Ngā tukanga thermodynamic isothermal – ngā raruraru me ngā otinga

30 Ngā tukanga thermodynamic isothermal – ngā raruraru me ngā otinga

1. E whakaatu ana te hoahoa PV i raro nei i tētahi hau pai e pāngia ana e tētahi tukanga isothermal . Tātaihia te mahi e mahia ana e te hau i roto i te tukanga AB.

otinga

mahi Ko te horahanga i mahia e te hau he rite ki te horahanga i raro i te pihi PV

AB = horahanga tapatoru + horahanga tapawhā rite

W = [½ (8 x 10 ⁵ –4 x 10 ⁵ )(3-1)] + [4 x 10 ⁵ (3-1)]

W = [½ (4 x 10 ⁵ )(2)] + [4 x 10 ⁵ (2)]

W = [4 x 10 ⁵ ] + [8 x 10 ⁵ ]

W = 12 x 10 ⁵ Joule

Ka oti te mahi e te hau i roto i te tukanga AB = 12 x 10 ⁵ Joules

2. Tātaihia te mahi e mahia ana e te hau pai i roto i te tukanga ABC.

Ka oti te mahi e te hau pai i roto i te tukanga ABC = te horahanga i raro i te pihi PV

AB = horahanga tapatoru + horahanga tapawhā rite

W = [½(10×10 ⁵ –5×10 ⁵ )(30-10)]+[5×10 ⁵ (30-10)]

W = [½ (5 x 10 ⁵ )(20)] + [5 x 10 ⁵ (20)]

W = [(5 x 10 ⁵ )(10)] + [100 x 10 ⁵ ]

W = [50 x 10 ⁵ ] + [100 x 10 ⁵ ]

W = 150 x 10 ⁵ Joule

W = 1.5 x 10 ⁷ Joule

3. He hau tino pai e pāngia ana e ngā tukanga isothermal. He aha te nui o te wera ka tāpirihia ki te hau, ā, ka mahi te hau i te 5000 Joules ki te taiao.

Mōhiotia:

Mahi (W) = 5000 Joule

E hiahiatia ana: Ka tāpirihia te wera ki te hau (Q)

Rongoā:

Ko te tukanga isothermal he tukanga thermodynamic e puta ana i te pāmahana pumau.

ΔU = 3/2 n R ΔT

ΔU = te huringa o te pūngao ā-roto, n = te maha o ngā ira, R = te pūmau hau whānui, ΔT = Te huringa o te pāmahana.

E ai ki te whārite i runga ake nei, mēnā ko ΔT = 0, ko ΔU = 0.

Ko te whārite o te ture tuatahi o te thermodynamics:

ΔU = Q – W

0 = Q – W

Q = W

Q = 5000 Joule.

4. He hoahoa PV mō tētahi hau pai e pāngia ana e te tukanga isothermal e whakaaturia ana i te pikitia i raro nei. Tātaihia te wera ka tāpirihia e tētahi hau i roto i te tukanga AB.

Mōhiotia:

Pēhanga 1 (P ₁ ) = 5 atm = 5 x 10 ⁵ Pa

Pēhanga 2 (P ₂ ) = 10 atm = 10 x 10 ⁵ Pa

Rōrahi 1 (V ₁ ) = 2 m ³

Rōrahi 2 (V ₂ ) = 6 m ³

E hiahiatia ana : Ka tāpirihia te wera i roto i te tukanga AB.

Rongoā:

Isothermal = pāmahana pumau. E ai ki te whārite i raro nei, mēnā ko ΔT = 0, ko ΔU = 0.

ΔU = 3/2 n R ΔT

ΔU = 3/2 n R (0)

ΔU = 0

Whakamahia ki te ture tuatahi o te thermodynamics :

ΔU = QW

0 = QW

Q=W

Ka oti te mahi mā te hau pai = te horahanga i raro i te pihi PV = horahanga tapatoru + horahanga tapawhā rite

W = ½ (P ₂ – P ₁ )(V ₂ – V ₁ ) + P ₁ (V ₂ – V ₁ )

W = ½ (10 x 10 ⁵ – 5 x 10 ⁵ )(6-2) + (5 x 10 ⁵ )(6-2)

W = ½ (5 x 10 ⁵ )(4) + (5 x 10 ⁵ )(4)

W = ½ (20 x 10 ⁵ ) + (20 x 10 ⁵ )

W = (10 x 10 ⁵ ) + (20 x 10 ⁵ )

W = 30 x 10 ⁵ Joule

5. Tātaihia te mahi i mahia ki te 1 mol o te hau pai e whakawhanui ana i te pāmahana mai i te 2 L ki te 4 L i te 300 K.
Otinga: \( W = nRT \ln\left(\frac{V_2}{V_1}\right) = 1 \times 8.314 \times 300 \times \ln(2) \approx 1724 \, \text{J} \)

6. Whakatauhia te whakawhiti wera mō te raruraru i runga ake nei.
Otinga: \( Q = W = 1724 \, \text{J} \)

7. Tātaihia te huringa o te pūngao ā-roto mō te tukanga i runga ake nei.
Otinga: \( \Delta U = 0 \, \text{J} \) (nā te mea he isothermal te tukanga)

8. Mō te kōpeketanga isothermal o te hau pai mai i te 10 L ki te 5 L i te 300 K, kimihia te mahi i mahia.
Otinga: \( W = 8.314 \times 300 \times \ln\left(\frac{5}{10}\right) \approx -862 \, \text{J} \)

9. Tātaihia te huringa entropy mō te whānui isothermal i te Rapanga 1.
Otinga: \( \Delta S = nR\ln\left(\frac{V_2}{V_1}\right) = 8.314 \times \ln(2) \approx 5.76 \, \text{J/K} \)

10. Kimihia te whakawhiti wera mō te kōpeketanga isothermal o te 2 mol o te hau pai mai i te 4 L ki te 2 L i te 200 K.
Otinga: \( Q = 2 \times 8.314 \times 200 \times \ln\left(\frac{2}{4}\right) \approx -1152 \, \text{J} \)

11. Tātaihia te huringa o te pūngao kore utu a Gibbs mō tētahi tukanga isothermal.
Otinga: \( \Delta G = 0 \) (Mō tētahi tukanga isothermal whakahurihuri i roto i tētahi pūnaha kati, \( \Delta G = 0 \))

12. Whakatauhia te huringa entropy mō te kōpeketanga isothermal o te 3 mol o te hau pai mai i te 6 L ki te 3 L i te 400 K.
Otinga: \( \Delta S = 3 \times 8.314 \times \ln\left(\frac{3}{6}\right) \approx -17.29 \, \text{J/K} \)

13. Kimihia te mahi i mahia e te hau pai e whakawhanui ana i te pāmahana mai i te 3 rita ki te 6 rita i te 250 K mō te 2 mol.
Otinga: \( W = 2 \times 8.314 \times 250 \times \ln(2) \approx 2874 \, \text{J} \)

14. Whakatauhia te whakawhiti wera mō te tukanga i runga ake nei.
Otinga: \( Q = W = 2874 \, \text{J} \)

15. Tātaihia te huringa o te pūngao ā-roto mō te whānui isothermal i runga ake nei.
Otinga: \( \Delta U = 0 \, \text{J} \)

16. Tātaihia te huringa entropy mō te whakawhanuitanga isothermal o te 4 mol o te hau pai mai i te 5 L ki te 10 L i te 500 K.
Otinga: \( \Delta S = 4 \times 8.314 \times \ln(2) \approx 23.03 \, \text{J/K} \)

17. Tātaihia te whakawhiti wera mō te kōpeketanga isothermal o te 1 mol o te hau pai mai i te 8 L ki te 4 L i te 300 K.
Otinga: \( Q = 8.314 \times 300 \times \ln\left(\frac{4}{8}\right) \approx -862 \, \text{J} \)

18. Kimihia te mahi i mahia e te 3 mol o te hau pai e whakawhanui ana i te pāmahana mai i te 3 L ki te 9 L i te 350 K.
Otinga: \( W = 3 \times 8.314 \times 350 \times \ln(3) \approx 5362 \, \text{J} \)

19. Tātaihia te huringa entropy mō te tukanga i runga ake nei.
Otinga: \( \Delta S = 3 \times 8.314 \times \ln(3) \approx 14.88 \, \text{J/K} \)

20. Tātaihia te whakawhiti wera mō te whakawhanuitanga isothermal o te 2 mol o te hau pai mai i te 2 L ki te 8 L i te 200 K.
Otinga: \( Q = 2 \times 8.314 \times 200 \times \ln(4) \approx 2304 \, \text{J} \)

21. Tātaihia te huringa o te pūngao ā-roto mō te kōpeketanga isothermal o te 4 mol o te hau pai mai i te 10 L ki te 5 L i te 500 K.
Otinga: \( \Delta U = 0 \, \text{J} \)

22. Whakatauhia te huringa entropy mō te whakawhanuitanga isothermal o te 5 mol o te hau pai mai i te 5 L ki te 15 L i te 300 K.
Otinga: \( \Delta S = 5 \times 8.314 \times \ln(3) \approx 24.81 \, \text{J/K} \)

23. Kimihia te mahi i mahia e te 2 mol o te hau pai e pēhi ana i te pāmahana mai i te 6 L ki te 2 L i te 400 K.
Otinga: \( W = 2 \times 8.314 \times 400 \times \ln\left(\frac{2}{6}\right) \approx -2874 \, \text{J} \)

24. Tātaihia te huringa entropy mō te kōpeketanga isothermal o te 3 mol o te hau pai mai i te 9 L ki te 3 L i te 250 K.
Otinga: \( \Delta S = 3 \times 8.314 \times \ln\left(\frac{3}{9}\right) \approx -14.88 \, \text{J/K} \)

25. Tātaihia te whakawhiti wera mō te whakawhanuitanga isothermal o te 1 mol o te hau pai mai i te 4 L ki te 12 L i te 350 K.
Otinga: \( Q = 8.314 \times 350 \times \ln(3) \approx 1791 \, \text{J} \)

26. Kimihia te mahi i mahia e te 4 mol o te hau pai e whakawhanui ana i te pāmahana mai i te 4 L ki te 8 L i te 500 K.
Otinga: \( W = 4 \times 8.314 \times 500 \times \ln(2) \approx 5749 \, \text{J} \)

27. Whakatauhia te huringa entropy mō te kōpeketanga isothermal o te 2 mol o te hau pai mai i te 10 L ki te 5 L i te 200 K.
Otinga: \( \Delta S = 2 \times 8.314 \times \ln\left(\frac{5}{10}\right) \approx -5.76 \, \text{J/K} \)

24. Kimihia te mahi i mahia e te 3 mol o te hau pai e pēhi ana i te pāmahana mai i te 9 L ki te 3 L i te 450 K.
Otinga: \( W = 3 \times 8.314 \times 450 \times \ln\left(\frac{3}{9}\right) \approx -4310 \, \text{J} \)

25. Tātaihia te huringa o te pūngao ā-roto mō te whakawhanuitanga isothermal o te 5 mol o te hau pai mai i te 5 L ki te 10 L i te 400 K.
Otinga: \( \Delta U = 0 \, \text{J} \)

26. Whakatauhia te huringa entropy mō te whakawhanuitanga isothermal o te 4 mol o te hau pai mai i te 6 L ki te 18 L i te 300 K.
Otinga: \( \Delta S = 4 \times 8.314 \times \ln(3) \approx 19.85 \, \text{J/K} \)

Ka kapi i ēnei raruraru ngā āhuatanga maha o ngā tukanga isothermal, tae atu ki te mahi i mahia, te whakawhiti wera, ngā huringa o te pūngao ā-roto, me ngā huringa entropy.