30 Pròiseasan teirmeadainimigeach isobarach – duilgheadasan agus fuasglaidhean
1. Tha an diagram PV gu h-ìosal a’ sealltainn gu bheil gas air leth freagarrach a’ dol tro phròiseas isobarach . Obraich a-mach an obair a nì an gas sa phròiseas AB.
Aithnichte:
Brùthadh (P) = 5 x 105 N / m²
Meud tùsail (V1 ) = 2 m3
Meud deireannach (V² ) = 6 m³
A dhìth: Obair (W)
fuasgladh:
W = P ( V2 – V1 )
W = (5 x 10 5 )(6 – 2) = (5 x 10 5 ) (4)
W = 20 x 10 5 = 2 x 10 6 Joules
2. Dè an diofar a tha eadar an obair a nì an gas ann am pròiseas AB agus pròiseas CD…
Aithnichte:
Pròiseas isobarach AB :
Brùthadh (P) = 6 atm = 6 x 105 N / m2
Meud tùsail (V1 ) = 1 liotair = 1 dm3 = 1 x 10-3 m3
Meud deireannach (V² ) = 3 liotairean = 3 dm³ = 3 x 10⁻³ m³
Pròiseas isobaric CD :
Brùthadh (P) = 4 atm = 4 x 105 N / m2
Meud tùsail (V1 ) = 2 liotair = 2 dm3 = 2 x 10-3 m3
Meud deireannach (V² ) = 5 liotairean = 5 dm³ = 3 x 10⁻³ m³
A dhìth : Tha an diofar san obair air a dhèanamh leis a’ ghas ann am pròiseas AB agus CD.
fuasgladh:
Nì an gas obair ann am pròiseas AB:
W = P ( V2 – V1 )
W = (6 x 10⁻⁶ ) (3 x 10⁻⁶ – 5 x 10⁻⁶ )
W = (6 x 10⁻⁶ ) (2 x 10⁻⁶ )
W = 12 x 102 = 1200 Joule
Tha an obair air a dhèanamh leis a’ ghas sa phròiseas CD:
W = P ( V2 – V1 )
W = (4 x 10⁻⁶ ) (5 x 10⁻⁶ – 5 x 10⁻⁶ )
W = (4 x 10⁻⁶ ) (3 x 10⁻⁶ )
W = 12 x 102 = 1200 Joule
Tha an diofar san obair air a dhèanamh leis a’ ghas sa phròiseas AB agus CD = 1200 – 1200 = 0.
3. Tha an obair a nì an gas sa phròiseas ABC….
Aithnichte:
Brùthadh 1 (P1 ) = 6 x 105 Pa = 6 x 105 N / m2
Brùthadh 2 (P2 ) = 3 x 105 Pa = 3 x 105 N / m2
Meud 1 (V1 ) = 2 cm3 = 2 x 10⁻⁶ m3
Meud 2 (V2 ) = 6 cm3 = 6 x 10⁻⁶ m3
A dhìth : Tha an obair air a dhèanamh ann am pròiseas ABC.
fuasgladh:
Ann am pròiseas AB, tha an tomhas-lìonaidh air a chumail seasmhach gus nach dèan an gas obair sam bith.
Rinn a' ghas obair sa phròiseas RC.
W = P2 ( V2 – V1 )
W = (3 x 10⁻⁶ ) (6 x 10⁻⁶ – 2 x 10⁻⁶ )
W = (3 x 10⁻⁶ ) (4 x 10⁻⁶ )
L = 12 x 10 -1
W = 1.2 Joule
Tha obair air a dhèanamh sa phròiseas ABC = tha obair air a dhèanamh sa phròiseas AB = 1.2 Joules.
4. Obraich a-mach an t-atharrachadh ann an lùth a-staigh airson 2 mhòl de ghas air leth a tha a’ dol tro leudachadh isobarach aig 300 K, far a bheil ΔV = 1 m3).
Fuasgladh: (ΔU = nC_vΔT), a’ cleachdadh (C_v = \frac{R}{γ-1}) (airson gas foirfe aon-atamach, (γ = \frac{5}{3})) agus (ΔT = \frac{PΔV}{nR), (ΔU = \frac{2\cdot 300 Δ1}{γ{5}{3}-1} timcheall air 1800 J).
5. Obraich a-mach an gluasad teas ann am pròiseas isobarach far a bheil 1 mòl de ghas diatomach air leth a’ leudachadh, \(C_p = \frac{7}{2}R\), agus \(\DeltaT = 50\ \text{K}\).
Fuasgladh: (Q = nC_pΔT = (7/2) ≤ 50 R = 1750 J) (a’ cleachdadh (R = 8.314 J/(mol·K)).
6. Lorg an obair a nì siostam a tha a’ dol tro leudachadh isobarach, (P = 3 atm), (Delta V = 4 L).
Fuasgladh: (W = PΔV = 3 × 4 = 12 L·atm).
7. Obraich a-mach an t-atharrachadh ann an entropy airson pròiseas isobarach far a bheil 2 mhòl de ghas air leth ag atharrachadh teòthachd le 20 K. Cleachd \(C_p = \frac{5}{2}R\).
Fuasgladh: (ΔS = nCp T2}{T1 = 2 \cdot \frac{5}{2}R \cdot \ln\frac{T1+20}{T1}).
8. Obraich a-mach an gluasad teas airson teannachadh isobaric de ghas foirfe aon-atamach, \(C_p = \frac{5}{2}R\), \(\DeltaT = -10\ \text{K}\).
Fuasgladh: (Q = nC_pΔT = 5/2 (-10) R timcheall air -415 J).
9. Lorg an obair a chaidh a dhèanamh air an t-siostam ann am pròiseas isobarach le \(P = 5\ \text{bar}\), \(\Delta V = -3\ \text{m}^3\).
Fuasgladh: (W = PΔV = 5 × (-3) = -15)).
10. Obraich a-mach an t-atharrachadh ann an lùth a-staigh airson pròiseas isobarach far a bheil \(n = 3\ \text{mol}\), \(C_v = 3R\), \(ΔT = 25\ \text{K}\).
Fuasgladh: (ΔU = nC_vΔT = 3⁻³R 25⁻¹ + 1883 J).
11. Obraich a-mach an t-atharrachadh entropy ann am pròiseas isobaric airson gas diatomic air leth freagarrach, \(n = 1\ \text{mol}\), \(\Delta T = 40\ \text{K}\), \(T_1 = 300\ \text{K}\).
Fuasgladh: (ΔS = nC_p(T2}{T1} = 7/2 R(340}{300).
12. Lorg an gluasad teas ann an leudachadh isobarach, \(P = 2\ \text{atm}\), \(\Delta V = 3\ \text{L}\), \(C_p = \frac{7}{2}R\).
Fuasgladh: (Q = PΔV + nC_pΔT = 2 × 3 + −7/2 RΔT).
13. Obraich a-mach an obair a chaidh a dhèanamh ann am pròiseas isobarach airson \(P = 4\ \text{bar}\), \(\Delta V = 5\ \text{m}^3\).
Fuasgladh: (W = PΔV = 4 × 5 = 20)).
14. Obraich a-mach an t-atharrachadh lùtha a-staigh airson teannachadh isobarach, (n = 2 mol), (Cv = 3/2 R), (Delta T = -30 K).
Fuasgladh: (ΔU = nC_vΔT = 2 \cdot \frac{3}{2}R \cdot (-30) \approx -753 \text{J}).
15. Lorg an t-atharrachadh entropy ann am pròiseas isobarach, (n = 1.5 mol), (DeltaT = 60 K), (T1 = 400 K), (Cp = 5/2 R).
Fuasgladh: (ΔS = nC_p\ln\frac{T_2}{T_1} = 1.5 \cdot \frac{5}{2}R\ln\frac{460}{400}\).
16. Obraich a-mach an gluasad teas airson leudachadh isobarach, (P = 3 bar), (Delta V = 2 m^3), (Cp = 5/2 R), (n = 2 mol).
Fuasgladh: (Q = PΔV + nC_pΔT = 3 × 2 + 2 ⋅ 5/2 RΔT).
17. Obraich a-mach an obair a chaidh a dhèanamh air 3 mòlan de ghas a tha a’ faighinn teannachadh isobaric, \(P = 5\ \text{atm}\), \(\Delta V = -4\ \text{L}\).
Fuasgladh: (W = PΔV = 5 × (-4) = -20 L·atm).
18. Obraich a-mach an t-atharrachadh lùtha a-staigh airson \(n = 4\ \text{mol}\), \(C_v = \frac{7}{2}R\), \(\DeltaT = 15\ \text{K}\) ann am pròiseas isobarach.
Fuasgladh: (ΔU = nC_vΔT = 4 \cdot \frac{7}{2}R \cdot 15 \approx 3157 \text{J}).
19. Lorg an gluasad teas ann am pròiseas isobarach, (P = 4 atm), (Delta V = 5 L), (n = 2 mol), (Cp = 5/2 R).
Fuasgladh: (Q = PΔV + nC_pΔT = 4 × 5 + 2 ⋅ 5/2 RΔT).
20. Obraich a-mach an obair a thèid a dhèanamh ann an teannachadh isobarach, \(P = 7\ \text{bar}\), \(\Delta V = -2\ \text{m}^3\).
Fuasgladh: (W = PΔV = 7 × (-2) = -14)).
21. Obraich a-mach an t-atharrachadh lùtha a-staigh airson 3 mòlan de ghas air leth a tha a’ dol tro phròiseas isobarach, \(C_v = \frac{5}{2}R\), \(\DeltaT = 20\ \text{K}\).
Fuasgladh: (ΔU = nC_vΔT = 3 \cdot \frac{5}{2}R \cdot 20 \approx 1256 \text{J}).
22. Lorg an t-atharrachadh entropy airson leudachadh isobarach, (n = 1 mol), (Cp = 7/2 R), (DeltaT = 30 K), (T1 = 250 K).
Fuasgladh: (ΔS = nC_p(T2}{T1} = 7/2 R(280}{250).
23. Obraich a-mach an gluasad teas ann am pròiseas isobarach, (P = 6 bar), (Delta V = 4 m^3), (n = 3 mol), (Cp = 3/2 R).
Fuasgladh: (Q = PΔV + nC_pΔT = 6 × 4 + 3 ⋅ 3/2 RΔT).
24. Obraich a-mach an obair a nì an siostam ann an leudachadh isobarach le \(P = 8\ \text{bar}\), \(\Delta V = 3\ \text{m}^3\).
Fuasgladh: (W = PΔV = 8 × 3 = 24)).
25. Obraich a-mach an t-atharrachadh lùtha a-staigh airson pròiseas isobarach far a bheil \(n = 2\ \text{mol}\), \(C_v = \frac{7}{2}R\), \(ΔT = -10\ \text{K}\).
Fuasgladh: (ΔU = nC_vΔT = 2 \cdot \frac{7}{2}R \cdot (-10) \approx -878 \text{J}).
26. Lorg an t-atharrachadh entropy airson gas diatomic ideal ann an teannachadh isobaric, \(n = 1.5\ \text{mol}\), \(T_1 = 350\ \text{K}\), \(\Delta T = -40\ \text{K}\).
Fuasgladh: (ΔS = nC_p\ln\frac{T_2}{T_1} = 1.5 \cdot \frac{7}{2}R\ln\frac{310}{350}\).
27. Obraich a-mach an gluasad teas airson 2 mhòl de ghas a tha a’ faighinn leudachadh isobarach, \(P = 5\ \text{bar}\), \(\Delta V = 6\ \text{m}^3\), \(C_p = \frac{5}{2}R\).
Fuasgladh: (Q = PΔV + nC_pΔT = 5 × 6 + 2 ⋅ 5/2 RΔT).
28. Obraich a-mach an obair a chaidh a dhèanamh air an t-siostam ann an teannachadh isobaric le \(P = 9\ \text{atm}\), \(\Delta V = -3\ \text{L}\).
Fuasgladh: (W = PΔV = 9 × (-3) = -27 L·atm).
29. Obraich a-mach an t-atharrachadh lùtha a-staigh airson 3 mòlan de ghas a tha a’ dol tro phròiseas isobarach, \(C_v = \frac{3}{2}R\), \(\DeltaT = 15\ \text{K}\).
Fuasgladh: (ΔU = nC_vΔT = 3 \cdot \frac{3}{2}R \cdot 15 \approx 564 \text{J}).
30. Lorg an t-atharrachadh entropy ann an leudachadh isobarach, (n = 4 mol), (Cp = 5/2 R), (DeltaT = 25 K), (T1 = 300 K).
Fuasgladh: (ΔS = nC_p\ln\frac{T_2}{T_1} = 4 \cdot \frac{5}{2}R\ln\frac{325}{300}\).
