Bayaanka gaarka ah ee sharciga labaad ee thermodynamics ma sharxi karo dhammaan hababka aan la beddeli karin, sidaa darteed waxaan u baahanahay bayaan guud. Bayaanka guud waxaa la filayaa inuu sharxo dhammaan hababka aan la beddeli karin ee ka dhacaya caalamka. Bayaanka guud ee sharciga labaad ee thermodynamics waxaa la sameeyay bartamihii qarnigii sagaal iyo tobnaad, iyada oo loo marayo tiro loo yaqaan entropy (S). Entropy waxaa markii ugu horreysay soo bandhigay Clausius waxaana laga sameeyay wareegga Carnot (matoorka kalooriga ee qumman). Sida laga soo xigtay Clausius, isbeddellada entropy waxaa la kulma nidaam, marka nidaamku helo kulayl dheeraad ah (Q) heerkul joogto ah, kaas oo lagu matalo isla'egta:
Δ S = Isbeddellada Entropy, Q = Kulayl, T = Heerkulka T
Entropy waa tiro sheegaysa xaaladda yar yar ee nidaamka si aan si toos ah loo ogaan karin. Taas oo la xisaabin karo oo keliya isbeddellada entropy. Sida isbeddel tamar gudaha ah oo ku yimaada sharciga koowaad ee thermodynamics.
Tusaale 1:
Gaaska ku jira weelka ayaa si isku mid ah u fida. Isbeddelka entropy-ga gaaska waa…
Xalalka
Inta lagu jiro habka adiabatic, kuleyl ma galo ama ka baxo nidaamka (gaaska). Maadaama Q = 0 markaas ΔS = 0. Entropy-ga nidaamku waa mid joogto ah. Ka waran cadaadiska adiabatic? Inta lagu jiro cadaadiska adiabatic, kuleyl ma galo ama ka baxo nidaamka (Q = 0). Sidaa darteed, entropy-ga nidaamku waa mid joogto ah.
Tusaale 2:
Matoorka Carnot wuxuu nuugaa kulaylka 2000 J marka uu gaaro 500 K, wuxuuna sii daayaa kulaylka 350 K. Xisaabi kulaylka la sii daayo, iyo isbeddelka guud ee entropy hal wareeg.
Xalalka
T H = 500 K
Q H = 2000 J
T L = 350 K
Q L = …..?
Haddii nidaamku helo kulayl, Q waa togan yahay, haddii nidaamku sii daayo kulayl, Q waa taban yahay.
Inta lagu jiro hal wareeg, matoorka Carnot wuxuu maraa laba hab oo isothermal ah oo la rogi karo (ballaarinta isothermal + cadaadiska isothermal) iyo laba hab oo adiabatic ah oo la rogi karo (ballaarinta adiabatic iyo cadaadiska adiabatic). Inta lagu jiro ballaarinta iyo cadaadiska, kuleyl ma soo galo ama ka baxo nidaamka (Q = 0). Tan iyo Q = 0, entropy-gu wuu isbeddelaa inta lagu jiro habka adiabatic = 0.
Inta lagu jiro fidinta kulaylka, matoorku wuxuu nuugaa kulaylka (Q) ee 2000 J heerkul (T) 500 K. Maadaama matoorku uu nuugo kulaylka, markaas Q waa togan yahay. Isbeddelka entropy-ga mashiinka inta lagu jiro fidinta kulaylka waa:
Inta lagu jiro cadaadiska isothermal-ka, matoorku wuxuu sii daayaa kuleyl (Q) ilaa 1400 J heerkul ah (T) 350 K. Maadaama matoorku uu sii daayo kulaylka, markaas Q waa taban. Isbeddelka entropy-ga mashiinka inta lagu jiro cadaadiska isothermal-ka waa:
Wadarta isbeddelka entropy = 4 J / K – 4 J / K = 0
Tusaale 3:
Matoorku wuxuu nuugaa 600 J oo kulayl ah heerkul dhan 300 °C, wuxuuna sii daayaa kulayl heerkulkiisu yahay 100 °C. Wuxuu xisaabiyaa kulaylka la sii daayo, wuxuuna beddelaa guud ahaan entropy hal wareeg.
Xalalka
T H = 300 K
Q H = 600 J
T L = 100 K
Q L = ?
Inta lagu jiro hal wareeg, matoorka Carnot wuxuu maraa laba hab oo isothermal ah oo la rogi karo (ballaarinta isothermal + cadaadiska isothermal) iyo laba hab oo adiabatic ah oo la rogi karo (cadaadiska adiabatic iyo ballaarinta adiabatic). Inta lagu jiro ballaarinta iyo cadaadiska adiabatic, kuleyl ma soo galo ama ka baxo nidaamka (Q = 0). Sababtoo ah Q = 0 markaa entropy-gu wuu isbeddelaa inta lagu jiro habka adiabatic = 0.
Inta lagu jiro fidinta kulaylka, matoorku wuxuu nuugaa kulaylka (Q) ee 600 J heerkul ah (T) 300 K. Maadaama matoorku uu nuugo kulaylka, markaas Q waa togan yahay. Isbeddelka entropy-ga mashiinka inta lagu jiro fidinta kulaylka waa:
Inta lagu jiro cadaadiska isothermal-ka, matoorku wuxuu sii daayaa kuleyl (Q) 200 J heerkul (T) 100 K. Maadaama matoorku uu sii daayo kulaylka, markaas Q waa taban. Isbeddelka entropy-ga mashiinka inta lagu jiro cadaadiska isothermal-ka waa:
Wadarta isbeddelka entropy = 2 J / K – 2 J / K = 0
Iyada oo ku saleysan tusaalaha lambar 2 iyo tusaalaha lambar 3, wadarta isbeddelka entropy ee habka la rogi karo = 0. Habka la rogi karo, entropy-ga guud had iyo jeer waa mid joogto ah.
Tusaale 4:
Baraf 2 kg ah oo heerkulkiisu yahay 0 °C wuxuu nuugaa kulaylka, sidaas darteed wuu dhalaalaa. Xisaabi isbeddelka entropy-ga barafka. (Kuleylka isku-dhafka biyaha = 3.34 x 10 5 J / Kg)
Xalalka
Cufka barafka = 2 kg
Heerkulka barafka = 0 o C + 273 = 273 K
Kulaylka isku-darka biyaha = 3.34 x 10 5 J / Kg
Kulaylka loo baahan yahay si uu 2 kg oo baraf ah ugu dhalaaliyo biyo:
Q = mL
Q = (2 kg)(3.34 x 10 5 J/Kg)
Q = 6.68 x 10 5 J
Q = 668 x 10 3 J
Inta lagu jiro habka dhalaalidda (baraf ilaa biyo), heerkulku waa mid joogto ah. Maadaama heerkulku uu yahay mid joogto ah, markaa isbeddelka entropy-ga barafku waa:
Tusaale 5:
Biyaha heerkulkoodu yahay 26°C waxaa lagu qasaa biyo heerkulkoodu yahay 22°C. Cufnaanta biyuhu waa 2 kg. Xisaabi isbeddelka entropy-ga biyaha. Biyaha kulul iyo biyaha qabow waxaa lagu qasaa weel si fiican loo dahaadhay oo xiran. Gudbinta kulaylku waa hab aan dib loo celin karin.
Xalalka
Kulayl gaar ah oo biyo ah (c) = 4180 J/Kg C o
Cufka biyaha = 2 kg
Cufka biyuhu waa isku mid, sidaa darteed heerkulka ugu dambeeya = 24 o C (26 o C + 22 o C / 2 = 48 o C / 2 = 24 o C).
Xaddiga kulaylka ee biyaha kulul sii daaya marka heerkulka laga dhimo 26 °C - 24 °C waa:
Q = mc ΔT = (2 kg) (4180 J / kg C o ) (26 o C – 24 o C) = (2 Kg) (4180 J / kg C o ) (2 o C) = 16720 J
Xaddiga kulaylka ee biyaha qabow nuugaan marka heerkulku kaco 22 o C - 24 o C waa:
Q = mc ΔT = (2 kg) (4180 J / kg C o ) (24 o C – 22 o C) = (2 kg) (4180 J / kg C o ) (2 o C) = 16720 J
Isbeddelka guud ee entropy = isbeddelka entropy ee biyaha kulul + isbeddelka entropy ee biyaha qabow
Δ S = Δ S biyo kulul + Δ S biyo qabow
Δ S = Q/T + Q/T
Celceliska heerkulka biyaha kulul = (26 o C + 24 o C) / 2 = 50 o C / 2 = 25 o C —- 25 + 273 = 298 K
Celceliska heerkulka biyaha qabow = (22 o C + 24 o C) / 2 = 46 o C / 2 = 23 o C —- 23 + 273 = 296 K
Biyaha kulul waxay sii daayaan kulaylka, sidaas darteed Q waa taban. Biyaha qabow waxay nuugaan kulaylka, sidaas darteed Q waa togan.
Δ S = Δ S biyo kulul + Δ S biyo qabow
Δ S = -Q/T + Q/T
Δ S = -16720/298 + 16720/296
Δ S = -56.107 + 56.486
Δ S = 0.379 J/K
Wadarta entropy-ga ayaa kordhay 0.379 J/K
In kasta oo entropy-ga qayb ahaan ee nidaamku uu hoos u dhaco (-56.107 J/K), entropy-ga qayb ahaan ee nidaamku wuxuu ku kordhaa tiro badan (+ 56.486 J/K) sidaa darteed entropy-ga guud had iyo jeer waa la kordhiyaa (+ 0.379 J/K).
Kordhinta entropy-ga guud ee habka aan la celin karin kuma khuseyso oo keliya wareejinta kulaylka ee u dhexeeya isku-darka biyaha kulul iyo kuwa qabow ee kor lagu falanqeeyay, laakiin sidoo kale waxay khuseysaa dhammaan kiisaska ay baaraan saynisyahannadu. Entropy-ga guud ee go'an haddii geeddi-socodku si dib-u-noqosho ah u dhaco. Haddii geeddi-socodku si aan dib-u-noqosho lahayn u dhaco, markaa entropy-ga guud had iyo jeer wuu kordhaa.
Dhammaan hababka dabiiciga ah ee nolol maalmeedkeena waa kuwo aan dib loo celin karin sidaa darteed entropy-ga oo dhan waa inuu kordhaa. Xaqiiqadan waxaa lagu soo koobay jumlada soo socota:
Geedi socod aan dib loo celin karin, entropy-ga guud ee nidaamka iyo deegaanku had iyo jeer way sii kordhayaan.
Hadalkani waa hadal guud oo ka hadlaya sharciga labaad ee thermodynamics. Sharciga labaad ee thermodynamics wuu ka duwan yahay sharciyada kale ee jirka. Badanaa, sharciyada fiisigiska waxaa lagu muujiyaa isle'egyada (sharciga Newton) ama qaabka sharciga waara (sharciga ilaalinta tamarta).
