30 mau kaʻina hana thermodynamics Isochoric - nā pilikia a me nā hoʻonā
1. Hōʻike ka kiʻikuhi PV ma lalo nei i kahi kinoea kūpono e hele ana i kahi kaʻina hana isochoric . E helu i ka hana a ke kinoea i hana ai ma ke kaʻina hana AB.
Lōlā:
He kaʻina hana isochoric (ka nui mau) ke kaʻina hana AB. He mau ka nui no laila ʻaʻohe hana e hana ʻia e ke kinoea.
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2. ʻEkolu mole o ke kinoea monoatomic ma 47 o C a ma ke kaomi 2 x 10 5 Pa, ke hana nei i ke kaʻina hana isochoric i piʻi ai ke kaomi 3 x 10 5 Pa. ʻO ka loli o ka ikehu kūloko o ke kinoea… Universal gas constant (R) = 8.315 J/mol.K
ʻIke ʻia:
Ka mahana mua (T 1 ) = 47 o C + 273 = 320 K
Kaomi mua (P 1 ) = 2 x 10 5 Pa
Kaomi hope loa (P 2 ) = 3 x 10 5 Pa
ʻO ke kūpaʻa kinoea honua (R) = 8.315 J/mol.K
Helu o nā mole (n) = 3
Makemake ʻia: Ka loli o ka ikehu kūloko o ke kinoea.
Lōlā:
I ke kaʻina hana isochoric, mālama ʻia ka nui i ʻole e hana ʻia kekahi hana e ke kinoea (W = 0).
ʻO ke kānāwai mua o ka thermodynamics :
ΔU = QW
ΔU = Q-0
ʻΔU = Q
ΔU = ikehu kūloko, Q = wela
Ikehu kūloko o ke kinoea:
ΔU = 3/2 n R ΔT = 3/2 n R (T 2 – T 1 )
Ke kānāwai o Gay-Lussac ( ka leo mau ) :
Ka loli o ka ikehu kūloko o ke kinoea:
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)
ʻO ΔU = 5986.8 Joule
3. Aia nā mole 0.2 o nā kinoea monatomic ma 27 o C i loko o kahi pahu pani. Hoʻohui ʻia ka wela i ke kinoea i lilo ai ka mahana o ke kinoea i 400 K… Universal gas constant (R) = 8.315 J/mol.K
ʻIke ʻia:
Helu o nā mole (n) = 0.2 mol
Ka mahana mua (T 1 ) = 27 o C + 273 = 300 K
Mahana hope loa (T 2 ) = 400 K
Kinoea mau loa (R) = 8.315 J/mol.K
Makemake ʻia : Hoʻohui ʻia ka wela (Q)
Lōlā:
I ke kaʻina hana isochoric, mālama ʻia ka nui i ʻole e hana ʻia kekahi hana e ke kinoea (W = 0).
ʻO ke kānāwai mua o ka thermodynamics:
ΔU = QW
ΔU = Q-0
ʻΔU = Q
ΔU = ikehu kūloko, Q = wela
Ka ikehu kūloko o ke kinoea:
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)
ʻO ΔU = 249.45 Joule
4. E helu i ka hoʻoili wela no kahi kinoea kūpono e hana ana i kahi kaʻina hana isochoric mai ka mahana mua o 300 K a i ka mahana hope loa o 400 K. Manaʻo ʻia he 2 mol o ke kinoea, a ʻo ka mana wela molar ma ka leo mau (Cᵥ) he 20 J/(mol K).
Hoʻonā: ΔQ = n × Cᵥ × ΔT = 2 mol × 20 J/(mol K) × (400 K – 300 K) = 4000 J
5. E huli i ka loli o ka ikehu kūloko no ka pilikia i luna.
Hoʻonā: ΔU = ΔQ = 4000 J
6. E hoʻoholo i ka hana i hana ʻia ma kahi ʻōnaehana i ka wā o ke kaʻina hana isochoric no nā kūlana i luna.
Hoʻonā: W = 0 J (ʻoiai ʻaʻole loli ka leo, ʻaʻohe hana i hana ʻia)
7. No ke kinoea maikaʻi monatomic e hana ana i kahi kaʻina hana isochoric, inā he 2 atm ke kaomi mua a he 3 atm ke kaomi hope loa, he aha ka lakio o nā mahana hope loa i nā mahana mua?
Hoʻonā: ʻOiai ʻo P₁/T₁ = P₂/T₂, ʻo T₂/T₁ = 3/2
8. He aha ka loli entropy no kahi kinoea kūpono i loko o kahi kaʻina hana isochoric ke loli ka mahana mai 300 K a i 600 K, a ʻo n = 2 mol, Cᵥ = 20 J/(mol·K)?
Hoʻonā: ΔS = n × Cᵥ × ln(T₂/T₁) = 2 × 20 × ln(600/300) ≈ 27.73 J/K
9. Inā ua wehewehe ʻia ke kūlana mua o kahi kinoea diatomic ideal e V = 2 L, P = 1 atm, a me T = 300 K, e ʻimi i ke kaomi hope loa inā pāpālua ʻia ka mahana i loko o kahi kaʻina hana isochoric.
Hoʻonā: P₂ = 2 × P₁ = 2 atm
10. E huli i ka loli o ka ikehu manuahi o Gibbs no kahi kaʻina hana isochoric.
Hoʻonā: ΔG = 0 (No ke kaʻina hana isochoric i loko o kahi ʻōnaehana pani, ΔG = 0)
11. E helu i ka mahana hope loa o kahi kinoea kūpono e hana ana i kahi kaʻina hana isochoric inā he 200 K ka mahana mua, a ʻo nā kaomi mua a me ka hope he 2 atm a me 4 atm.
Hoʻonā: T₂ = 2 × T₁ = 400 K
12. No ke kinoea kūpono, inā ʻo ka mana wela ma ka leo mau (Cᵥ) he 30 J/(mol·K), e ʻimi i ka hoʻoili wela ke loli ka mahana mai 300 K a i 450 K, me 3 mol o ke kinoea.
Hoʻonā: ΔQ = n × Cᵥ × ΔT = 3 × 30 × 150 = 13500 J
13. No ke kaʻina hana like me luna, e helu i ka loli o ka ikehu kūloko.
Hoʻonā: ΔU = ΔQ = 13500 J
14. E hoʻoholo i ka loli entropy no kahi kaʻina hana isochoric me n = 1 mol, Cᵥ = 25 J/(mol·K), T₁ = 200 K, a me T₂ = 400 K.
Hoʻonā: ΔS = n × Cᵥ × ln(T₂/T₁) = 25 × ln(2) ≈ 17.33 J/K
15. E huli i ka hana i hana ʻia e ka ʻōnaehana i ka wā o ke kaʻina hana isochoric o 3 mol o ke kinoea, a loli ka mahana mai 200 K a i 300 K.
Hoʻonā: W = 0 J (ʻoiai ʻaʻole loli ka leo, ʻaʻohe hana i hana ʻia)
16. E helu i ka hoʻoili wela no kahi kinoea kūpono e hana ana i kahi kaʻina hana isochoric me ka mahana mua o 150 K, ka mahana hope loa o 300 K, a me Cᵥ = 15 J/(mol·K) no 4 mol o ke kinoea.
Hoʻonā: ΔQ = n × Cᵥ × ΔT = 4 × 15 × 150 = 9000 J
17. He aha ka loli entropy no kahi kinoea kūpono i loko o kahi kaʻina hana isochoric me n = 1 mol, Cᵥ = 30 J/(mol·K), T₁ = 100 K, a me T₂ = 200 K?
Hoʻonā: ΔS = n × Cᵥ × ln(T₂/T₁) = 30 × ln(2) ≈ 20.79 J/K
18. E hoʻoholo i ke kaomi hope loa o kahi kinoea e hana ana i kahi kaʻina hana isochoric, i hāʻawi ʻia ʻo P₁ = 5 atm, T₁ = 250 K, a me T₂ = 500 K.
Hoʻonā: P₂ = (T₂/T₁) × P₁ = 2 × 5 atm = 10 atm
19. E huli i ka hoʻoili wela no 5 mol o kahi kinoea maikaʻi monatomic e hana ana i kahi kaʻina hana isochoric mai 300 K a i 600 K. Manaʻo ʻia ʻo Cᵥ = 15 J/(mol K).
Hoʻonā: ΔQ = n × Cᵥ × ΔT = 5 × 15 × 300 = 22500 J
20. He aha ka loli o ka ikehu kūloko no ka pilikia ma luna?
Hoʻonā: ΔU = ΔQ = 22500 J
21. E hoʻoholo i ka loli entropy no kahi kaʻina hana isochoric kahi n = 2 mol, Cᵥ = 25 J/(mol K), T₁ = 300 K, a me T₂ = 600 K.
Hoʻonā: ΔS = n × Cᵥ × ln(T₂/T₁) = 2 × 25 × ln(2) ≈ 34.66 J/K
22. E helu i ka mahana hope loa o 1 mol o kahi kinoea maikaʻi monatomic e hana ana i kahi kaʻina hana isochoric inā ʻo ka mahana mua he 400 K, a ʻo nā kaomi mua a me ka hope he 3 atm a me 6 atm.
Hoʻonā: T₂ = 2 × T₁ = 800 K
23. No ke kinoea diatomic ideal e hana ana i kahi kaʻina hana isochoric, e helu i ka loli o ka ikehu kūloko ke loli ka mahana mai 300 K a i 600 K, me 2 mol o ke kinoea, a ʻo Cᵥ = 30 J/(mol·K).
Hoʻonā: ΔU = n × Cᵥ × ΔT = 2 × 30 × 300 = 18000 J
24. E helu i ka hoʻoili wela no kahi kinoea kūpono e hana ana i kahi kaʻina hana isochoric me ka mahana mua o 100 K, ka mahana hope loa o 300 K, a me Cᵥ = 20 J/(mol·K) no 2 mol o ke kinoea.
Hoʻonā: ΔQ = n × Cᵥ × ΔT = 2 × 20 × 200 = 8000 J
25. E huli i ka hana i hana ʻia ma ka ʻōnaehana i ka wā o ke kaʻina hana isochoric no nā kūlana i luna.
Hoʻonā: W = 0 J (ʻoiai ʻaʻole loli ka leo, ʻaʻohe hana i hana ʻia)
26. He aha ka loli entropy no kahi kinoea kūpono i loko o kahi kaʻina hana isochoric ke loli ka mahana mai 400 K a i 800 K, a ʻo n = 3 mol, Cᵥ = 20 J/(mol·K)?
Hoʻonā: ΔS = n × Cᵥ × ln(T₂/T₁) = 3 × 20 × ln(2) ≈ 41.58 J/K
27. E huli i ka loli o ka ikehu manuahi o Gibbs no kahi kaʻina hana isochoric.
Hoʻonā: ΔG = 0 (No ke kaʻina hana isochoric i loko o kahi ʻōnaehana pani, ΔG = 0)
28. E hoʻoholo i ke kaomi hope loa o kahi kinoea e hana ana i kahi kaʻina hana isochoric, i hāʻawi ʻia ʻo P₁ = 3 atm, T₁ = 300 K, a me T₂ = 450 K.
Hoʻonā: P₂ = (T₂/T₁) × P₁ = 1.5 × 3 atm = 4.5 atm
29. E helu i ka loli o ka ikehu kūloko no kahi ʻōnaehana e hana ana i kahi kaʻina hana isochoric me 3 mol o ke kinoea, Cᵥ = 20 J/(mol K), a loli ka mahana mai 200 K a i 400 K.
Hoʻonā: ΔU = n × Cᵥ × ΔT = 3 × 20 × 200 = 12000 J
30. E hoʻoholo i ka loli entropy no kahi kaʻina hana isochoric kahi n = 4 mol, Cᵥ = 30 J/(mol K), T₁ = 150 K, a me T₂ = 300 K.
Hoʻonā: ΔS = n × Cᵥ × ln(T₂/T₁) = 4 × 30 × ln(2) ≈ 55.86 J/K
Uhi kēia mau pilikia i nā manaʻo like ʻole e pili ana i nā kaʻina hana isochoric, e like me ka hoʻoili wela, ka loli ikehu kūloko, ka hana i hana ʻia, ka loli entropy, a me nā mea hou aku.
