30 Cov txheej txheem thermodynamics Isochoric - teeb meem thiab kev daws teeb meem
1. Daim duab PV hauv qab no qhia txog cov roj zoo tagnrho uas dhau los ntawm cov txheej txheem iso choric . Xam seb cov roj ua haujlwm li cas hauv cov txheej txheem AB.
Tshuaj:
Txheej Txheem AB yog ib txheej txheem isochoric (qhov ntim tas li). Qhov ntim yog tas li kom tsis muaj haujlwm ua los ntawm cov roj.
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2. Peb moles ntawm cov pa roj monoatomic ntawm 47 o C thiab ntawm qhov siab 2 x 10 5 Pa, dhau los ntawm cov txheej txheem isochoric kom qhov siab nce 3 x 10 5 Pa. Qhov kev hloov pauv ntawm lub zog sab hauv ntawm cov roj yog ... Universal gas constant (R) = 8.315 J / mol.K
Paub:
Kub pib (T1 ) = 47 o C + 273 = 320 K
Lub siab pib (P1 ) = 2 x 105 Pa
Qhov siab kawg (P2 ) = 3 x 105 Pa
Lub zog roj tas mus li (R) = 8.315 J/mol.K
Tus naj npawb ntawm moles (n) = 3
Xav tau: Kev hloov pauv ntawm lub zog sab hauv ntawm cov roj.
Tshuaj:
Hauv cov txheej txheem isochoric, qhov ntim tau khaws cia tas li kom tsis muaj haujlwm ua los ntawm cov roj (W = 0).
Txoj cai thib ib ntawm thermodynamics :
ΔU = QW
ΔU = Q-0
ΔU = Q
ΔU = lub zog sab hauv, Q = cua sov
Lub zog sab hauv ntawm cov roj:
ΔU = 3/2 n R ΔT = 3/2 n R (T 2 – T 1 )
Txoj Cai Gay-Lussac ( qhov ntim tas li ) :
Kev hloov pauv ntawm lub zog sab hauv ntawm cov roj:
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. 0.2 moles ntawm cov pa roj monatomic ntawm 27 o C nyob rau hauv ib lub thawv kaw. Lub cua sov raug ntxiv rau cov pa roj kom qhov kub ntawm cov pa roj dhau los ua 400 K yog ... Universal gas constant (R) = 8.315 J / mol.K
Paub:
Tus naj npawb ntawm moles (n) = 0.2 mol
Kub pib (T1 ) = 27 o C + 273 = 300 K
Qhov kub kawg (T2 ) = 400 K
Cov pa roj tas mus li (R) = 8.315 J/mol.K
Xav tau : Kub ntxiv (Q)
Tshuaj:
Hauv cov txheej txheem isochoric, qhov ntim tau khaws cia tas li kom tsis muaj haujlwm ua los ntawm cov roj (W = 0).
Txoj cai thib ib ntawm thermodynamics:
ΔU = QW
ΔU = Q-0
ΔU = Q
ΔU = lub zog sab hauv, Q = cua sov
Lub zog sab hauv ntawm cov roj:
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. Xam qhov cua sov hloov pauv rau ib qho roj zoo tagnrho uas tab tom ua ib qho txheej txheem isochoric los ntawm qhov kub pib ntawm 300 K mus rau qhov kub kawg ntawm 400 K. Xav tias 2 mol ntawm cov roj, thiab lub peev xwm cua sov molar ntawm qhov ntim tas li (Cᵥ) yog 20 J/(mol K).
Kev daws teeb meem: ΔQ = n × Cᵥ × ΔT = 2 mol × 20 J/(mol K) × (400 K – 300 K) = 4000 J
5. Nrhiav qhov kev hloov pauv ntawm lub zog sab hauv rau qhov teeb meem saum toj no.
Kev daws teeb meem: ΔU = ΔQ = 4000 J
6. Txheeb xyuas txoj haujlwm ua tiav rau ntawm lub kaw lus thaum lub sijhawm isochoric rau cov xwm txheej saum toj no.
Kev daws teeb meem: W = 0 J (vim tias qhov ntim tsis hloov, tsis muaj haujlwm ua tiav)
7. Rau ib qho roj imale monatomic uas tab tom ua ib qho isochoric process, yog tias qhov siab pib yog 2 atm thiab qhov siab kawg yog 3 atm, qhov sib piv ntawm qhov kub kawg thiab qhov kub pib yog dab tsi?
Kev daws teeb meem: Vim tias P₁/T₁ = P₂/T₂, T₂/T₁ = 3/2
8. Qhov kev hloov pauv entropy rau ib qho roj zoo tagnrho hauv cov txheej txheem isochoric thaum qhov kub hloov pauv ntawm 300 K mus rau 600 K, thiab n = 2 mol, Cᵥ = 20 J/(mol·K) yog dab tsi?
Kev daws teeb meem: ΔS = n × Cᵥ × ln(T₂/T₁) = 2 × 20 × ln(600/300) ≈ 27.73 J/K
9. Yog tias lub xeev pib ntawm cov roj diatomic ideal yog txhais los ntawm V = 2 L, P = 1 atm, thiab T = 300 K, nrhiav qhov siab kawg yog tias qhov kub tau ob npaug hauv cov txheej txheem isochoric.
Kev daws teeb meem: P₂ = 2 × P₁ = 2 atm
10. Nrhiav qhov kev hloov pauv ntawm Gibbs lub zog dawb rau ib qho txheej txheem isochoric.
Kev daws teeb meem: ΔG = 0 (Rau cov txheej txheem isochoric hauv lub kaw lus kaw, ΔG = 0)
11. Xam qhov kub kawg ntawm cov pa roj zoo tagnrho uas tab tom ua haujlwm isochoric yog tias qhov kub pib yog 200 K, thiab qhov siab pib thiab kawg yog 2 atm thiab 4 atm, raws li.
Kev daws teeb meem: T₂ = 2 × T₁ = 400 K
12. Rau ib qho roj zoo tagnrho, yog tias lub peev xwm cua sov ntawm qhov ntim tas li (Cᵥ) yog 30 J/(mol·K), nrhiav qhov hloov pauv cua sov thaum qhov kub hloov ntawm 300 K mus rau 450 K, nrog 3 mol ntawm roj.
Kev daws teeb meem: ΔQ = n × Cᵥ × ΔT = 3 × 30 × 150 = 13500 J
13. Rau tib txoj kev ua haujlwm li saum toj no, xam qhov kev hloov pauv ntawm lub zog sab hauv.
Kev daws teeb meem: ΔU = ΔQ = 13500 J
14. Txheeb xyuas qhov kev hloov pauv entropy rau cov txheej txheem isochoric nrog n = 1 mol, Cᵥ = 25 J/(mol K), T₁ = 200 K, thiab T₂ = 400 K.
Kev daws teeb meem: ΔS = n × Cᵥ × ln(T₂/T₁) = 25 × ln(2) ≈ 17.33 J/K
15. Nrhiav txoj haujlwm uas lub kaw lus ua thaum lub sijhawm isochoric ntawm 3 mol ntawm cov roj, thiab qhov kub hloov pauv ntawm 200 K mus rau 300 K.
Kev daws teeb meem: W = 0 J (vim tias qhov ntim tsis hloov, tsis muaj haujlwm ua tiav)
16. Xam qhov cua sov hloov pauv rau ib qho roj zoo tagnrho uas tab tom ua ib qho txheej txheem isochoric nrog qhov kub pib ntawm 150 K, qhov kub kawg ntawm 300 K, thiab Cᵥ = 15 J/(mol·K) rau 4 mol ntawm cov roj.
Kev daws teeb meem: ΔQ = n × Cᵥ × ΔT = 4 × 15 × 150 = 9000 J
17. Qhov kev hloov pauv entropy rau ib qho roj zoo tagnrho hauv cov txheej txheem isochoric nrog n = 1 mol, Cᵥ = 30 J/(mol·K), T₁ = 100 K, thiab T₂ = 200 K yog dab tsi?
Kev daws teeb meem: ΔS = n × Cᵥ × ln(T₂/T₁) = 30 × ln(2) ≈ 20.79 J/K
18. Txheeb xyuas qhov siab kawg ntawm cov roj uas tab tom ua ib qho txheej txheem isochoric, muab tias P₁ = 5 atm, T₁ = 250 K, thiab T₂ = 500 K.
Kev daws teeb meem: P₂ = (T₂/T₁) × P₁ = 2 × 5 atm = 10 atm
19. Nrhiav qhov hloov pauv cua sov rau 5 mol ntawm cov roj monatomic ideal uas tab tom ua cov txheej txheem isochoric ntawm 300 K txog 600 K. Xav tias Cᵥ = 15 J/(mol K).
Kev daws teeb meem: ΔQ = n × Cᵥ × ΔT = 5 × 15 × 300 = 22500 J
20. Qhov kev hloov pauv ntawm lub zog sab hauv rau qhov teeb meem saum toj no yog dab tsi?
Kev daws teeb meem: ΔU = ΔQ = 22500 J
21. Txheeb xyuas qhov kev hloov pauv entropy rau cov txheej txheem isochoric qhov twg n = 2 mol, Cᵥ = 25 J/(mol K), T₁ = 300 K, thiab T₂ = 600 K.
Kev daws teeb meem: ΔS = n × Cᵥ × ln(T₂/T₁) = 2 × 25 × ln(2) ≈ 34.66 J/K
22. Xam qhov kub kawg ntawm 1 mol ntawm cov roj monatomic ideal uas tab tom ua isochoric process yog tias qhov kub pib yog 400 K, thiab qhov siab pib thiab kawg yog 3 atm thiab 6 atm, raws li.
Kev daws teeb meem: T₂ = 2 × T₁ = 800 K
23. Rau ib qho roj diatomic ideal uas tab tom ua ib qho txheej txheem isochoric, xam qhov kev hloov pauv ntawm lub zog sab hauv thaum qhov kub hloov ntawm 300 K mus rau 600 K, nrog 2 mol ntawm cov roj, thiab Cᵥ = 30 J/(mol·K).
Kev daws teeb meem: ΔU = n × Cᵥ × ΔT = 2 × 30 × 300 = 18000 J
24. Xam qhov cua sov hloov pauv rau ib qho roj zoo tagnrho uas tab tom ua ib qho txheej txheem isochoric nrog qhov kub pib ntawm 100 K, qhov kub kawg ntawm 300 K, thiab Cᵥ = 20 J/(mol·K) rau 2 mol ntawm cov roj.
Kev daws teeb meem: ΔQ = n × Cᵥ × ΔT = 2 × 20 × 200 = 8000 J
25. Nrhiav txoj haujlwm ua tiav rau ntawm lub kaw lus thaum lub sijhawm ua haujlwm isochoric rau cov xwm txheej saum toj no.
Kev daws teeb meem: W = 0 J (vim tias qhov ntim tsis hloov, tsis muaj haujlwm ua tiav)
26. Qhov kev hloov pauv entropy rau ib qho roj zoo tagnrho hauv cov txheej txheem isochoric thaum qhov kub hloov pauv ntawm 400 K mus rau 800 K, thiab n = 3 mol, Cᵥ = 20 J/(mol·K) yog dab tsi?
Kev daws teeb meem: ΔS = n × Cᵥ × ln(T₂/T₁) = 3 × 20 × ln(2) ≈ 41.58 J/K
27. Nrhiav qhov kev hloov pauv ntawm Gibbs lub zog dawb rau ib qho txheej txheem isochoric.
Kev daws teeb meem: ΔG = 0 (Rau cov txheej txheem isochoric hauv lub kaw lus kaw, ΔG = 0)
28. Txheeb xyuas qhov siab kawg ntawm cov roj uas tab tom ua ib qho txheej txheem isochoric, muab tias P₁ = 3 atm, T₁ = 300 K, thiab T₂ = 450 K.
Kev daws teeb meem: P₂ = (T₂/T₁) × P₁ = 1.5 × 3 atm = 4.5 atm
29. Xam qhov kev hloov pauv ntawm lub zog sab hauv rau ib lub cev uas tab tom ua ib qho txheej txheem isochoric nrog 3 mol ntawm cov roj, Cᵥ = 20 J/(mol K), thiab qhov kub hloov pauv ntawm 200 K mus rau 400 K.
Kev daws teeb meem: ΔU = n × Cᵥ × ΔT = 3 × 20 × 200 = 12000 J
30. Txheeb xyuas qhov kev hloov pauv entropy rau cov txheej txheem isochoric qhov twg n = 4 mol, Cᵥ = 30 J/(mol K), T₁ = 150 K, thiab T₂ = 300 K.
Kev daws teeb meem: ΔS = n × Cᵥ × ln(T₂/T₁) = 4 × 30 × ln(2) ≈ 55.86 J/K
Cov teeb meem no npog ntau lub tswv yim ntsig txog cov txheej txheem isochoric, xws li kev hloov pauv cua sov, kev hloov pauv zog sab hauv, kev ua haujlwm tiav, kev hloov pauv entropy, thiab ntau ntxiv.
