Tsarin Thermodynamic na Labari: Isothermal Adiabatic Isochoric Isobaric
Akwai matakai guda huɗu na thermodynamic, wato Isothermal, isochoric, isobaric da adiabatic process.
Tsarin Isothermal (zafin jiki mai ɗorewa)
A cikin tsarin isothermal, zafin tsarin yana kasancewa daidai. A ka'ida, tsarin da aka bincika shine iskar gas mai kyau. Zafin iskar gas mai kyau yana daidai gwargwado kai tsaye da makamashin iskar gas mai kyau (U = 3/2 n RT). T baya canzawa, don haka U shima baya canzawa. Don haka, idan aka yi amfani da shi ga tsarin isothermal, dokar farko ta lissafin thermodynamic ta zama:
Δ U = Q – W
Makamashin ciki ba ya canzawa, don haka Δ U = 0.
0 = Q – W
Q = W
Dangane da wannan lissafi, a cikin tsarin isothermal (zafin jiki mai ɗorewa), ana amfani da zafi (Q) da aka ƙara wa tsarin don yin aiki (W).
An kwatanta canjin matsin lamba da girma na tsarin a cikin tsarin isothermal ta hanyar jadawalin da ke ƙasa:
Girman tsarin farko = V1 (ƙaramin girma) da matsin lamba na tsarin = P1 (babban matsin lamba). Domin zafin tsarin ya kasance daidai to bayan an ƙara zafi a cikin tsarin, tsarin yana faɗaɗa kuma yana aiki akan muhalli. Bayan tsarin ya yi aiki akan muhalli, ƙarar tsarin yana canzawa zuwa V2 (ƙaruwar tsarin yana ƙaruwa) da kuma canjin matsin lamba zuwa P2 (rage matsin lamba na tsarin). Siffar jadawalin tana lanƙwasa saboda matsin lamba na tsarin baya canzawa akai-akai yayin aikin. Adadin aikin da aka yi tsarin = yanki mai inuwa.
Tsarin Adiabatic
A cikin tsarin adiabatic, babu wani zafi da aka ƙara a cikin tsarin ko kuma ya bar tsarin (Q = 0). Tsarin adiabatic na iya faruwa a cikin tsarin rufewa mai kyau. Ga tsarin rufewa mai kyau, yawanci babu zafi da ke gudana cikin tsarin ko kuma ya bar tsarin. Tsarin adiabatic kuma na iya faruwa a cikin tsarin rufewa waɗanda ba a ware su ba.
A wannan yanayin, dole ne a yi aikin cikin sauri don kada zafi ya kwarara zuwa tsarin ko ya bar tsarin. Idan aka yi amfani da shi ga tsarin adiabatic, dokar farko, lissafin Thermodynamic zai canza:
Δ U = Q – W
Babu zafi a ciki ko a waje da tsarin, don haka Q = 0.
Δ U = 0 – W
Δ U = -W
Idan aka danna tsarin da sauri (ana yin aiki akan tsarin), to aikin yana da kyau. Domin W yana da kyau, to U yana da kyau (kuzarin da ke cikin tsarin yana ƙaruwa). Akasin haka, idan tsarin ya faɗaɗa da sauri (tsarin yana aiki), to W yana da kyau. Tunda W yana da kyau, U yana da kyau (kuzarin da ke cikin tsarin yana raguwa). Kuzarin da ke cikin tsarin (iskar gas mai kyau) yana daidai da zafin jiki (U = 3/2 n RT), saboda haka idan kuzarin da ke cikin tsarin ya ƙaru to zafin tsarin ma yana ƙaruwa. Akasin haka, idan kuzarin da ke cikin tsarin ya ragu, to zafin tsarin yana raguwa.
An kwatanta canjin matsin lamba da girma na tsarin a cikin tsarin adiabatic ta hanyar 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 don ƙaruwar girma iri ɗaya, matsin tsarin yana raguwa sosai a cikin tsarin adiabatic fiye 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, don haka idan zafin tsarin ya faɗi, matsin tsarin shima yana raguwa. Sabanin tsarin isothermal, zafin tsarin koyaushe yana da daidaito. Don haka, a cikin tsarin isothermal, zafin jiki baya tasiri ga raguwar matsin lamba.
Misali ɗaya na tsarin adiabatically yana faruwa a cikin injin ƙonewa na ciki, kamar injin dizal da injin mai. A cikin injunan dizal, ana saka iska a cikin silinda, kuma iskar da ke cikin silinda ana matse ta da sauri ta amfani da piston (ana yin aiki akan iska). Tsarin matse adiabatic (rage girman tsarin) an kwatanta shi da lanƙwasa 2-1. Saboda saurin matsin lamba na adiabatic, zafin jiki yana tashi da sauri. A lokaci guda, ana fesa dizal cikin silinda ta hanyar allura, kuma cakuda yana tashi nan take. A cikin injin mai, ana saka cakuda iska da mai a cikin silinda sannan a matse shi da sauri ta amfani da piston. Saboda ana tura shi da sauri ta adiabat, zafin jiki yana tashi da sauri. A lokaci guda, walƙiya yana kunna wuta don haka tsarin ƙonewa ya faru.
Tsarin Isochoric (ƙari mai ɗorewa)
A cikin tsarin Isochoric, girman tsarin yana nan a tsaye. Tunda girman tsarin koyaushe yana nan a tsaye, tsarin ba zai iya aiki akan muhalli ba. Muhalli kuma ba zai iya yin aiki akan tsarin ba. Idan aka yi amfani da shi ga tsarin isochoric, dokar farko ta lissafin thermodynamic ta canza zuwa:
Δ U = Q – W
Tsarin ba ya aiki akan muhalli, don haka W = 0
Δ U = Q – 0
Δ U = Q
Daga wannan 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 kuzari a cikin tsarin. An kwatanta canje-canje a cikin matsin lamba da girma na tsarin a cikin tsarin isochoric ta hanyar jadawalin da ke ƙasa:
Da farko, matsin lamba na tsarin = p 1 (ƙaramin matsin lamba). Ƙarin zafin tsarin yana sa kuzarin da ke cikin tsarin ya ƙaru. Yayin da kuzarin da ke cikin tsarin ke ƙaruwa, zafin tsarin (iskar gas mai kyau) yana ƙaruwa (U = 3/2 n RT). Zafin jiki yana daidai da matsin lamba kai tsaye. Saboda haka, idan zafin tsarin ya ƙaru, to matsin lamba na tsarin yana ƙaruwa (p 2 ). Saboda yawan tsarin da ke ci gaba, babu wani aiki da aka yi (babu yanki mai inuwa).
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 koyaushe yana dawwama. Akwai wasu nau'ikan aiki waɗanda ba sa buƙatar canje-canjen girma. Don haka ko da girman tsarin bai canza ba, har yanzu ana iya yin aiki a kan tsarin. Misali, akwai fanka + batirin a cikin akwati mai rufewa. Fanka zai iya juyawa ta amfani da makamashi ta hanyar batirin. A wannan yanayin, fanka, batura, da iska a cikin akwati ana ɗaukar su a matsayin tsarin.
Lokacin da fanka ta juya, fanka tana aiki, tana wasa a cikin akwati. A lokaci guda, kuzarin motsi na fanka yana canzawa zuwa makamashi a cikin iska. Ba shakka, makamashin lantarki a cikin batirin yana raguwa saboda ya canza siffar zuwa makamashi a cikin iska. Wannan misali ya nuna cewa a cikin tsarin isochoric (ƙara koyaushe yana da daidaito), har yanzu ana iya yin aiki akan tsarin (aikin da ba ya haɗa da canje-canjen girma).
Tsarin Isobaric (matsi mai ɗorewa)
A cikin tsarin isobaric, matsin lamba na tsarin yana kasancewa akai-akai. Tunda matsin lamba yana nan akai-akai, canjin kuzari na ciki ( Δ U), zafi (Q) da aiki (W) a cikin tsarin isobaric ba sifili bane. Don haka, dabarar thermodynamics ta doka ta farko ba ta canza ba.
ΔU = Q - W
An kwatanta canje-canje a cikin matsin lamba da ƙarar iskar gas a cikin tsarin isobaric ta hanyar jadawalin da ke ƙasa:
Da farko, girman tsarin = V1 (ƙaramin girma). Saboda matsin lamba yana kasancewa akai-akai, don haka bayan an ƙara zafi a cikin tsarin, tsarin yana faɗaɗa kuma yana aiki akan muhalli. Bayan aiki akan muhalli, girman tsarin yana canzawa zuwa V2 (ƙaruwar tsarin yana ƙaruwa). Adadin aikin (W) da aka yi tsarin = yanki mai inuwa.
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 ke yi ya fi ƙanƙanta?
Aikin da iskar gas ke yi a tsarin adiabatic ya yi ƙasa da aikin da iskar gas ke yi a tsarin isothermal. Yankin inuwa = aikin da iskar gas ke yi yayin aikin faɗaɗawa (ƙara yawan iskar gas). Yankin inuwa a tsarin adiabatic ya yi ƙasa da yankin inuwa na tsarin isothermal.
Tambaya ta 2:
An nuna hanyoyin thermodynamic a cikin zane mai ƙasa. Lanƙwasa ab da dc = hanyoyin isochoric (ƙara mai ɗorewa). Lanƙwasa bc da ad = tsarin isobaric (matsi mai ɗorewa). A cikin tsarin ab, ana ƙara zafi (Q) Joules 600 zuwa tsarin. A cikin tsarin bc, ana ƙara zafi (Q) Joules 800 zuwa tsarin.
a) Canje-canje a cikin makamashi a cikin tsarin ab
b) Canje-canje a cikin makamashi a cikin tsarin abc
c) Jimlar zafi da aka ƙara wa tsarin ADC
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
Magani
a) Canje-canje a cikin makamashin ciki a cikin tsarin ab
A cikin tsarin ab, ana ƙara zafi 600 J a cikin tsarin. Tsarin ab = tsarin isochoric (ƙara mai ɗorewa). A cikin tsarin isochoric, ƙara zafi a cikin tsarin yana ƙara kuzari ne kawai a cikin tsarin. Don haka, makamashi yana canzawa a cikin tsarin bayan karɓar zafi:
ΔU = Q
ΔU = 600 J
b) Canje-canje a cikin makamashi a cikin tsarin abc
Tsarin ab = tsarin isochoric (ƙarfin da ya dace). A cikin tsarin ab, ana ƙara zafi 600 J a cikin tsarin. Saboda yawan da ya dace, babu wani aiki da tsarin ke yi.
Tsarin bc = tsarin isobaric (matsi mai ɗorewa). A cikin tsarin bc, ana ƙara zafi (Q) 800 Joules zuwa tsarin. A cikin tsarin isobaric, tsarin zai iya yin aiki. Adadin aikin da tsarin ke yi a cikin tsarin bc (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 Joule 2
W = Joule 800
Jimlar zafi da aka ƙara wa tsarin a cikin tsarin abc shine:
Jimlar Q = Q ab + Q bc
Jimlar Q = 600 J + 800 J
Jimlar Q = Joules 1400
Jimillar aikin da tsarin ya yi a tsarin abc shine:
Jimlar W = W ab + W bc
Jimlar W = 0 + W bc
Jimlar W = 0 + Joule 800
Jimlar W = Joule 800
Canje-canje a cikin makamashin ciki a cikin tsari abc = 600 J
c) Jimlar zafi da aka ƙara wa tsarin ADC
Za a iya ƙididdige jimlar zafi da aka ƙara wa tsarin ta hanyar lissafi a ƙasa:
ΔU = Q-W
Q = ΔU + W
Jimlar zafi da aka ƙara wa tsari adc = canje-canje a cikin kuzarin ciki a cikin adc + aiki a cikin tsari adc.
Zafi da aiki suna da hannu a cikin canja wurin makamashi tsakanin tsarin da muhalli, yayin da canje-canjen makamashi na ciki sakamakon canja wurin makamashi tsakanin tsarin da muhalli ne. Saboda haka, canjin makamashi ba ya dogara da tsarin canja wurin makamashi ba. A gefe guda kuma, zafi da aiki sun dogara ne akan tsarin. A cikin tsarin isochoric (tsarin ƙara mai ɗorewa), canja wurin makamashi yana faruwa ne kawai a cikin yanayin zafi, yayin da aiki ba haka bane. A cikin tsarin isobaric (matsi mai ɗorewa), canja wurin makamashi ya ƙunshi zafi da aiki. Ko da yake ba ya dogara da tsarin ba, makamashi yana canzawa dangane da yanayin farko da yanayin tsarin ƙarshe. Idan yanayin farko da na ƙarshe iri ɗaya ne, canje-canje a cikin makamashi koyaushe iri ɗaya ne, kodayake tsarin ya bambanta.
Yanayin farko da na ƙarshe na tsarin abc a cikin jadawalin da ke sama = yanayin farko da na ƙarshe na tsarin adc. Saboda haka, makamashin ciki yana canzawa a cikin tsarin adc = 600 J.
Jimlar aikin (W) da aka yi akan adc = tsarin W akan ad + W akan tsarin dc.
Tsarin talla tsari ne na isobaric (matsi mai ɗorewa), yayin da tsarin dc tsari ne na isochoric (ƙara mai ɗorewa). Saboda yawan da ya dace, babu wani aiki da aka yi akan tsarin dc. Da farko, muna ƙididdige aikin da aka yi akan tsarin talla.
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 ADC shine:
Q = ΔU + W
Q = 600 J + 400 J
Q = 1000 J
Tambaya ta 3:
Lita 1 na ruwa yana juyawa zuwa lita 1671 na tururi idan aka tafasa a matsin lamba na atm 1. Lissafa canjin kuzarin ciki da aikin da ruwa ke yi lokacin da ya ƙafe ... (Zafin tururi don ruwa = L V = 22.6 x 10 5 J/Kg)
Magani
Yawan ruwa = 1000 kg/ m3
Zafin tururin ruwa (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
Canje-canje a cikin makamashin ciki = Zafi da aka ƙara a ruwa an rage Aikin da ruwa ke yi lokacin da aka fitar da shi. Kidaya ta farko Zafi (Q) da aka ƙara a ruwa…
Q = m L V
Yawan ruwa = nauyin ruwa / girman ruwa
Nauyin ruwa (m) = yawan ruwa x girman 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 ruwa ya yi lokacin da aka fitar da shi. 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 = Joules 1691.71 x 105
W = 1.7 x 105 Joules
Canje-canje a cikin makamashin ciki na 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
21 x 10 5 Ana amfani da zafi na Joule da aka ƙara a cikin ruwa don ƙara kuzarin ciki (cinye ƙarfin juriya tsakanin ƙwayoyin da ke riƙe ruwa). A wata ma'anar, ana amfani da 21 x 10 5 J don mayar da ruwa zuwa tururi. Lokacin da ruwa ya zama tururi, ana amfani da sauran 1.7 x 105 J don yin aiki.
Tambaya ta 4:
Mole 1 na iskar gas a cikin silinda yana faɗaɗa da sauri ta hanyar adiabatic. Da farko, zafin iskar gas = 1000 K. Bayan faɗaɗawa, zafin iskar gas yana raguwa zuwa 500 K. Kayyade aikin da iskar gas ɗin ta yi…
Magani
Faɗaɗar iskar gas tana faruwa ne ta adiabatic. A cikin tsarin adiabatic, babu wani zafi da ke shiga ko fita daga tsarin. Don haka, aikin da aka yi a cikin iskar gas = canjin makamashi a cikin iskar gas.
ΔU = Q – W ko W = Q – Δ U → Q = 0
W = 0 – ΔU
W = – ΔU
Za mu iya ƙididdige canje-canjen makamashi a cikin iskar gas ta amfani da lissafin makamashi a cikin iskar gas mai kyau:
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, yawan aikin da iskar gas ke yi shine:
W = – ΔU
W = – (- 6236.25 J)
W = 6236.25 J
