Izinqubo ezingama-30 ze-thermodynamics ze-Isobaric - izinkinga nezixazululo
1. Umdwebo we-PV ongezansi ukhombisa igesi efanelekile edlula enkambisweni ye-iso baric . Bala umsebenzi owenziwa yigesi enkambisweni ye-AB.
Kwaziwa:
Ingcindezi (P) = 5 x 10 5 N/m 2
Umthamo wokuqala (V 1 ) = 2 m 3
Umthamo wokugcina (V 2 ) = 6 m 3
Okufunwayo: Umsebenzi (W)
Isixazululo:
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 amaJoules
2. Uyini umehluko womsebenzi owenziwe yigesi ku-process AB kanye ne-process CD…
Kwaziwa:
Inqubo ye-Isobaric AB :
Ingcindezi (P) = 6 atm = 6 x 10 5 N/m 2
Umthamo wokuqala (V 1 ) = 1 ilitha = 1 dm 3 = 1 x 10 -3 m 3
Umthamo wokugcina (V 2 ) = amalitha ama-3 = 3 dm 3 = 3 x 10 -3 m 3
I-CD yenqubo ye-Isobaric :
Ingcindezi (P) = 4 atm = 4 x 10 5 N/m 2
Umthamo wokuqala (V 1 ) = 2 amalitha = 2 dm 3 = 2 x 10 -3 m 3
Umthamo wokugcina (V 2 ) = amalitha ama-5 = 5 dm 3 = 5 x 10 -3 m 3
Okufunwayo : Umehluko womsebenzi wenziwa yigesi enqubweni i-AB ne-CD.
Isixazululo:
Umsebenzi wenziwa yigesi eqhubekayo 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 amaJoule
Umsebenzi wenziwa yi-CD ye-gas in process:
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 amaJoule
Umehluko womsebenzi wenziwa yigesi enqubweni i-AB kanye ne-CD = 1200 – 1200 = 0.
3. Umsebenzi wenziwa yigesi eqhubekayo i-ABC….
Kwaziwa:
Ingcindezi 1 (P 1 ) = 6 x 10 5 Pa = 6 x 10 5 N/m 2
Ingcindezi 2 (P 2 ) = 3 x 10 5 Pa = 3 x 10 5 N/m 2
Umqulu 1 (V 1 ) = 2 cm 3 = 2 x 10 -6 m 3
Umqulu 2 (V 2 ) = 6 cm 3 = 6 x 10 -6 m 3
Okufunwayo : Umsebenzi wenziwa ngenqubo ABC.
Isixazululo:
Enqubweni ye-AB, ivolumu igcinwa ingaguquguquki ukuze kungabikho msebenzi owenziwa yigesi.
Umsebenzi wenziwa yigesi enqubweni ye-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
Umsebenzi wenziwa enqubweni ABC = umsebenzi wenziwa enqubweni AB = 1.2 Joules.
4. Nquma ushintsho lwamandla angaphakathi kwama-moles amabili egesi efanelekile edlula ekunwetshweni kwe-isobaric ku-300 K, lapho \(\Delta V = 1\ \text{m}^3\).
Isixazululo: \(\Delta U = nC_v\Delta T\), kusetshenziswa \(C_v = \frac{R}{\gamma-1}\) (kwegesi efanele ye-monatomic, \(\gamma = \frac{5}{3}\)) kanye \(\Delta T = \frac{P\Delta V}{nR}\), \(\Delta U = \frac{2\cdot 300 \cdot 1}{\frac{5}{3}-1} \approx 1800\ \text{J}\).
5. Bala ukudluliselwa kokushisa enqubweni ye-isobaric lapho i-mole eyi-1 yegesi ye-diatomic ideal ikhula khona, \(C_p = \frac{7}{2}R\), kanye \(\Delta T = 50\ \text{K}\).
Isixazululo: \(Q = nC_p\Delta T = \frac{7}{2} \cdot 50 \cdot R \approx 1750\ \text{J}\) (kusetshenziswa \(R = 8.314\ \text{J/(mol·K)}\)).
6. Thola umsebenzi owenziwe uhlelo oludlula ekunwetshweni kwe-isobaric, \(P = 3\ \text{atm}\), \(\Delta V = 4\ \text{L}\).
Isixazululo: \(W = P\Delta V = 3 \izikhathi 4 = 12\ \umbhalo{L·atm}\).
7. Nquma ushintsho ku-entropy yenqubo ye-isobaric lapho ama-moles amabili egesi elifanele eshintsha izinga lokushisa ngo-20 K. Sebenzisa \(C_p = \frac{5}{2}R\).
Isixazululo: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 2 \cdot \frac{5}{2}R \cdot \ln\frac{T_1+20}{T_1}\).
8. Bala ukudluliselwa kokushisa kokucindezela kwe-isobaric kwegesi efanele ye-monatomic, \(C_p = \frac{5}{2}R\), \(\Delta T = -10\ \text{K}\).
Isixazululo: \(Q = nC_p\Delta T = \frac{5}{2} \cdot (-10) \cdot R \approx -415\ \text{J}\).
9. Thola umsebenzi owenziwe ohlelweni ngenqubo ye-isobaric nge-\(P = 5\ \text{bar}\), \(\Delta V = -3\ \text{m}^3\).
Isixazululo: \(W = P\Delta V = 5 \izikhathi (-3) = -15\ \text{bar m}^3\).
10. Nquma ushintsho kumandla angaphakathi enqubweni ye-isobaric lapho \(n = 3\ \text{mol}\), \(C_v = 3R\), \(\Delta T = 25\ \text{K}\).
Isixazululo: \(\Delta U = nC_v\Delta T = 3 \cdot 3R \cdot 25 \approx 1883\ \text{J}\).
11. Bala ushintsho lwe-entropy enqubweni ye-isobaric yegesi efanele ye-diatomic, \(n = 1\ \text{mol}\), \(\Delta T = 40\ \text{K}\), \(T_1 = 300\ \text{K}\).
Isixazululo: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = \frac{7}{2}R\ln\frac{340}{300}\).
12. Thola ukudluliselwa kokushisa ku-expansion ye-isobaric, \(P = 2\ \text{atm}\), \(\Delta V = 3\ \text{L}\), \(C_p = \frac{7}{2}R\).
Isixazululo: \(Q = P\Delta V + nC_p\Delta T = 2 \times 3 + \frac{7}{2}R\Delta T\).
13. Nquma umsebenzi owenziwe ngenqubo ye-isobaric ye-\(P = 4\ \text{bar}\), \(\Delta V = 5\ \text{m}^3\).
Isixazululo: \(W = P\Delta V = 4 \times 5 = 20\ \text{bar m}^3\).
14. Bala ushintsho lwamandla angaphakathi lokucindezelwa kwe-isobaric, \(n = 2\ \text{mol}\), \(C_v = \frac{3}{2}R\), \(\Delta T = -30\ \text{K}\).
Isixazululo: \(\Delta U = nC_v\Delta T = 2 \cdot \frac{3}{2}R \cdot (-30) \approx -753\ \text{J}\).
15. Thola ushintsho lwe-entropy enqubweni ye-isobaric, \(n = 1.5\ \text{mol}\), \(\Delta T = 60\ \text{K}\), \(T_1 = 400\ \text{K}\), \(C_p = \frac{5}{2}R\).
Isixazululo: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 1.5 \cdot \frac{5}{2}R\ln\frac{460}{400}\).
16. Nquma ukudluliselwa kokushisa kokwandiswa kwe-isobaric, \(P = 3\ \text{bar}\), \(\Delta V = 2\ \text{m}^3\), \(C_p = \frac{5}{2}R\), \(n = 2\ \text{mol}\).
Isixazululo: \(Q = P\Delta V + nC_p\Delta T = 3 \times 2 + 2 \cdot \frac{5}{2}R\Delta T\).
17. Bala umsebenzi owenziwe kuma-mole amathathu egesi ecindezelwa yi-isobaric, \(P = 5\ \text{atm}\), \(\Delta V = -4\ \text{L}\).
Isixazululo: \(W = P\Delta V = 5 \izikhathi (-4) = -20\ \umbhalo{L·atm}\).
18. Nquma ushintsho lwamandla angaphakathi lwe-\(n = 4\ \text{mol}\), \(C_v = \frac{7}{2}R\), \(\Delta T = 15\ \text{K}\) enqubweni ye-isobaric.
Isixazululo: \(\Delta U = nC_v\Delta T = 4 \cdot \frac{7}{2}R \cdot 15 \approx 3157\ \text{J}\).
19. Thola ukudluliselwa kokushisa kwinqubo ye-isobaric, \(P = 4\ \text{atm}\), \(\Delta V = 5\ \text{L}\), \(n = 2\ \text{mol}\), \(C_p = \frac{5}{2}R\).
Isixazululo: \(Q = P\Delta V + nC_p\Delta T = 4 \times 5 + 2 \cdot \frac{5}{2}R\Delta T\).
20. Nquma umsebenzi owenziwe ngokucindezelwa kwe-isobaric, \(P = 7\ \text{bar}\), \(\Delta V = -2\ \text{m}^3\).
Isixazululo: \(W = P\Delta V = 7 \izikhathi (-2) = -14\ \text{bar m}^3\).
21. Bala ushintsho lwamandla angaphakathi lwama-mole amathathu egesi efanelekile edlula enkambisweni ye-isobaric, \(C_v = \frac{5}{2}R\), \(\Delta T = 20\ \text{K}\).
Isixazululo: \(\Delta U = nC_v\Delta T = 3 \cdot \frac{5}{2}R \cdot 20 \approx 1256\ \text{J}\).
22. Thola ushintsho lwe-entropy lokwandiswa kwe-isobaric, \(n = 1\ \text{mol}\), \(C_p = \frac{7}{2}R\), \(\Delta T = 30\ \text{K}\), \(T_1 = 250\ \text{K}\).
Isixazululo: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = \frac{7}{2}R\ln\frac{280}{250}\).
23. Nquma ukudluliselwa kokushisa kwinqubo ye-isobaric, \(P = 6\ \text{bar}\), \(\Delta V = 4\ \text{m}^3\), \(n = 3\ \text{mol}\), \(C_p = \frac{3}{2}R\).
Isixazululo: \(Q = P\Delta V + nC_p\Delta T = 6 \times 4 + 3 \cdot \frac{3}{2}R\Delta T\).
24. Bala umsebenzi owenziwe uhlelo ekunwetshweni kwe-isobaric nge-\(P = 8\ \text{bar}\), \(\Delta V = 3\ \text{m}^3\).
Isixazululo: \(W = P\Delta V = 8 \times 3 = 24\ \text{bar m}^3\).
25. Nquma ushintsho lwamandla angaphakathi lwenqubo ye-isobaric lapho \(n = 2\ \text{mol}\), \(C_v = \frac{7}{2}R\), \(\Delta T = -10\ \text{K}\).
Isixazululo: \(\Delta U = nC_v\Delta T = 2 \cdot \frac{7}{2}R \cdot (-10) \approx -878\ \text{J}\).
26. Thola ushintsho lwe-entropy lwegesi elifanele le-diatomic ekucindezelweni kwe-isobaric, \(n = 1.5\ \text{mol}\), \(T_1 = 350\ \text{K}\), \(\Delta T = -40\ \text{K}\).
Isixazululo: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 1.5 \cdot \frac{7}{2}R\ln\frac{310}{350}\).
27. Nquma ukudluliselwa kokushisa kwama-moles amabili egesi edlula ekunwetshweni kwe-isobaric, \(P = 5\ \text{bar}\), \(\Delta V = 6\ \text{m}^3\), \(C_p = \frac{5}{2}R\).
Isixazululo: \(Q = P\Delta V + nC_p\Delta T = 5 \times 6 + 2 \cdot \frac{5}{2}R\Delta T\).
28. Bala umsebenzi owenziwe ohlelweni ngokucindezelwa kwe-isobaric nge-\(P = 9\ \text{atm}\), \(\Delta V = -3\ \text{L}\).
Isixazululo: \(W = P\Delta V = 9 \izikhathi (-3) = -27\ \umbhalo{L·atm}\).
29. Nquma ushintsho lwamandla angaphakathi kuma-mole amathathu egesi edlula enkambisweni ye-isobaric, \(C_v = \frac{3}{2}R\), \(\Delta T = 15\ \text{K}\).
Isixazululo: \(\Delta U = nC_v\Delta T = 3 \cdot \frac{3}{2}R \cdot 15 \approx 564\ \text{J}\).
30. Thola ushintsho lwe-entropy ekunwetshweni kwe-isobaric, \(n = 4\ \text{mol}\), \(C_p = \frac{5}{2}R\), \(\Delta T = 25\ \text{K}\), \(T_1 = 300\ \text{K}\).
Isixazululo: \(\Delta S = nC_p\ln\frac{T_2}{T_1} = 4 \cdot \frac{5}{2}R\ln\frac{325}{300}\).
