Usoro 30 nke thermodynamics Isobaric - nsogbu na ngwọta
1. Ihe osise PV dị n'okpuru na-egosi gas zuru oke nke na-agafe usoro iso baric . Gbakọọ na gas na-arụ ọrụ ahụ n'usoro AB.
A maara:
Nrụgide (P) = 5 x 10 5 N/m 2
Mpịakọta mbụ (V1 ) = 2 m 3
Olu ikpeazụ (V2 ) = 6 m 3
Achọtara: Ọrụ (W)
Ngwọta:
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. Kedu ihe dị iche n'ọrụ gas rụrụ na usoro AB na usoro CD…
A maara:
Usoro isobaric AB :
Nrụgide (P) = 6 atm = 6 x 10 5 N/m 2
Mpịakọta mbụ (V 1 ) = lita 1 = 1 dm 3 = 1 x 10 -3 m 3
Olu ikpeazụ (V 2 ) = lita 3 = 3 dm 3 = 3 x 10 -3 m 3
CD usoro Isobaric :
Nrụgide (P) = 4 atm = 4 x 10 5 N/m 2
Mpịakọta mbụ (V 1 ) = lita 2 = 2 dm 3 = 2 x 10 -3 m 3
Olu ikpeazụ (V 2 ) = lita 5 = 5 dm 3 = 5 x 10 -3 m 3
Achọrọ : Ihe dị iche n'ọrụ ahụ bụ gas dị na usoro AB na CD.
Ngwọta:
A na-arụ ọrụ ahụ site na gas dị n'ime AB:
W = P ( V2 – V1 )
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
A na-arụ ọrụ ahụ site na CD usoro gas:
W = P ( V2 – V1 )
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
Ọdịiche nke ọrụ ahụ bụ gas dị na usoro AB na CD = 1200 - 1200 = 0.
3. A na-arụ ọrụ site na gas dị n'usoro ABC bụ….
A maara:
Nrụgide 1 (P 1 ) = 6 x 10 5 Pa = 6 x 10 5 N/m 2
Nrụgide 2 (P 2 ) = 3 x 10 5 Pa = 3 x 10 5 N/m 2
Mpịakọta nke 1 (V 1 ) = 2 cm 3 = 2 x 10 -6 m 3
Mpịakọta nke 2 (V 2 ) = 6 cm 3 = 6 x 10 -6 m 3
A chọrọ ya : A na-arụ ọrụ n'usoro ABC.
Ngwọta:
N'ime usoro AB, a na-eme ka olu ahụ dịgide otu ebe ka gas ghara ịrụ ọrụ ọ bụla.
E ji gas rụọ ọrụ n'oge usoro BC.
W = P2 ( V2 – V1 )
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 = Joule 1.2
A na-arụ ọrụ n'usoro ABC = a na-arụ ọrụ n'usoro AB = 1.2 Joules.
4. Chọpụta mgbanwe dị na ike dị n'ime maka mole abụọ nke gas zuru oke nke na-agafe mgbasawanye isobaric na 300 K, ebe \(\Delta V = 1\ \text{m}^3\).
Ngwọta: \(\Delta U = nC_v\Delta T\), site na iji \(C_v = \frac{R}{\gamma-1}\) (maka gas kacha mma nke monatomic, \(\gamma = \frac{5}{3}\)) na \(\Delta T = \frac{P\Delta V}{nR}\), \(\Delta U = \frac{2\cdot 300 \cdot 1}{\frac{5}{3}-1} \approx 1800\ \text{J}\).
5. Gbakọọ nnyefe okpomọkụ n'ime usoro isobaric ebe 1 mole nke gas diatomic kacha mma na-agbasa, \(C_p = \frac{7}{2}R\), na \(\Delta T = 50\ \text{K}\).
Ngwọta: \(Q = nC_p\Delta T = \frac{7}{2} \cdot 50 \cdot R \approx 1750\\text{J}\) (iji \(R = 8.314\ \text{J/(mol·K)}\)).
6. Chọta ọrụ sistemụ na-eme ka mgbasawanye isobaric rụọ, \(P = 3\ \text{atm}\), \(\Delta V = 4\ \text{L}\).
Ngwọta: \(W = P\Delta V = ugboro atọ 4 = 12\ \text{L·atm}\).
7. Chọpụta mgbanwe dị na entropy maka usoro isobaric ebe mole abụọ nke gas zuru oke na-agbanwe okpomọkụ site na 20 K. Jiri \(C_p = \frac{5}{2}R\).
Ngwọta: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 2 \cdot \frac{5}{2}R \cdot \ln\frac{T_1+20}{T_1}\).
8. Gbakọọ nnyefe okpomọkụ maka mkpakọ isobaric nke gas monoatomic kacha mma, \(C_p = \frac{5}{2}R\), \(\Delta T = -10\ \text{K}\).
Ngwọta: \(Q = nC_p\Delta T = \frac{5}{2} \cdot (-10) \cdot R \approx -415\ \text{J}\).
9. Chọta ọrụ e mere na sistemụ ahụ n'usoro isobaric na \(P = 5\ \text{bar}\), \(\Delta V = -3\ \text{m}^3\).
Ngwọta: \(W = P\Delta V = ugboro ise (-3) = -15\ \text{bar}^3\).
10. Chọpụta mgbanwe dị na ike dị n'ime maka usoro isobaric ebe \(n = 3\ \text{mol}\), \(C_v = 3R\), \(\Delta T = 25\ \text{K}\).
Ngwọta: \(\Delta U = nC_v\Delta T = 3 \cdot 3R \cdot 25 \ihe dịka 1883\ \text{J}\).
11. Gbakọọ mgbanwe entropy na usoro isobaric maka gas diatomic zuru oke, \(n = 1\ \text{mol}\), \(\Delta T = 40\ \text{K}\), \(T_1 = 300\ \text{K}\).
Ngwọta: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = \frac{7}{2}R\ln\frac{340}{300}\).
12. Chọta nnyefe okpomọkụ na mgbasawanye isobaric, \(P = 2\ \text{atm}\), \(\Delta V = 3\ \text{L}\), \(C_p = \frac{7}{2}R\).
Ngwọta: \(Q = P\Delta V + nC_p\Delta T = ugboro abụọ 3 + \frac{7}{2}R\Delta T\).
13. Chọpụta ọrụ e mere n'usoro isobaric maka \(P = 4\ \text{bar}\), \(\Delta V = 5\ \text{m}^3\).
Ngwọta: \(W = P\Delta V = ugboro anọ 5 = 20\ \text{bar}^3\).
14. Gbakọọ mgbanwe ike dị n'ime maka mkpakọ isobaric, \(n = 2\ \text{mol}\), \(C_v = \frac{3}{2}R\), \(\Delta T = -30\ \text{K}\).
Ngwọta: \(\Delta U = nC_v\Delta T = 2 \cdot \frac{3}{2}R \cdot (-30) \approx -753\ \text{J}\).
15. Chọta mgbanwe entropy n'ime usoro isobaric, \(n = 1.5\ \text{mol}\), \(\Delta T = 60\ \text{K}\), \(T_1 = 400\ \text{K}\), \(C_p = \frac{5}{2}R\).
Ngwọta: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 1.5 \cdot \frac{5}{2}R\ln\frac{460}{400}\).
16. Chọpụta nnyefe okpomọkụ maka mgbasawanye isobaric, \(P = 3\ \text{bar}\), \(\Delta V = 2\ \text{m}^3\), \(C_p = \frac{5}{2}R\), \(n = 2\ \text{mol}\).
Ngwọta: \(Q = P\Delta V + nC_p\Delta T = ugboro atọ 2 + 2 \cdot \frac{5}{2}R\Delta T\).
17. Gbakọọ ọrụ e mere na mole atọ nke gas nke na-enweta nrụgide isobaric, \(P = 5\ \text{atm}\), \(\Delta V = -4\ \text{L}\).
Ngwọta: \(W = P\Delta V = ugboro ise (-4) = -20\ \text{L·atm}\).
18. Chọpụta mgbanwe ike dị n'ime maka \(n = 4\ \text{mol}\), \(C_v = \frac{7}{2}R\), \(\Delta T = 15\ \text{K}\) n'usoro isobaric.
Ngwọta: \(\Delta U = nC_v\Delta T = 4 \cdot \frac{7}{2}R \cdot 15 \approx 3157\ \text{J}\).
19. Chọta nnyefe okpomọkụ n'ime usoro isobaric, \(P = 4\ \text{atm}\), \(\Delta V = 5\ \text{L}\), \(n = 2\ \text{mol}\), \(C_p = \frac{5}{2}R\).
Ngwọta: \(Q = P\Delta V + nC_p\Delta T = ugboro atọ 5 + 2 \cdot \frac{5}{2}R\Delta T\).
20. Chọpụta ọrụ e mere na mkpakọ isobaric, \(P = 7\ \text{bar}\), \(\Delta V = -2\ \text{m}^3\).
Ngwọta: \(W = P\Delta V = ugboro ise (-2) = -14\ \text{bar}^3\).
21. Gbakọọ mgbanwe ike dị n'ime maka mole atọ nke gas zuru oke nke na-agafe usoro isobaric, \(C_v = \frac{5}{2}R\), \(\Delta T = 20\ \text{K}\).
Ngwọta: \(\Delta U = nC_v\Delta T = 3 \cdot \frac{5}{2}R \cdot 20 \approx 1256\ \text{J}\).
22. Chọta mgbanwe entropy maka mgbasawanye isobaric, \(n = 1\ \text{mol}\), \(C_p = \frac{7}{2}R\), \(\Delta T = 30\ \text{K}\), \(T_1 = 250\ \text{K}\).
Ngwọta: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = \frac{7}{2}R\ln\frac{280}{250}\).
23. Chọpụta mbufe okpomọkụ n'ime usoro isobaric, \(P = 6\ \text{bar}\), \(\Delta V = 4\ \text{m}^3\), \(n = 3\ \text{mol}\), \(C_p = \frac{3}{2}R\).
Ngwọta: \(Q = P\Delta V + nC_p\Delta T = ugboro atọ 4 + 3 \cdot \frac{3}{2}R\Delta T\).
24. Gbakọọ ọrụ sistemụ ahụ rụrụ na mgbasawanye isobaric site na iji \(P = 8\ \text{bar}\), \(\Delta V = 3\ \text{m}^3\).
Ngwọta: \(W = P\Delta V = ugboro anọ 3 = 24\ \text{bar}^3\).
25. Chọpụta mgbanwe ike dị n'ime maka usoro isobaric ebe \(n = 2\ \text{mol}\), \(C_v = \frac{7}{2}R\), \(\Delta T = -10\ \text{K}\).
Ngwọta: \(\Delta U = nC_v\Delta T = 2 \cdot \frac{7}{2}R \cdot (-10) \approx -878\ \text{J}\).
26. Chọta mgbanwe entropy maka gas diatomic zuru oke na mkpakọ isobaric, \(n = 1.5\ \text{mol}\), \(T_1 = 350\ \text{K}\), \(\Delta T = -40\ \text{K}\).
Ngwọta: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 1.5 \cdot \frac{7}{2}R\ln\frac{310}{350}\).
27. Chọpụta nnyefe okpomọkụ maka moles abụọ nke gas nke na-agbasa isobaric, \(P = 5\ \text{bar}\), \(\Delta V = 6\ \text{m}^3\), \(C_p = \frac{5}{2}R\).
Ngwọta: \(Q = P\Delta V + nC_p\Delta T = ugboro atọ 6 + 2 \cdot \frac{5}{2}R\Delta T\).
28. Gbakọọ ọrụ e mere na sistemụ ahụ na mkpakọ isobaric site na iji \(P = 9\\text{atm}\), \(\Delta V = -3\\text{L}\).
Ngwọta: \(W = P\Delta V = ugboro ise (-3) = -27\ \text{L·atm}\).
29. Chọpụta mgbanwe ike dị n'ime maka mole atọ nke gas nke na-eme usoro isobaric, \(C_v = \frac{3}{2}R\), \(\Delta T = 15\ \text{K}\).
Ngwọta: \(\Delta U = nC_v\Delta T = 3 \cdot \frac{3}{2}R \cdot 15 \approx 564\ \text{J}\).
30. Chọta mgbanwe entropy na mgbasawanye isobaric, \(n = 4\ \text{mol}\), \(C_p = \frac{5}{2}R\), \(\Delta T = 25\ \text{K}\), \(T_1 = 300\ \text{K}\).
Ngwọta: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 4 \cdot \frac{5}{2}R\ln\frac{325}{300}\).
