tsarin d-c tsari ne na isochoric (ƙarfin da ke ɗorewa). Saboda girman yana da daidaito, babu wani aiki da aka yi a tsarin d-c. Da farko, muna ƙididdige aikin da aka yi a tsarin a-d.
W ad = P ( V2 - V1 )
W ad = P1 ( V2 - V1 )
W ad = 2 x 10 5 N/m 2 (4 x 10 ‐3 m 3 ‐ 2 x 10 ‐3 m 3 )
W ad = 2 x 10 5 N/m 2 (2 x 10 ‐3 m 3 )
W ad = 4 x 10 Joule 2
W ad = Joule 400
Jimlar W = W a cikin tsari a‐d + W a cikin tsari d‐c
Jimlar W = Joules 400 + 0
Jimlar W = Joule 400
Saboda haka, adadin zafi da aka ƙara wa tsarin a-d-c shine:
Q = ΔU + W
Q = 600 J + 400 J
Q = 1000 J
Misali tambaya ta 3:
Lita 1 na ruwa yana juyawa zuwa lita 1671 na tururi idan aka tafasa a matsin lamba na atm 1. Kayyade canjin kuzarin ciki da adadin aikin da ruwan ya yi lokacin da ya ƙafe… (Zafin tururin ruwa = L V = 22,6 x 10 5 J/Kg)
Tattaunawa
Yawan ruwa = 1000 kg/ m3
L V = 22,6 x 10 5 J/Kg
P = 1 atm = 1,013 x 10 5 Pa = 1,013 x 10 5 N/m 2
V 1 = lita 1 = 1 dm 3 = 1 x 10 ‐3 m 3 (Yawan ruwa)
V 2 = lita 1671 = 1671 dm 3 = 1671 x 10 ‐3 m 3 (Ƙarar tururi)
a) Canje-canje a cikin makamashin ciki
Canji a cikin makamashin ciki = Zafi da aka ƙara wa ruwa - Aikin da ruwa ke yi idan ya ƙafe. Da farko, bari mu ƙididdige zafi (Q) da aka ƙara wa ruwa...
Q = mL V
Nauyin ruwa (m)?
Yawan ruwa = yawan ruwa / girman ruwa
Nauyin ruwa (m) = (yawan ruwa) (yawan ruwa)
Nauyin ruwa (m) = (1000 kg/m3 ) ( 1 x 10 ‐3 m3 )
Nauyin ruwa (m) = (1000 kg/m3 ) (0,001 m3 )
Nauyin ruwa (m) = 1 Kg
Q = (1 kg)(22,6 x 10 5 J/kg)
Q = 22,6 x 10 5 J
Lissafa aikin (W) da ruwan ya yi lokacin da ya ƙafe. Tafasar ruwa tana faruwa ne a matsin lamba akai-akai (tsarin isobaric).
W = p (V 2 – V 1 )
W = 1,013 x 10 5 N/m 2 (1671 x 10 ‐3 m 3 – 1 x 10 ‐3 m 3 )
W = 1,013 x 10 5 N/m 2 (1670 x 10 ‐3 m 3 )
W = 1691,71 x 10 Joules 2
W = 1,7 x 10 Joules 5
Canje-canje a cikin makamashi a cikin ruwa:
ΔU = Q - W
ΔU = 22,6 x 10 5 J - 1 .7 x 10 5 J
ΔU = 20,9 x 10 5 J
ΔU = 21 x 10 5 J
Ana amfani da zafi mai girman 21 x 10 5 J da aka ƙara wa ruwan don ƙara kuzarin cikinsa (cin nasara kan ƙarfin jan hankali tsakanin ƙwayoyin da ke riƙe ruwan). A wata ma'anar, ana amfani da 21 x 10 5 J don canza ruwan zuwa tururi. Da zarar ruwan ya zama tururi, ana amfani da sauran 1,7 x 10 5 J don yin aiki.
Misali tambaya ta 4:
Mole 1 na iskar gas a cikin silinda yana faɗaɗa da sauri ta hanyar dual. Zafin farko na iskar gas shine 1000 K. Bayan faɗaɗawa, zafin iskar gas ɗin yana raguwa zuwa 500 K. Kayyade aikin da iskar gas ɗin ta yi... Tattaunawa
Faɗaɗar iskar gas tana faruwa ne ta hanyar adiabatic. A cikin tsarin adiabatic, babu wani zafi da ke shiga ko fita daga tsarin. Saboda haka, aikin da iskar gas ke yi = canjin makamashin cikin iskar gas. A lissafi, an rubuta wannan kamar haka:
ΔU = Q − W ko W = Q − Δ U → Q = 0
W = 0 − ΔU
W = − ΔU
Za mu iya ƙididdige canjin makamashin ciki na iskar gas ta amfani da daidaitaccen lissafin makamashin ciki na iskar gas:
ΔU = ƙarshen U - farkon U
ΔU = 3/2 nR (T na ƙarshe - T na farko)
ΔU = 3/2 (1 mol) (8,315 J/mol.K) (500 K - 1000 K)
ΔU = 3/2 (1 mol) (8,315 J/mol.K) (-500 K)
ΔU = ‐6236,25 J
Saboda haka, adadin aikin da iskar gas ke yi shine:
W = − ΔU
W = − ( − 6236, 25 J )
W = 6236, 25 J
