Njira 30 za Isochoric thermodynamics - mavuto ndi mayankho
1. Chithunzi cha PV pansipa chikuwonetsa mpweya wabwino womwe umachitika mu njira ya iso choric . Werengani ntchito yomwe yachitika ndi mpweya mu ndondomekoyi AB.
Yankho:
Njira ya AB ndi njira ya isochoric (voliyumu yokhazikika). Voliyumuyo ndi yokhazikika kotero kuti palibe ntchito yomwe imachitika ndi mpweya.
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2. Ma mole atatu a mpweya wa monoatomic pa 47 o C ndipo pa mphamvu ya 2 x 10 5 Pa, amadutsa mu njira ya isochoric kotero kuti mphamvu imawonjezeka ndi 3 x 10 5 Pa. Kusintha kwa mphamvu yamkati ya mpweya ndi… Universal gas constant (R) = 8.315 J/mol.K
Zodziwika:
Kutentha koyambirira (T 1 ) = 47 o C + 273 = 320 K
Kupanikizika koyambirira (P 1 ) = 2 x 10 5 Pa
Kupanikizika komaliza (P2 ) = 3 x 10 5 Pa
Mpweya wosasinthika wa Universal (R) = 8.315 J/mol.K
Chiwerengero cha ma moles (n) = 3
Kufunidwa: Kusintha kwa mphamvu yamkati mwa mpweya.
Yankho:
Mu njira ya isochoric, voliyumu imasungidwa yokhazikika kotero kuti palibe ntchito yomwe imachitika ndi mpweya (W = 0).
Lamulo loyamba la thermodynamics :
ΔU = QW
ΔU = Q-0
ΔU = Q
ΔU = mphamvu yamkati, Q = kutentha
Mphamvu yamkati ya mpweya:
ΔU = 3/2 n R ΔT = 3/2 n R (T 2 – T 1 )
Lamulo la Gay-Lussac ( voliyumu yosasinthasintha ) :
Kusintha kwa mphamvu yamkati ya mpweya:
ΔU = 3/2 n R (T 2 – T 1 ) = 3/2 (3)(8.315)(480-320)
ΔU = 3/2 (24.945) (160) = 3/2 (3991.2)
ΔU = 5986.8 Joule
3. Ma moles 0.2 a mpweya wa monatomic pa 27 o C ali mu chidebe chotsekedwa. Kutentha kumawonjezedwa ku mpweya kotero kuti kutentha kwa mpweya kumakhala 400 K ndi… Universal gas constant (R) = 8.315 J/mol.K
Zodziwika:
Chiwerengero cha ma moles (n) = 0.2 mol
Kutentha koyambirira (T 1 ) = 27 o C + 273 = 300 K
Kutentha komaliza (T2 ) = 400 K
Mpweya wokhazikika wa chilengedwe chonse (R) = 8.315 J/mol.K
Kufunidwa : Kutentha kumawonjezedwa (Q)
Yankho:
Mu njira ya isochoric, voliyumu imasungidwa yofanana kotero kuti palibe ntchito yomwe imachitika ndi mpweya (W = 0).
Lamulo loyamba la thermodynamics:
ΔU = QW
ΔU = Q-0
ΔU = Q
ΔU = mphamvu yamkati, Q = kutentha
Mphamvu yamkati ya mpweya:
ΔU = 3/2 n R ΔT = 3/2 n R (T 2 – T 1 )
ΔU = 3/2 (0.2) (8.315) (400-300)
ΔU = 3/2 (0.2)(8.315)(100)
ΔU = 249.45 Joule
4. Werengani kutentha komwe kumasamutsidwa kuti mupeze mpweya wabwino womwe ukudutsa mu njira ya isochoric kuyambira kutentha koyambirira kwa 300 K mpaka kutentha komaliza kwa 400 K. Tiyerekeze kuti 2 mol ya mpweya, ndipo mphamvu ya kutentha kwa molar pa voliyumu yokhazikika (Cᵥ) ndi 20 J/(mol K).
Yankho: ΔQ = n × Cᵥ × ΔT = 2 mol × 20 J/(mol K) × (400 K – 300 K) = 4000 J
5. Pezani kusintha kwa mphamvu yamkati pa vuto lomwe lili pamwambapa.
Yankho: ΔU = ΔQ = 4000 J
6. Dziwani ntchito yomwe yachitika pa dongosolo panthawi ya isochoric process pazifukwa zomwe zili pamwambapa.
Yankho: W = 0 J (popeza voliyumu siisintha, palibe ntchito yomwe yachitika)
7. Kuti mpweya wabwino kwambiri ukhale wofanana ndi wa monatomic womwe ukudutsa mu njira ya isochoric, ngati kupanikizika koyamba kuli 2 atm ndipo kupanikizika komaliza kuli 3 atm, kodi chiŵerengero cha kutentha komaliza ndi koyambirira ndi chotani?
Yankho: Popeza P₁/T₁ = P₂/T₂, T₂/T₁ = 3/2
8. Kodi kusintha kwa entropy kwa mpweya wabwino mu njira ya isochoric ndi chiyani pamene kutentha kumasintha kuchoka pa 300 K kufika pa 600 K, ndipo n = 2 mol, Cᵥ = 20 J/(mol·K)?
Yankho: ΔS = n × Cᵥ × ln(T₂/T₁) = 2 × 20 × ln(600/300) ≈ 27.73 J/K
9. Ngati mkhalidwe woyamba wa mpweya wabwino wa diatomic ufotokozedwa ndi V = 2 L, P = 1 atm, ndi T = 300 K, pezani kupanikizika komaliza ngati kutentha kwawirikiza kawiri mu njira ya isochoric.
Yankho: P₂ = 2 × P₁ = 2 atm
10. Pezani kusintha kwa mphamvu ya Gibbs yaulere pa njira ya isochoric.
Yankho: ΔG = 0 (Pa njira ya isochoric mu dongosolo lotsekedwa, ΔG = 0)
11. Werengani kutentha komaliza kwa mpweya wabwino womwe ukudutsa mu njira ya isochoric ngati kutentha koyambirira kuli 200 K, ndipo kupsinjika koyambirira ndi komaliza kuli 2 atm ndi 4 atm, motsatana.
Yankho: T₂ = 2 × T₁ = 400 K
12. Kuti mupeze mpweya wabwino, ngati mphamvu ya kutentha pa voliyumu yosasintha (Cᵥ) ndi 30 J/(mol·K), pezani kusamutsa kutentha pamene kutentha kukusintha kuchoka pa 300 K kufika pa 450 K, ndi 3 mol ya mpweya.
Yankho: ΔQ = n × Cᵥ × ΔT = 3 × 30 × 150 = 13500 J
13. Pa njira yomweyi monga momwe zilili pamwambapa, werengerani kusintha kwa mphamvu yamkati.
Yankho: ΔU = ΔQ = 13500 J
14. Dziwani kusintha kwa entropy kwa njira ya isochoric ndi n = 1 mol, Cᵥ = 25 J/(mol K), T₁ = 200 K, ndi T₂ = 400 K.
Yankho: ΔS = n × Cᵥ × ln(T₂/T₁) = 25 × ln(2) ≈ 17.33 J/K
15. Pezani ntchito yomwe yachitika ndi dongosololi panthawi ya isochoric process ya 3 mol ya mpweya, ndipo kutentha kumasintha kuchoka pa 200 K kufika pa 300 K.
Yankho: W = 0 J (popeza voliyumu siisintha, palibe ntchito yomwe yachitika)
16. Werengani kutentha komwe kumasamutsidwa kuti mupeze mpweya wabwino womwe ukudutsa mu njira ya isochoric yokhala ndi kutentha koyambirira kwa 150 K, kutentha komaliza kwa 300 K, ndi Cᵥ = 15 J/(mol·K) pa 4 mol ya mpweya.
Yankho: ΔQ = n × Cᵥ × ΔT = 4 × 15 × 150 = 9000 J
17. Kodi kusintha kwa entropy kwa mpweya wabwino mu njira ya isochoric ndi chiyani ndi n = 1 mol, Cᵥ = 30 J/(mol·K), T₁ = 100 K, ndi T₂ = 200 K?
Yankho: ΔS = n × Cᵥ × ln(T₂/T₁) = 30 × ln(2) ≈ 20.79 J/K
18. Dziwani mphamvu yomaliza ya mpweya womwe ukudutsa mu njira ya isochoric, poganizira kuti P₁ = 5 atm, T₁ = 250 K, ndi T₂ = 500 K.
Yankho: P₂ = (T₂/T₁) × P₁ = 2 × 5 atm = 10 atm
19. Pezani kutentha kwa 5 mol ya mpweya wabwino wa monatomic womwe ukudutsa mu njira ya isochoric kuyambira 300 K mpaka 600 K. Tiyerekeze kuti Cᵥ = 15 J/(mol K).
Yankho: ΔQ = n × Cᵥ × ΔT = 5 × 15 × 300 = 22500 J
20. Kodi kusintha kwa mphamvu yamkati pa vuto lomwe lili pamwambapa ndi kotani?
Yankho: ΔU = ΔQ = 22500 J
21. Dziwani kusintha kwa entropy kwa njira ya isochoric pomwe n = 2 mol, Cᵥ = 25 J/(mol K), T₁ = 300 K, ndi T₂ = 600 K.
Yankho: ΔS = n × Cᵥ × ln(T₂/T₁) = 2 × 25 × ln(2) ≈ 34.66 J/K
22. Werengani kutentha komaliza kwa 1 mol ya mpweya wabwino wa monatomic womwe ukudutsa mu njira ya isochoric ngati kutentha koyambirira ndi 400 K, ndipo kupsinjika koyambirira ndi komaliza ndi 3 atm ndi 6 atm, motsatana.
Yankho: T₂ = 2 × T₁ = 800 K
23. Kuti mupeze mpweya wabwino wa diatomic womwe ukudutsa mu njira ya isochoric, werengerani kusintha kwa mphamvu yamkati pamene kutentha kumasintha kuchoka pa 300 K kufika pa 600 K, ndi 2 mol ya mpweya, ndipo Cᵥ = 30 J/(mol·K).
Yankho: ΔU = n × Cᵥ × ΔT = 2 × 30 × 300 = 18000 J
24. Werengani kutentha komwe kumasamutsidwa kuti mupeze mpweya wabwino womwe ukudutsa mu njira ya isochoric yokhala ndi kutentha koyambirira kwa 100 K, kutentha komaliza kwa 300 K, ndi Cᵥ = 20 J/(mol·K) pa 2 mol ya mpweya.
Yankho: ΔQ = n × Cᵥ × ΔT = 2 × 20 × 200 = 8000 J
25. Pezani ntchito yomwe yachitika pa dongosololi panthawi ya isochoric process pazifukwa zomwe zili pamwambapa.
Yankho: W = 0 J (popeza voliyumu siisintha, palibe ntchito yomwe yachitika)
26. Kodi kusintha kwa entropy kwa mpweya wabwino mu njira ya isochoric ndi chiyani pamene kutentha kumasintha kuchoka pa 400 K kufika pa 800 K, ndipo n = 3 mol, Cᵥ = 20 J/(mol·K)?
Yankho: ΔS = n × Cᵥ × ln(T₂/T₁) = 3 × 20 × ln(2) ≈ 41.58 J/K
27. Pezani kusintha kwa mphamvu ya Gibbs yaulere pa njira ya isochoric.
Yankho: ΔG = 0 (Pa njira ya isochoric mu dongosolo lotsekedwa, ΔG = 0)
28. Dziwani mphamvu yomaliza ya mpweya womwe ukudutsa mu njira ya isochoric, poganizira kuti P₁ = 3 atm, T₁ = 300 K, ndi T₂ = 450 K.
Yankho: P₂ = (T₂/T₁) × P₁ = 1.5 × 3 atm = 4.5 atm
29. Werengani kusintha kwa mphamvu yamkati ya dongosolo lomwe likuchita njira ya isochoric ndi 3 mol ya mpweya, Cᵥ = 20 J/(mol K), ndipo kutentha kumasintha kuchokera pa 200 K mpaka 400 K.
Yankho: ΔU = n × Cᵥ × ΔT = 3 × 20 × 200 = 12000 J
30. Dziwani kusintha kwa entropy kwa njira ya isochoric pomwe n = 4 mol, Cᵥ = 30 J/(mol K), T₁ = 150 K, ndi T₂ = 300 K.
Yankho: ΔS = n × Cᵥ × ln(T₂/T₁) = 4 × 30 × ln(2) ≈ 55.86 J/K
Mavutowa akuphatikizapo mfundo zosiyanasiyana zokhudzana ndi njira za isochoric, monga kusamutsa kutentha, kusintha kwa mphamvu yamkati, ntchito yochitidwa, kusintha kwa entropy, ndi zina zambiri.
