Izinqubo ezingama-30 ze-Isothermal thermodynamic - izinkinga nezixazululo
1. Umdwebo we-PV ongezansi ukhombisa igesi efanelekile edlula enkambisweni ye-isothermal . Bala umsebenzi owenziwa yigesi enkambisweni ye-AB.
Isixazululo
Work okwenziwe yigesi kulingana nendawo engaphansi kwejika le-PV
AB = indawo kanxantathu + indawo kanxantathu
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 105 amaJoules
Umsebenzi wenziwa yigesi enqubweni AB = 12 x 10 5 Joules
2. Bala ukuthi umsebenzi wenziwa yigesi ekahle enqubweni ye-ABC.
Umsebenzi wenziwa yigesi efanelekile enqubweni i-ABC = indawo engaphansi kwejika le-PV
AB = indawo kanxantathu + indawo kanxantathu
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 105 amaJoules
W = 1.5 x 105 amaJoules
3. Igesi efanelekile edlula ezinqubweni ze-isothermal. Kuyini ukushisa okufakwayo kugesi ukuze igesi isebenze ngama-Joules angu-5000 emvelweni.
Kwaziwa:
Umsebenzi (W) = 5000 Joule
Okufunwayo: Ukushisa kwengezwa kugesi (Q)
Isixazululo:
Inqubo ye-isothermal inqubo ye-thermodynamic eyenzeka ekushiseni okungaguquki.
ΔU = 3/2 n R ΔT
ΔU = ushintsho lwamandla angaphakathi, n = inani lama-moles, R = igesi engaguquki yonke, ΔT = ushintsho lokushisa.
Ngokusho kwesibalo esingenhla, uma u-ΔT = 0 khona-ke u-ΔU = 0.
Isibalo somthetho wokuqala we-thermodynamics:
ΔU = Q - W
0 = Q – W
Q = W
Q = amaJoules angu-5000.
4. Umdwebo we-PV wegesi efanelekile edlula enkambisweni ye-isothermal eboniswe esithombeni esingezansi. Bala ukushisa kwengezwa yigesi enkambisweni i-AB.
Kwaziwa:
Ingcindezi 1 (P 1 ) = 5 atm = 5 x 10 5 Pa
Ingcindezi 2 (P 2 ) = 10 atm = 10 x 10 5 Pa
Umqulu 1 (V 1 ) = 2 m 3
Umqulu 2 (V 2 ) = 6 m 3
Okufunwayo : Ukushisa kwengezwa enqubweni AB.
Isixazululo:
Isothermal = izinga lokushisa elingaguquki. Ngokusho kwesibalo esingezansi, uma i-ΔT = 0 khona-ke i-ΔU = 0.
ΔU = 3/2 n R ΔT
ΔU = 3/2 n R (0)
ΔU = 0
Sebenzisa umthetho wokuqala we-thermodynamics :
ΔU = QW
0 = QW
Q=W
Umsebenzi wenziwa ngegesi efanelekile = indawo engaphansi kwejika le-PV = indawo kanxantathu + indawo kanxantathu
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 amaJoule
5. Bala umsebenzi owenziwe ku-1 mol yegesi ekhula kahle ngokusuka ku-2 L kuya ku-4 L ku-300 K.
Isixazululo: \( W = nRT \ln\left(\frac{V_2}{V_1}\right) = 1 \times 8.314 \times 300 \times \ln(2) \approx 1724 \, \text{J} \)
6. Nquma ukudluliselwa kokushisa kwenkinga engenhla.
Isixazululo: \( Q = W = 1724 \, \text{J} \)
7. Bala ushintsho lwamandla angaphakathi enqubo engenhla.
Isixazululo: \( \Delta U = 0 \, \text{J} \) (njengoba inqubo i-isothermal)
8. Ukuze uthole ukucindezelwa kwegesi okufana nokushisa kusuka ku-10 L kuya ku-5 L ku-300 K, thola umsebenzi osuqediwe.
Isixazululo: \( W = 8.314 \times 300 \times \ln\left(\frac{5}{10}\right) \approx -862 \, \text{J} \)
9. Bala ushintsho lwe-entropy lokwanda kwe-isothermal ku-Inkinga 1.
Isixazululo: \( \Delta S = nR\ln\left(\frac{V_2}{V_1}\right) = 8.314 \times \ln(2) \approx 5.76 \, \text{J/K} \)
10. Thola ukudluliselwa kokushisa kokucindezela kwe-isothermal okungu-2 mol wegesi efanele kusukela ku-4 L kuya ku-2 L ku-200 K.
Isixazululo: \( Q = 2 \izikhathi 8.314 \izikhathi 200 \izikhathi \ln\left(\frac{2}{4}\right) \approx -1152 \, \text{J} \)
11. Bala ushintsho kumandla amahhala e-Gibbs enqubo ye-isothermal.
Isixazululo: \( \Delta G = 0 \) (Ngenqubo ye-isothermal eguquguqukayo ohlelweni oluvaliwe, \( \Delta G = 0 \))
12. Nquma ushintsho lwe-entropy lokucindezela kwe-isothermal okungu-3 mol wegesi efanele kusukela ku-6 L kuya ku-3 L ku-400 K.
Isixazululo: \( \Delta S = 3 \times 8.314 \times \ln\left(\frac{3}{6}\right) \approx -17.29 \, \text{J/K} \)
13. Thola umsebenzi owenziwe yigesi ekhula kahle kakhulu kusukela ku-3 L kuya ku-6 L ku-250 K ngama-mol amabili.
Isixazululo: \( W = 2 \izikhathi ezingu-8.314 \izikhathi ezingu-250 \izikhathi \ln(2) \cishe kube ngu-2874 \, \umbhalo{J} \)
14. Nquma ukudluliselwa kokushisa kwenqubo engenhla.
Isixazululo: \( Q = W = 2874 \, \text{J} \)
15. Bala ushintsho lwamandla angaphakathi okwandisa okungaphezulu kwe-isothermal.
Isixazululo: \( \Delta U = 0 \, \text{J} \)
16. Bala ushintsho lwe-entropy lokwanda kwe-isothermal okungu-4 mol wegesi efanele kusukela ku-5 L kuya ku-10 L ku-500 K.
Isixazululo: \( \Delta S = 4 \times 8.314 \times \ln(2) \approx 23.03 \, \text{J/K} \)
17. Nquma ukudluliselwa kokushisa kokucindezela kwe-isothermal kwe-1 mol yegesi efanele kusukela ku-8 L kuya ku-4 L ku-300 K.
Isixazululo: \( Q = 8.314 \times 300 \times \ln\left(\frac{4}{8}\right) \approx -862 \, \text{J} \)
18. Thola umsebenzi owenziwe ngama-mol angu-3 wegesi ekhula ngokusuka ku-3 L kuya ku-9 L ku-350 K.
Isixazululo: \( W = 3 \izikhathi ezingu-8.314 \izikhathi ezingu-350 \izikhathi \ln(3) \cishe kube ngu-5362 \, \umbhalo{J} \)
19. Bala ushintsho lwe-entropy lwenqubo engenhla.
Isixazululo: \( \Delta S = 3 \times 8.314 \times \ln(3) \approx 14.88 \, \text{J/K} \)
20. Nquma ukudluliselwa kokushisa kokwanda kwe-isothermal okungu-2 mol wegesi efanele kusukela ku-2 L kuya ku-8 L ku-200 K.
Isixazululo: \( Q = 2 \izikhathi ezingu-8.314 \izikhathi ezingu-200 \izikhathi \ln(4) \cishe kube ngu-2304 \, \umbhalo{J} \)
21. Bala ushintsho lwamandla angaphakathi ukuze uthole ukucindezelwa kwe-isothermal okungu-4 mol wegesi efanele kusukela ku-10 L kuya ku-5 L ku-500 K.
Isixazululo: \( \Delta U = 0 \, \text{J} \)
22. Nquma ushintsho lwe-entropy lokwanda kwe-isothermal okungu-5 mol wegesi efanele kusukela ku-5 L kuya ku-15 L ku-300 K.
Isixazululo: \( \Delta S = 5 \times 8.314 \times \ln(3) \approx 24.81 \, \text{J/K} \)
23. Thola umsebenzi owenziwe ngama-mol amabili wegesi efanelekile yokucindezela igesi ngokusuka ku-6 L kuya ku-2 L ku-400 K.
Isixazululo: \( W = 2 \times 8.314 \times 400 \times \ln\left(\frac{2}{6}\right) \approx -2874 \, \text{J} \)
24. Bala ushintsho lwe-entropy lokucindezela kwe-isothermal okungu-3 mol wegesi efanele kusukela ku-9 L kuya ku-3 L ku-250 K.
Isixazululo: \( \Delta S = 3 \times 8.314 \times \ln\left(\frac{3}{9}\right) \approx -14.88 \, \text{J/K} \)
25. Nquma ukudluliselwa kokushisa kokwanda kwe-isothermal okungu-1 mol wegesi efanele kusukela ku-4 L kuya ku-12 L ku-350 K.
Isixazululo: \( Q = 8.314 \izikhathi ezingu-350 \izikhathi \ln(3) \cishe 1791 \, \umbhalo{J} \)
26. Thola umsebenzi owenziwe ngama-mol angu-4 wegesi ekhula ngokusuka ku-4 L kuya ku-8 L ku-500 K.
Isixazululo: \( W = 4 \izikhathi ezingu-8.314 \izikhathi ezingu-500 \izikhathi \ln(2) \cishe kube ngu-5749 \, \umbhalo{J} \)
27. Nquma ushintsho lwe-entropy lokucindezela kwe-isothermal okungu-2 mol wegesi efanele kusukela ku-10 L kuya ku-5 L ku-200 K.
Isixazululo: \( \Delta S = 2 \times 8.314 \times \ln\left(\frac{5}{10}\right) \approx -5.76 \, \text{J/K} \)
24. Thola umsebenzi owenziwe ngama-mol amabili wegesi efanelekile yokucindezela igesi ngokusuka ku-9 L kuya ku-3 L ku-450 K.
Isixazululo: \( W = 3 \times 8.314 \times 450 \times \ln\left(\frac{3}{9}\right) \approx -4310 \, \text{J} \)
25. Bala ushintsho lwamandla angaphakathi ukuze kukhuliswe igesi eshisayo engu-5 mol kusuka ku-5 L kuya ku-10 L ku-400 K.
Isixazululo: \( \Delta U = 0 \, \text{J} \)
26. Nquma ushintsho lwe-entropy lokwanda kwe-isothermal okungu-4 mol wegesi efanele kusukela ku-6 L kuya ku-18 L ku-300 K.
Isixazululo: \( \Delta S = 4 \times 8.314 \times \ln(3) \approx 19.85 \, \text{J/K} \)
Lezi zinkinga zihlanganisa izici ezahlukene zezinqubo ze-isothermal, okuhlanganisa umsebenzi owenziwe, ukudluliselwa kokushisa, izinguquko zamandla angaphakathi, kanye nezinguquko ze-entropy.
