Ka'idar kinetic na gas da dokar farko ta thermodynamics - matsaloli da mafita
1. Iskar gas mai kyau tana cikin akwati mai girman lita 4 kuma matsin lambarta shine atm 3 (atm 1 = 10 5 Nm -2 ). Ana dumama iskar gas mai kyau a matsin lamba akai-akai daga 27 o C zuwa 87 o C. Ƙarfin zafin iskar gas shine 9 JK -1 . Menene ƙarar gas na ƙarshe da canjin kuzarin ciki na iskar gas?
Magani
Tsarin isobaric (matsi mai ɗorewa)
An sani:
Girman farko na iskar gas (V1 ) = lita 4
Zafin iskar gas na farko (T 1 ) = 27 o C + 273 = 300 K
Zafin gas na ƙarshe (T 2 ) = 87 o C + 273 = 360 K
Matsin iskar gas (P) = 3 atm = 3 x 10 5 Nm -2
Ƙarfin zafi na iskar gas (C) = 9 JK -1
Ana so: Ƙarar gas ta ƙarshe (V2 ) da canjin makamashin ciki na iskar gas (ΔU)
Magani:
Ƙayyade ƙarar ƙarshe ta amfani da lissafin dokar Charles (tsarin isobaric ko matsin lamba mai ɗorewa):
Canjin girma:
Lita 1 = 0.001 m3
Ƙarar farko (V1 ) = 4 (0.001 m3 ) = 0.004 m3
Ƙarar ƙarshe (V2 ) = 4.8 (0.001 m3 ) = 0.0048 m3
Sauyin girma (ΔV) = V 2 – V 1 = 0.0048 m 3 – 0.004 m 3 = 0.008 m 3.
Canjin yanayin zafi:
Canjin zafin jiki (ΔT) = T 2 – T 1 = 360 K – 300 K = 60 K
Tantance canjin makamashin ciki (ΔU) na iskar gas mai kyau ta amfani da lissafin dokar thermodynamics ta farko.
ΔU = Q-W
ΔU = canjin kuzarin ciki, Q = zafi, W = aiki
Ƙayyade aiki (W) a matsin lamba akai-akai:
W = P ΔV = (3 x 10 5 )(0.0008) = (3 x 10 1 )(8) = (30)(8) = Joules 240
Ƙayyade zafi (Q) ta amfani da lissafin ƙarfin zafi (C):
C = Q / ΔT
Q = (C) (ΔT) = (9) (60) = 540 Joules
Ƙayyade canjin makamashin ciki:
ΔU = Q – W = Joules 540 – Joules 240 = Joules 300.
2. Ana sanya lita 6 na iskar gas mai kyau a 2 atm (1 atm = 10 5 Nm -2 ). Ana dumama iskar gas daga 27 o C zuwa 77 o C a matsin lamba akai-akai. Idan ƙarfin zafi na iskar gas shine 5 JK -1 , menene ƙarar ƙarshe da canjin makamashin ciki na iskar gas.
Magani:
Tsarin isobaric (matsi mai ɗorewa)
An sani:
Girman farko na iskar gas mai kyau (V1 ) = lita 6
Zafin farko na iskar gas mai kyau (T 1 ) = 27 o C + 273 = 300 K
Zafin ƙarshe na iskar gas mai kyau (T2 ) = 77 o C + 273 = 350 K
Matsin iskar gas mai kyau (P) = 2 atm = 2 x 10 5 Nm -2
Ƙarfin zafi na iskar gas (C) = 5 JK -1
Ana so: Ƙarar ƙarshe ta iskar gas (V2 ) da canjin makamashin ciki na iskar gas (ΔU)
Magani:
Ƙayyade ƙarar gas ta ƙarshe ta amfani da lissafin dokar Charles (tsarin isobaric ko matsin lamba mai ɗorewa):
Canjin girma:
Lita 1 = 0.001 m3
Ƙarar farko (V1 ) = 6 (0.001 m3 ) = 0.006 m3
Ƙarar ƙarshe (V2 ) = 7 (0.001 m3 ) = 0.007 m3
Sauyin girma (ΔV) = V 2 – V 1 = 0.007 m 3 – 0.006 m 3 = 0.001 m 3
Canjin yanayin zafi:
Canjin zafin jiki (ΔT) = T 2 – T 1 = 350 K – 300 K = 50 K
Tantance canjin makamashin ciki (ΔU) na iskar gas masu kyau ta amfani da lissafin dokar thermodynamics ta farko.
ΔU = Q-W
ΔU = canjin kuzarin ciki, Q = zafi, W = aiki
Ƙayyade aiki (W) a matsin lamba akai-akai:
W = P ΔV = (2 x 10 5 )(0.001) = (2 x 10 2 )(1) = (200)(1) = Joules 200
Ƙayyade zafi (Q) ta amfani da lissafin ƙarfin zafi (C):
C = Q / ΔT
Q = (C) (ΔT) = (5) (50) = 250 Joules
Ƙayyade canjin makamashin ciki:
ΔU = Q – W = Joules 250 – Joules 200 = Joules 50.
- Menene manyan zato na ka'idar motsi na iskar gas?
- amsa: Ka'idar motsi na iskar gas ta ɗauka cewa: (a) Iskar gas ta ƙunshi adadi mai yawa na ƙananan barbashi waɗanda ke cikin motsi bazuwar akai-akai; (b) Waɗannan barbashi suna da nisa da girmansu; (c) Haɗuwa tsakanin barbashi na iskar gas, ko tsakanin barbashi da bangon akwatinsa, suna da laushi (watau, babu kuzarin motsi da aka rasa); (d) Babu ƙarfin haɗin molecular tsakanin barbashi na iskar gas; kuma (e) Matsakaicin kuzarin motsi na barbashi na iskar gas yana daidai da cikakken zafin iskar gas.
- Ta yaya matsakaicin kuzarin motsi na ƙwayoyin iskar gas yake da alaƙa da zafin iskar?
- amsa: Matsakaicin kuzarin motsi na ƙwayoyin iskar gas yana daidai da cikakken zafin jiki (a cikin Kelvin) na iskar gas. Yayin da zafin jiki ke ƙaruwa, matsakaicin kuzarin motsi na ƙwayoyin ma yana ƙaruwa.
- Menene muhimmancin sifili a fannin motsin kwayoyin halitta?
- amsa: Sifili cikakke (0 Kelvin) a ka'ida shine zafin jiki wanda duk motsin kwayoyin halitta ke tsayawa. Yana wakiltar mafi ƙarancin zafin jiki inda babu wani abu da zai iya yin sanyi kuma babu wani kuzarin zafi da ya rage a cikin wani abu.
- Menene dokar farko ta thermodynamics dangane da makamashin ciki, zafi, da aiki?
- amsa: Dokar farko ta thermodynamics ta bayyana cewa canjin makamashin ciki na tsarin daidai yake da zafin da aka ƙara wa tsarin ban da aikin da tsarin ke yi a kewayensa: ΔU = Q – W.
- A cikin tsarin isochoric, me ke faruwa da aikin da aka yi ta ko a kan tsarin?
- amsa: A cikin tsarin isochoric, ƙarar ta kasance ba ta canzawa. Saboda haka, babu wani aiki da aka yi ta ko kuma a kan tsarin, domin aiki a irin waɗannan yanayi ana bayar da shi ta hanyar aikin ƙarar matsin lamba, wanda zai zama sifili idan ƙarar ba ta canza ba.
- Me ake nufi idan muka ce iskar gas "mafi kyau" ce?
- amsa: Iskar gas mai "daidai" ita ce wadda ke bin ƙa'idar iskar gas mai kyau (PV = nRT) a ƙarƙashin dukkan yanayin zafi da matsin lamba. Hakanan yana nufin cewa iskar gas tana bin ƙa'idodin ka'idar motsi daidai, ba tare da ƙarfin intermolecular da kuma haɗuwa mai laushi ba.
- Ta yaya iskar gas ta gaske ke karkata daga halayen iskar gas mai kyau?
- amsa: Gas na gaske yana karkacewa daga ɗabi'a mai kyau a matsin lamba mai yawa da ƙarancin zafi. Wannan ya faru ne saboda kasancewar ƙarfin da ke tsakanin ƙwayoyin halitta da kuma girman ƙwayoyin gas mai iyaka. An bayyana karkacewar ta hanyar lissafin van der Waals da sauran daidaitattun daidaito.
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Me yasa za a iya ɗaukar dokar farko ta thermodynamics a matsayin dokar kiyayewa?
- amsa: Dokar farko ta thermodynamics za a iya ɗaukarta a matsayin dokar kiyayewa domin ta bayyana cewa ba za a iya ƙirƙirar ko lalata makamashi ba, sai dai a canza shi ko a canza shi daga wata siffa zuwa wata siffa. Wannan yana nuna ƙa'idar kiyaye makamashi.
