Maitiro makumi matatu eIsobaric thermodynamics - matambudziko nemhinduro
1. Dhayagiramu yePV iri pazasi inoratidza gasi rakakodzera rinoitwa nenzira ye iso baric . Verenga basa rinoitwa negasi mukuita kwe AB.
Zvinozivikanwa:
Kumanikidzwa (P) = 5 x 10 5 N/m 2
Vhoriyamu yekutanga (V 1 ) = 2 m 3
Vhoriyamu yekupedzisira (V 2 ) = 6 m 3
Kudiwa: Basa (W)
Solution:
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. Musiyano uripi pakati pebasa rinoitwa negasi mu process AB ne process CD…
Zvinozivikanwa:
Maitiro eIsobaric AB :
Kumanikidzwa (P) = 6 atm = 6 x 10 5 N/m 2
Vhoriyamu yekutanga (V 1 ) = 1 litre = 1 dm 3 = 1 x 10 -3 m 3
Vhoriyamu yekupedzisira (V 2 ) = marita matatu = 3 dm 3 = 3 x 10 -3 m 3
CD yeIsobaric process :
Kumanikidzwa (P) = 4 atm = 4 x 10 5 N/m 2
Vhoriyamu yekutanga (V 1 ) = 2 marita = 2 dm 3 = 2 x 10 -3 m 3
Vhoriyamu yekupedzisira (V 2 ) = marita mashanu = 5 dm 3 = 5 x 10 -3 m 3
Zvinodiwa : Musiyano webasa unoitwa negasi riri muprocess AB neCD.
Solution:
Basa rinoitwa negasi riri mukuita 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
Basa rinoitwa negasi riri muprocess CD:
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
Musiyano webasa unoitwa negasi riri mukuita AB neCD = 1200 - 1200 = 0.
3. Basa rinoitwa negasi riri mukuita ABC iri….
Zvinozivikanwa:
Kumanikidzwa 1 (P 1 ) = 6 x 10 5 Pa = 6 x 10 5 N/m 2
Kumanikidzwa 2 (P 2 ) = 3 x 10 5 Pa = 3 x 10 5 N/m 2
Vhoriyamu 1 (V 1 ) = 2 cm 3 = 2 x 10 -6 m 3
Vhoriyamu 2 (V 2 ) = 6 cm 3 = 6 x 10 -6 m 3
Zvinodiwa : Basa rinoitwa zviri kuitika ABC.
Solution:
Mukuita kwe AB, vhoriyamu inochengetwa yakafanana kuitira kuti pasave nebasa rinoitwa negasi.
Basa rakaitwa negasi mukuita kweBC.
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
Basa rinoitwa mukuita ABC = basa rinoitwa mukuita AB = 1.2 Joules.
4. Sarudza shanduko musimba remukati memamoles maviri egasi rakakodzera riri kuwedzera kweisobaric pa300 K, uko \(\Delta V = 1\ \text{m}^3\).
Mhinduro: \(\Delta U = nC_v\Delta T\), uchishandisa \(C_v = \frac{R}{\gamma-1}\) (yegasi rakanaka remonatomic, \(\gamma = \frac{5}{3}\)) uye \(\Delta T = \frac{P\Delta V}{nR}\), \(\Delta U = \frac{2\cdot 300 \cdot 1}{\frac{5}{3}-1} \approx 1800\ \text{J}\).
5. Verengai kutamiswa kwekupisa mumaitiro e isobaric apo mole imwe ye diatomic ideal gas inowedzera, \(C_p = \frac{7}{2}R\), uye \(\Delta T = 50\ \text{K}\).
Mhinduro: \(Q = nC_p\Delta T = \frac{7}{2} \cdot 50 \cdot R \approx 1750\ \text{J}\) (uchishandisa \(R = 8.314\ \text{J/(mol·K)}\)).
6. Tsvaga basa rakaitwa nesystem iri kuwedzera isobaric, \(P = 3\ \text{atm}\), \(\Delta V = 4\ \text{L}\).
Mhinduro: \(W = P\Delta V = 3 \kawa 4 = 12\ \text{L·atm}\).
7. Sarudza shanduko mu entropy yemaitiro e isobaric apo ma moles maviri egasi rakakodzera anochinja tembiricha ne20 K. Shandisa \(C_p = \frac{5}{2}R\).
Mhinduro: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 2 \cdot \frac{5}{2}R \cdot \ln\frac{T_1+20}{T_1}\).
8. Verengai kutamiswa kwekupisa kwe isobaric compression ye monatomic ideal gas, \(C_p = \frac{5}{2}R\), \(\Delta T = -10\ \text{K}\).
Mhinduro: \(Q = nC_p\Delta T = \frac{5}{2} \cdot (-10) \cdot R \approx -415\ \text{J}\).
9. Tsvaga basa rakaitwa pasystem nenzira ye isobaric ne \(P = 5\ \text{bar}\), \(\Delta V = -3\ \text{m}^3\).
Mhinduro: \(W = P\Delta V = 5 \nguva (-3) = -15\ \text{bar m}^3\).
10. Sarudza shanduko musimba remukati memuviri wemaitiro e-isobaric apo \(n = 3\ \text{mol}\), \(C_v = 3R\), \(\Delta T = 25\ \text{K}\).
Mhinduro: \(\Delta U = nC_v\Delta T = 3 \cdot 3R \cdot 25 \approx 1883\ \text{J}\).
11. Verenga shanduko ye entropy mumaitiro e isobaric kune diatomic ideal gas, \(n = 1\ \text{mol}\), \(\Delta T = 40\ \text{K}\), \(T_1 = 300\ \text{K}\).
Mhinduro: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = \frac{7}{2}R\ln\frac{340}{300}\).
12. Tsvaga kutamiswa kwekupisa mukuwedzera kwe isobaric, \(P = 2\ \text{atm}\), \(\Delta V = 3\ \text{L}\), \(C_p = \frac{7}{2}R\).
Mhinduro: \(Q = P\Delta V + nC_p\Delta T = 2 \kawa 3 + \frac{7}{2}R\Delta T\).
13. Sarudza basa rinoitwa nenzira ye isobaric ye \(P = 4\ \text{bar}\), \(\Delta V = 5\ \text{m}^3\).
Mhinduro: \(W = P\Delta V = 4 \kawa 5 = 20\ \text{bar m}^3\).
14. Verenga shanduko yesimba remukati memuviri pakushandiswa kwe isobaric compression, \(n = 2\ \text{mol}\), \(C_v = \frac{3}{2}R\), \(\Delta T = -30\ \text{K}\).
Mhinduro: \(\Delta U = nC_v\Delta T = 2 \cdot \frac{3}{2}R \cdot (-30) \approx -753\ \text{J}\).
15. Tsvaga shanduko ye entropy mumaitiro e isobaric, \(n = 1.5\ \text{mol}\), \(\Delta T = 60\ \text{K}\), \(T_1 = 400\ \text{K}\), \(C_p = \frac{5}{2}R\).
Mhinduro: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 1.5 \cdot \frac{5}{2}R\ln\frac{460}{400}\).
16. Sarudza kutamiswa kwekupisa kwekuwedzera kwe isobaric, \(P = 3\ \text{bar}\), \(\Delta V = 2\ \text{m}^3\), \(C_p = \frac{5}{2}R\), \(n = 2\ \text{mol}\).
Mhinduro: \(Q = P\Delta V + nC_p\Delta T = 3 \times 2 + 2 \cdot \frac{5}{2}R\Delta T\).
17. Verenga basa rakaitwa pamamoles matatu egasi riri pasi pekumanikidzwa kwe isobaric, \(P = 5\ \text{atm}\), \(\Delta V = -4\ \text{L}\).
Mhinduro: \(W = P\Delta V = 5 \nguva (-4) = -20\ \chinyorwa{L·atm}\).
18. Sarudza shanduko yesimba remukati ye \(n = 4\ \text{mol}\), \(C_v = \frac{7}{2}R\), \(\Delta T = 15\ \text{K}\) mukuita kwe isobaric.
Mhinduro: \(\Delta U = nC_v\Delta T = 4 \cdot \frac{7}{2}R \cdot 15 \approx 3157\ \text{J}\).
19. Tsvaga kutamiswa kwekupisa mumaitiro e isobaric, \(P = 4\ \text{atm}\), \(\Delta V = 5\ \text{L}\), \(n = 2\ \text{mol}\), \(C_p = \frac{5}{2}R\).
Mhinduro: \(Q = P\Delta V + nC_p\Delta T = 4 \times 5 + 2 \cdot \frac{5}{2}R\Delta T\).
20. Sarudza basa rinoitwa nekudzvanywa kwe isobaric, \(P = 7\ \text{bar}\), \(\Delta V = -2\ \text{m}^3\).
Mhinduro: \(W = P\Delta V = 7 \nguva (-2) = -14\ \text{bar m}^3\).
21. Verenga shanduko yesimba remukati me3 moles yegasi rakakodzera riri kuitwa muitiro we isobaric, \(C_v = \frac{5}{2}R\), \(\Delta T = 20\ \text{K}\).
Mhinduro: \(\Delta U = nC_v\Delta T = 3 \cdot \frac{5}{2}R \cdot 20 \approx 1256\ \text{J}\).
22. Tsvaga shanduko ye entropy yekuwedzera kwe isobaric, \(n = 1\ \text{mol}\), \(C_p = \frac{7}{2}R\), \(\Delta T = 30\ \text{K}\), \(T_1 = 250\ \text{K}\).
Mhinduro: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = \frac{7}{2}R\ln\frac{280}{250}\).
23. Sarudza kutamiswa kwekupisa mumaitiro e isobaric, \(P = 6\ \text{bar}\), \(\Delta V = 4\ \text{m}^3\), \(n = 3\ \text{mol}\), \(C_p = \frac{3}{2}R\).
Mhinduro: \(Q = P\Delta V + nC_p\Delta T = 6 \times 4 + 3 \cdot \frac{3}{2}R\Delta T\).
24. Verenga basa rakaitwa nesystem iyi mukuwedzera kwe isobaric uchishandisa \(P = 8\ \text{bar}\), \(\Delta V = 3\ \text{m}^3\).
Mhinduro: \(W = P\Delta V = 8 \kawa 3 = 24\ \text{bar m}^3\).
25. Sarudza shanduko yesimba remukati memaitiro e isobaric apo \(n = 2\ \text{mol}\), \(C_v = \frac{7}{2}R\), \(\Delta T = -10\ \text{K}\).
Mhinduro: \(\Delta U = nC_v\Delta T = 2 \cdot \frac{7}{2}R \cdot (-10) \approx -878\ \text{J}\).
26. Tsvaga shanduko ye entropy ye diatomic ideal gas mu isobaric compression, \(n = 1.5\ \text{mol}\), \(T_1 = 350\ \text{K}\), \(\Delta T = -40\ \text{K}\).
Mhinduro: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 1.5 \cdot \frac{7}{2}R\ln\frac{310}{350}\).
27. Sarudza kutamiswa kwekupisa kwema moles maviri egasi riri kuyerera mu isobaric expansion, \(P = 5\ \text{bar}\), \(\Delta V = 6\ \text{m}^3\), \(C_p = \frac{5}{2}R\).
Mhinduro: \(Q = P\Delta V + nC_p\Delta T = 5 \times 6 + 2 \cdot \frac{5}{2}R\Delta T\).
28. Verenga basa rakaitwa pasystem uchishandisa isobaric compression ne \(P = 9\ \text{atm}\), \(\Delta V = -3\ \text{L}\).
Mhinduro: \(W = P\Delta V = 9 \nguva (-3) = -27\ \chinyorwa{L·atm}\).
29. Sarudza shanduko yesimba remukati memamoles matatu egasi riri kuita isobaric process, \(C_v = \frac{3}{2}R\), \(\Delta T = 15\ \text{K}\).
Mhinduro: \(\Delta U = nC_v\Delta T = 3 \cdot \frac{3}{2}R \cdot 15 \approx 564\ \text{J}\).
30. Tsvaga shanduko ye entropy mukuwedzera kwe isobaric, \(n = 4\ \text{mol}\), \(C_p = \frac{5}{2}R\), \(\Delta T = 25\ \text{K}\), \(T_1 = 300\ \text{K}\).
Mhinduro: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 4 \cdot \frac{5}{2}R\ln\frac{325}{300}\).
