Njira 30 za Isobaric thermodynamics - mavuto ndi mayankho
1. Chithunzi cha PV chomwe chili pansipa chikuwonetsa mpweya wabwino womwe umadutsa mu njira ya iso baric . Werengani ntchito yomwe yachitika ndi mpweya mu ndondomeko ya AB.
Zodziwika:
Kupanikizika (P) = 5 x 10 5 N/m 2
Kuchuluka koyambirira (V 1 ) = 2 m 3
Voliyumu yomaliza (V 2 ) = 6 m 3
Akufuna: Ntchito (W)
Yankho:
W = P (V 2 – V 1 )
W = (5 x 10 5 )(6 – 2) = (5 x 10 5 ) (4)
W = 20 x 10 5 = 2 x 10 6 Joules
2. Kodi kusiyana kwa ntchito yochitidwa ndi mpweya mu process AB ndi process CD ndi kotani?
Zodziwika:
Njira ya Isobaric AB :
Kupanikizika (P) = 6 atm = 6 x 10 5 N/m 2
Voliyumu yoyambirira (V 1 ) = lita imodzi = 1 dm 3 = 1 x 10 -3 m 3
Voliyumu yomaliza (V 2 ) = malita 3 = 3 dm 3 = 3 x 10 -3 m 3
CD ya Isobaric process :
Kupanikizika (P) = 4 atm = 4 x 10 5 N/m 2
Voliyumu yoyambirira (V 1 ) = malita awiri = 2 dm 3 = 2 x 10 -3 m 3
Voliyumu yomaliza (V 2 ) = malita 5 = 5 dm 3 = 5 x 10 -3 m 3
Kufunidwa : Kusiyana kwa ntchito kumachitika ndi mpweya womwe umagwiritsidwa ntchito mu AB ndi CD.
Yankho:
Ntchito imachitika ndi mpweya womwe ukuchitika AB:
W = P (V 2 – V 1 )
W = (6 x 10 5 )(3 x 10 -3 – 1 x 10 -3 )
W = (6 x 10 5 )(2 x 10 -3 )
W = 12 x 10 2 = 1200 Joule
Ntchito imachitika ndi CD ya gasi yomwe ikugwira ntchito:
W = P (V 2 – V 1 )
W = (4 x 10 5 )(5 x 10 -3 – 2 x 10 -3 )
W = (4 x 10 5 )(3 x 10 -3 )
W = 12 x 10 2 = 1200 Joule
Kusiyana kwa ntchito kumachitika ndi mpweya womwe ukugwiritsidwa ntchito mu AB ndi CD = 1200 - 1200 = 0.
3. Ntchito imagwiridwa ndi mpweya womwe ukuchitika. ABC ndi….
Zodziwika:
Kupanikizika 1 (P 1 ) = 6 x 10 5 Pa = 6 x 10 5 N/m 2
Kupanikizika 2 (P 2 ) = 3 x 10 5 Pa = 3 x 10 5 N/m 2
Voliyumu 1 (V 1 ) = 2 cm 3 = 2 x 10 -6 m 3
Voliyumu 2 (V 2 ) = 6 cm 3 = 6 x 10 -6 m 3
Akufuna : Ntchito yachitika mu ndondomeko ABC.
Yankho:
Mu ndondomekoyi AB, voliyumu imasungidwa yofanana kotero kuti palibe ntchito yomwe imachitika ndi mpweya.
Ntchito inachitidwa ndi mpweya mu ndondomeko ya BC.
W = P 2 (V 2 – V 1 )
W = (3 x 10 5 )(6 x 10 -6 – 2 x 10 -6 )
W = (3 x 10 5 )(4 x 10 -6 )
W = 12 x 10 -1
W = 1.2 Joule
Ntchito yachitika mu ndondomeko ABC = ntchito yachitika mu ndondomeko AB = 1.2 Joules.
4. Dziwani kusintha kwa mphamvu yamkati mwa ma mole awiri a mpweya wabwino womwe ukupitilira kukula kwa isobaric pa 300 K, pomwe \(\Delta V = 1\ \text{m}^3\).
Yankho: \(\Delta U = nC_v\Delta T\), pogwiritsa ntchito \(C_v = \frac{R}{\gamma-1}\) (pa mpweya wabwino wa monatomic, \(\gamma = \frac{5}{3}\)) ndi \(\Delta T = \frac{P\Delta V}{nR}\), \(\Delta U = \frac{2\cdot 300 \cdot 1}{\frac{5}{3}-1} \approx 1800\ \text{J}\).
5. Werengani kusamutsa kutentha mu njira ya isobaric pomwe mole imodzi ya mpweya wabwino wa diatomic imakula, \(C_p = \frac{7}{2}R\), ndi \(\Delta T = 50\ \text{K}\).
Yankho: \(Q = nC_p\Delta T = \frac{7}{2} \cdot 50 \cdot R \approx 1750\ \text{J}\) (pogwiritsa ntchito \(R = 8.314\ \text{J/(mol·K)}\)).
6. Pezani ntchito yomwe yachitika ndi dongosolo lomwe likupitilira kukulitsa kwa isobaric, \(P = 3\ \text{atm}\), \(\Delta V = 4\ \text{L}\).
Yankho: \(W = P\Delta V = 3 \nthawi 4 = 12\ \malemba{L·atm}\).
7. Dziwani kusintha kwa entropy ya njira ya isobaric pomwe ma mole awiri a mpweya woyenera amasintha kutentha ndi 20 K. Gwiritsani ntchito \(C_p = \frac{5}{2}R\).
Yankho: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 2 \cdot \frac{5}{2}R \cdot \ln\frac{T_1+20}{T_1}\).
8. Werengani kutentha kwa mpweya wa monatomic ideal, \(C_p = \frac{5}{2}R\), \(\Delta T = -10\ \text{K}\).
Yankho: \(Q = nC_p\Delta T = \frac{5}{2} \cdot (-10) \cdot R \approx -415\ \text{J}\).
9. Pezani ntchito yomwe yachitika pa dongosololi mu njira ya isobaric ndi \(P = 5\ \text{bar}\), \(\Delta V = -3\ \text{m}^3\).
Yankho: \(W = P\Delta V = 5 \times (-3) = -15\ \text{bar m}^3\).
10. Dziwani kusintha kwa mphamvu yamkati ya njira ya isobaric pomwe \(n = 3\ \text{mol}\), \(C_v = 3R\), \(\Delta T = 25\ \text{K}\).
Yankho: \(\Delta U = nC_v\Delta T = 3 \cdot 3R \cdot 25 \approx 1883\ \text{J}\).
11. Werengani kusintha kwa entropy mu njira ya isobaric ya mpweya wabwino wa diatomic, \(n = 1\ \text{mol}\), \(\Delta T = 40\ \text{K}\), \(T_1 = 300\ \text{K}\).
Yankho: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = \frac{7}{2}R\ln\frac{340}{300}\).
12. Pezani kusamutsa kutentha mu expansion ya isobaric, \(P = 2\ \text{atm}\), \(\Delta V = 3\ \text{L}\), \(C_p = \frac{7}{2}R\).
Yankho: \(Q = P\Delta V + nC_p\Delta T = 2 \times 3 + \frac{7}{2}R\Delta T\).
13. Dziwani ntchito yomwe yachitika mu njira ya isobaric ya \(P = 4\ \text{bar}\), \(\Delta V = 5\ \text{m}^3\).
Yankho: \(W = P\Delta V = 4 \times 5 = 20\ \text{bar m}^3\).
14. Werengani kusintha kwa mphamvu yamkati ya kupsinjika kwa isobaric, \(n = 2\ \text{mol}\), \(C_v = \frac{3}{2}R\), \(\Delta T = -30\ \text{K}\).
Yankho: \(\Delta U = nC_v\Delta T = 2 \cdot \frac{3}{2}R \cdot (-30) \approx -753\ \text{J}\).
15. Pezani kusintha kwa entropy mu njira ya isobaric, \(n = 1.5\ \text{mol}\), \(\Delta T = 60\ \text{K}\), \(T_1 = 400\ \text{K}\), \(C_p = \frac{5}{2}R\).
Yankho: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 1.5 \cdot \frac{5}{2}R\ln\frac{460}{400}\).
16. Dziwani momwe kutentha kumasamutsidwira pakukula kwa isobaric, \(P = 3\ \text{bar}\), \(\Delta V = 2\ \text{m}^3\), \(C_p = \frac{5}{2}R\), \(n = 2\ \text{mol}\).
Yankho: \(Q = P\Delta V + nC_p\Delta T = 3 \times 2 + 2 \cdot \frac{5}{2}R\Delta T\).
17. Werengani ntchito yochitidwa pa ma mole atatu a mpweya womwe ukuphwanyidwa ndi isobaric, \(P = 5\ \text{atm}\), \(\Delta V = -4\ \text{L}\).
Yankho: \(W = P\Delta V = 5 \times (-4) = -20\ \text{L·atm}\).
18. Dziwani kusintha kwa mphamvu yamkati ya \(n = 4\ \text{mol}\), \(C_v = \frac{7}{2}R\), \(\Delta T = 15\ \text{K}\) mu njira ya isobaric.
Yankho: \(\Delta U = nC_v\Delta T = 4 \cdot \frac{7}{2}R \cdot 15 \approx 3157\ \text{J}\).
19. Pezani kusamutsa kutentha mu njira ya isobaric, \(P = 4\ \text{atm}\), \(\Delta V = 5\ \text{L}\), \(n = 2\ \text{mol}\), \(C_p = \frac{5}{2}R\).
Yankho: \(Q = P\Delta V + nC_p\Delta T = 4 \times 5 + 2 \cdot \frac{5}{2}R\Delta T\).
20. Dziwani ntchito yochitidwa mu isobaric compression, \(P = 7\ \text{bar}\), \(\Delta V = -2\ \text{m}^3\).
Yankho: \(W = P\Delta V = 7 \times (-2) = -14\ \text{bar m}^3\).
21. Werengani kusintha kwa mphamvu yamkati mwa ma mole atatu a mpweya wabwino womwe ukudutsa mu njira ya isobaric, \(C_v = \frac{5}{2}R\), \(\Delta T = 20\ \text{K}\).
Yankho: \(\Delta U = nC_v\Delta T = 3 \cdot \frac{5}{2}R \cdot 20 \approx 1256\ \text{J}\).
22. Pezani kusintha kwa entropy kwa expansion ya isobaric, \(n = 1\ \text{mol}\), \(C_p = \frac{7}{2}R\), \(\Delta T = 30\ \text{K}\), \(T_1 = 250\ \text{K}\).
Yankho: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = \frac{7}{2}R\ln\frac{280}{250}\).
23. Dziwani momwe kutentha kumayendera mu njira ya isobaric, \(P = 6\ \text{bar}\), \(\Delta V = 4\ \text{m}^3\), \(n = 3\ \text{mol}\), \(C_p = \frac{3}{2}R\).
Yankho: \(Q = P\Delta V + nC_p\Delta T = 6 \times 4 + 3 \cdot \frac{3}{2}R\Delta T\).
24. Werengani ntchito yochitidwa ndi dongosololi mu expansion ya isobaric ndi \(P = 8\ \text{bar}\), \(\Delta V = 3\ \text{m}^3\).
Yankho: \(W = P\Delta V = 8 \times 3 = 24\ \text{bar m}^3\).
25. Dziwani kusintha kwa mphamvu yamkati pa njira ya isobaric komwe \(n = 2\ \text{mol}\), \(C_v = \frac{7}{2}R\), \(\Delta T = -10\ \text{K}\).
Yankho: \(\Delta U = nC_v\Delta T = 2 \cdot \frac{7}{2}R \cdot (-10) \approx -878\ \text{J}\).
26. Pezani kusintha kwa entropy kwa mpweya wabwino wa diatomic mu kupsinjika kwa isobaric, \(n = 1.5\ \text{mol}\), \(T_1 = 350\ \text{K}\), \(\Delta T = -40\ \text{K}\).
Yankho: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 1.5 \cdot \frac{7}{2}R\ln\frac{310}{350}\).
27. Dziwani momwe kutentha kumayendera kwa ma mole awiri a mpweya womwe ukupitilira kukula kwa isobaric, \(P = 5\ \text{bar}\), \(\Delta V = 6\ \text{m}^3\), \(C_p = \frac{5}{2}R\).
Yankho: \(Q = P\Delta V + nC_p\Delta T = 5 \times 6 + 2 \cdot \frac{5}{2}R\Delta T\).
28. Werengani ntchito yomwe yachitika pa dongosololi mu isobaric compression ndi \(P = 9\ \text{atm}\), \(\Delta V = -3\ \text{L}\).
Yankho: \(W = P\Delta V = 9 \times (-3) = -27\ \text{L·atm}\).
29. Dziwani kusintha kwa mphamvu yamkati mwa ma mole atatu a mpweya womwe ukudutsa mu njira ya isobaric, \(C_v = \frac{3}{2}R\), \(\Delta T = 15\ \text{K}\).
Yankho: \(\Delta U = nC_v\Delta T = 3 \cdot \frac{3}{2}R \cdot 15 \approx 564\ \text{J}\).
30. Pezani kusintha kwa entropy mu expansion ya isobaric, \(n = 4\ \text{mol}\), \(C_p = \frac{5}{2}R\), \(\Delta T = 25\ \text{K}\), \(T_1 = 300\ \text{K}\).
Yankho: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 4 \cdot \frac{5}{2}R\ln\frac{325}{300}\).
