30 Ngā tukanga thermodynamics isobaric – ngā raruraru me ngā otinga
1. E whakaatu ana te hoahoa PV i raro nei i tētahi hau pai e pāngia ana e te tukanga isobaric . Tātaihia te mahi e mahia ana e te hau i roto i te tukanga AB.
Mōhiotia:
Pēhanga (P) = 5 x 105 N / m2
Te rōrahi tīmatanga (V 1 ) = 2 m 3
Te rōrahi whakamutunga (V 2 ) = 6 m 3
E hiahiatia ana: Mahi (W)
Rongoā:
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 Ngā Joule
2. He aha te rerekētanga o te mahi i mahia e te hau i roto i te tukanga AB me te tukanga CD…
Mōhiotia:
Te tukanga isobaric AB :
Pēhanga (P) = 6 atm = 6 x 105 N / m2
Te rōrahi tīmatanga (V 1 ) = 1 rita = 1 dm 3 = 1 x 10 -3 m 3
Te rōrahi whakamutunga (V 2 ) = 3 rita = 3 dm 3 = 3 x 10 -3 m 3
CD tukanga isobaric :
Pēhanga (P) = 4 atm = 4 x 105 N / m2
Te rōrahi tīmatanga (V 1 ) = 2 rita = 2 dm 3 = 2 x 10 -3 m 3
Te rōrahi whakamutunga (V 2 ) = 5 rita = 5 dm 3 = 5 x 10 -3 m 3
E hiahiatia ana : Ko te rerekētanga o te mahi ka mahia e te hau i roto i te tukanga AB me te CD.
Rongoā:
Ka mahia te mahi e te hau i roto i te tukanga 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 102 = 1200 Joule
Ka mahia te mahi e te hau kei roto i te tukanga 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 102 = 1200 Joule
Ko te rerekētanga o te mahi ka mahia e te hau i roto i te tukanga AB me te CD = 1200 – 1200 = 0.
3. Ko te hau e mahi ana i te mahi. Ko ABC….
Mōhiotia:
Pēhanga 1 (P1 ) = 6 x 105 Pa = 6 x 105 N / m2
Pēhanga 2 (P 2 ) = 3 x 10 5 Pa = 3 x 10 5 N/m 2
Rōrahi 1 (V 1 ) = 2 cm 3 = 2 x 10 -6 m 3
Rōrahi 2 (V 2 ) = 6 cm 3 = 6 x 10 -6 m 3
E hiahiatia ana : Ka oti te mahi i roto i te tukanga ABC.
Rongoā:
I te tukanga AB, ka pumau tonu te rōrahi kia kore ai he mahi e mahia e te hau.
I oti te mahi e te hau i roto i te tukanga 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
Ka oti te mahi i roto i te tukanga ABC = ka oti te mahi i roto i te tukanga AB = 1.2 Joules.
4. Tāutuhia te huringa o te pūngao ā-roto mō ngā mole e 2 o te hau pai e pāngia ana e te whakawhanuitanga isobaric i te 300 K, ko \(\Delta V = 1\ \text{m}^3\).
Otinga: \(\Delta U = nC_v\Delta T\), mā te whakamahi i te \(C_v = \frac{R}{\gamma-1}\) (mō te hau pai monoatomic, \(\gamma = \frac{5}{3}\)) me te \(\Delta T = \frac{P\Delta V}{nR}\), \(\Delta U = \frac{2\cdot 300 \cdot 1}{\frac{5}{3}-1} \approx 1800\ \text{J}\).
5. Tātaihia te whakawhiti wera i roto i tētahi tukanga isobaric ina whakawhanuitia te 1 mole o tētahi hau pai rua-atomic, \(C_p = \frac{7}{2}R\), me \(\Delta T = 50\ \text{K}\).
Otinga: \(Q = nC_p\Delta T = \frac{7}{2} \cdot 50 \cdot R \approx 1750\ \text{J}\) (mā te whakamahi i te \(R = 8.314\ \text{J/(mol·K)}\)).
6. Kimihia te mahi i mahia e tētahi pūnaha e pāngia ana e te whakawhanuitanga isobaric, \(P = 3\ \text{atm}\), \(\Delta V = 4\ \text{L}\).
Otinga: \(W = P\Delta V = 3 \times 4 = 12\ \text{L·atm}\).
7. Whakatauhia te huringa o te entropy mō tētahi tukanga isobaric ina huri te pāmahana o ngā mole e 2 o tētahi hau pai mā te 20 K. Whakamahia \(C_p = \frac{5}{2}R\).
Otinga: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 2 \cdot \frac{5}{2}R \cdot \ln\frac{T_1+20}{T_1}\).
8. Tātaihia te whakawhiti wera mō te kōpeketanga isobaric o te hau pai monoatomic, \(C_p = \frac{5}{2}R\), \(\Delta T = -10\ \text{K}\).
Otinga: \(Q = nC_p\Delta T = \frac{5}{2} \cdot (-10) \cdot R \approx -415\ \text{J}\).
9. Kimihia te mahi i mahia i runga i te pūnaha i roto i tētahi tukanga isobaric me \(P = 5\ \text{bar}\), \(\Delta V = -3\ \text{m}^3\).
Otinga: \(W = P\Delta V = 5 \times (-3) = -15\ \text{bar m}^3\).
10. Whakatauhia te huringa o te pūngao ā-roto mō tētahi tukanga isobaric ina \(n = 3\ \text{mol}\), \(C_v = 3R\), \(\Delta T = 25\ \text{K}\).
Otinga: \(\Delta U = nC_v\Delta T = 3 \cdot 3R \cdot 25 \approx 1883\ \text{J}\).
11. Tātaihia te huringa entropy i roto i tētahi tukanga isobaric mō tētahi hau pai diatomic, \(n = 1\ \text{mol}\), \(\Delta T = 40\ \text{K}\), \(T_1 = 300\ \text{K}\).
Otinga: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = \frac{7}{2}R\ln\frac{340}{300}\).
12. Kimihia te whakawhiti wera i roto i te whakawhanuitanga isobaric, \(P = 2\ \text{atm}\), \(\Delta V = 3\ \text{L}\), \(C_p = \frac{7}{2}R\).
Otinga: \(Q = P\Delta V + nC_p\Delta T = 2 \times 3 + \frac{7}{2}R\Delta T\).
13. Tāutuhia te mahi i mahia i roto i tētahi tukanga isobaric mō \(P = 4\ \text{bar}\), \(\Delta V = 5\ \text{m}^3\).
Otinga: \(W = P\Delta V = 4 \times 5 = 20\ \text{bar m}^3\).
14. Tātaihia te huringa pūngao ā-roto mō te kōpeketanga isobaric, \(n = 2\ \text{mol}\), \(C_v = \frac{3}{2}R\), \(\Delta T = -30\ \text{K}\).
Otinga: \(\Delta U = nC_v\Delta T = 2 \cdot \frac{3}{2}R \cdot (-30) \approx -753\ \text{J}\).
15. Kimihia te huringa entropy i roto i tētahi tukanga isobaric, \(n = 1.5\ \text{mol}\), \(\Delta T = 60\ \text{K}\), \(T_1 = 400\ \text{K}\), \(C_p = \frac{5}{2}R\).
Otinga: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 1.5 \cdot \frac{5}{2}R\ln\frac{460}{400}\).
16. Tātaihia te whakawhiti wera mō te whakawhanuitanga isobaric, \(P = 3\ \text{bar}\), \(\Delta V = 2\ \text{m}^3\), \(C_p = \frac{5}{2}R\), \(n = 2\ \text{mol}\).
Otinga: \(Q = P\Delta V + nC_p\Delta T = 3 \times 2 + 2 \cdot \frac{5}{2}R\Delta T\).
17. Tātaihia te mahi i mahia ki runga i ngā mole e 3 o te hau e pāngia ana e te kōpeketanga isobaric, \(P = 5\ \text{atm}\), \(\Delta V = -4\ \text{L}\).
Otinga: \(W = P\Delta V = 5 \times (-4) = -20\ \text{L·atm}\).
18. Whakatauhia te huringa pūngao ā-roto mō \(n = 4\ \text{mol}\), \(C_v = \frac{7}{2}R\), \(\Delta T = 15\ \text{K}\) i roto i tētahi tukanga isobaric.
Otinga: \(\Delta U = nC_v\Delta T = 4 \cdot \frac{7}{2}R \cdot 15 \approx 3157\ \text{J}\).
19. Kimihia te whakawhiti wera i roto i tētahi tukanga isobaric, \(P = 4\ \text{atm}\), \(\Delta V = 5\ \text{L}\), \(n = 2\ \text{mol}\), \(C_p = \frac{5}{2}R\).
Otinga: \(Q = P\Delta V + nC_p\Delta T = 4 \times 5 + 2 \cdot \frac{5}{2}R\Delta T\).
20. Tāutuhia te mahi i mahia i roto i te kōpeketanga isobaric, \(P = 7\ \text{bar}\), \(\Delta V = -2\ \text{m}^3\).
Otinga: \(W = P\Delta V = 7 \times (-2) = -14\ \text{bar m}^3\).
21. Tātaihia te huringa pūngao ā-roto mō ngā mole e 3 o te hau pai e pāngia ana e te tukanga isobaric, \(C_v = \frac{5}{2}R\), \(\Delta T = 20\ \text{K}\).
Otinga: \(\Delta U = nC_v\Delta T = 3 \cdot \frac{5}{2}R \cdot 20 \approx 1256\ \text{J}\).
22. Kimihia te huringa entropy mō te whakawhanuitanga isobaric, \(n = 1\ \text{mol}\), \(C_p = \frac{7}{2}R\), \(\Delta T = 30\ \text{K}\), \(T_1 = 250\ \text{K}\).
Otinga: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = \frac{7}{2}R\ln\frac{280}{250}\).
23. Whakatauhia te whakawhiti wera i roto i tētahi tukanga isobaric, \(P = 6\ \text{bar}\), \(\Delta V = 4\ \text{m}^3\), \(n = 3\ \text{mol}\), \(C_p = \frac{3}{2}R\).
Otinga: \(Q = P\Delta V + nC_p\Delta T = 6 \times 4 + 3 \cdot \frac{3}{2}R\Delta T\).
24. Tātaihia te mahi i mahia e te pūnaha i roto i te whakawhanuitanga isobaric me \(P = 8\ \text{bar}\), \(\Delta V = 3\ \text{m}^3\).
Otinga: \(W = P\Delta V = 8 \times 3 = 24\ \text{bar m}^3\).
25. Whakatauhia te huringa pūngao ā-roto mō tētahi tukanga isobaric ina \(n = 2\ \text{mol}\), \(C_v = \frac{7}{2}R\), \(\Delta T = -10\ \text{K}\).
Otinga: \(\Delta U = nC_v\Delta T = 2 \cdot \frac{7}{2}R \cdot (-10) \approx -878\ \text{J}\).
26. Kimihia te huringa entropy mō te hau pai rua-atomic i roto i te kōpeketanga isobaric, \(n = 1.5\ \text{mol}\), \(T_1 = 350\ \text{K}\), \(\Delta T = -40\ \text{K}\).
Otinga: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 1.5 \cdot \frac{7}{2}R\ln\frac{310}{350}\).
27. Tātaihia te whakawhiti wera mō ngā mole e 2 o te hau e pāngia ana e te whakawhanuitanga isobaric, \(P = 5\ \text{bar}\), \(\Delta V = 6\ \text{m}^3\), \(C_p = \frac{5}{2}R\).
Otinga: \(Q = P\Delta V + nC_p\Delta T = 5 \times 6 + 2 \cdot \frac{5}{2}R\Delta T\).
28. Tātaihia te mahi i mahia ki te pūnaha i roto i te kōpeketanga isobaric me te \(P = 9\ \text{atm}\), \(\Delta V = -3\ \text{L}\).
Otinga: \(W = P\Delta V = 9 \times (-3) = -27\ \text{L·atm}\).
29. Tāutuhia te huringa pūngao ā-roto mō ngā mole e 3 o te hau e pāngia ana e te tukanga isobaric, \(C_v = \frac{3}{2}R\), \(\Delta T = 15\ \text{K}\).
Otinga: \(\Delta U = nC_v\Delta T = 3 \cdot \frac{3}{2}R \cdot 15 \approx 564\ \text{J}\).
30. Kimihia te huringa entropy i roto i te whakawhanuitanga isobaric, \(n = 4\ \text{mol}\), \(C_p = \frac{5}{2}R\), \(\Delta T = 25\ \text{K}\), \(T_1 = 300\ \text{K}\).
Otinga: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 4 \cdot \frac{5}{2}R\ln\frac{325}{300}\).
