Izinjini zokushisa ezingu-30 (ukusetshenziswa komthetho wesibili we-thermodynamics) – izinkinga nezixazululo
1. Okokufaka ukushisa Q H = 3000 Joules kanye nokokukhipha ukushisa Q L = 1000 Joules. Iyini ukusebenza kahle kwenjini yokushisa?
Kwaziwa:
Okokufaka ukushisa (Q H ) = 3000 Joules
Ukukhishwa kokushisa (Q L ) = 1000 Joules
Umsebenzi owenziwe yinjini (W) = 3000 – 1000 = 2000 Joules
Okufunwayo: Ukusebenza kahle kwenjini yokushisa (e)
Isixazululo:
2. Injini yokushisa ikhiqiza amaJoules angu-2000 omsebenzi womshini futhi injini ikhipha ukushisa endaweni ezungezile ngesilinganiso samaJoules angu-500. Iyini ukusebenza kahle kwenjini yokushisa?
Kwaziwa:
Umsebenzi wenziwa yinjini (W) = ama-Joules angu-2000
Ukukhishwa kokushisa (Q L ) = 5000 Joules
Okokufaka ukushisa (Q H ) = 2000 + 5000 = 7000 ama-Joules
Kufunwa: Ukusebenza kahle (e)
Isixazululo:
3. Injini yokushisa inamandla okusebenza angu-30%. Uma injini ikhiqiza ama-Joules angu-10,000 omsebenzi womshini, kungakanani ukushisa okukhishwa njengokushisa okulahliwe kule njini?
Kwaziwa:
Ukusebenza kahle (e) = 30% = 30/100 = 0.3
Umsebenzi wenziwa ngenjini (W) = ama-Joules angu-3,000
Okufunwayo : Ukushisa okukhiphayo (Q L )
Isixazululo:
Ukushisa okukhiphayo (Q L ) = ukushisa okufakwayo (Q H ) – umsebenzi wenziwa yinjini (W)
Q L = 10,000 Joules - 3,000 Joules
Q L = 7,000 Joule
4. Nquma ukusebenza kahle kwenjini yeCarnot esebenza phakathi kwamachibi amabili emazingeni okushisa angu-500 K no-300 K.
Isixazululo: Sisebenzisa ifomula yokusebenza kahle kweCarnot, \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}}\), sithola \(\eta = 1 – \frac{300}{500} = 0.4\) noma \(40\%\).
5. Injini yokushisa imunca ama-2000 J okushisa kusuka endaweni yokugcina amanzi ashisayo bese ikhipha ama-1200 J aye endaweni yokugcina amanzi abandayo. Bala umsebenzi owenziwe yinjini.
Isixazululo: Ukusebenzisa umthetho wokuqala we-thermodynamics, \(Q_{\text{hot}} = W + Q_{\text{cold}}\), umsebenzi owenziwe ngu-\(W = 2000 – 1200 = 800\ \text{J}\).
6. Bala ukusebenza kahle kwenjini yokushisa emunca ama-J angu-1000 kusuka endaweni yokugcina amanzi ashisayo futhi yenze umsebenzi wama-J angu-600.
Isixazululo: \(\eta = \frac{W}{Q_{\text{hot}}} = \frac{600}{1000} = 0.6\) noma \(60\%\).
7. Injini yokushisa isebenza phakathi kuka-400 K no-200 K. Nquma ukusebenza kahle okukhulu ngangokunokwenzeka.
Isixazululo: \(\eta_{\text{max}} = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{200}{400} = 0.5\) noma \(50\%\).
8. Injini yokushisa yenqaba ama-J angu-300 iye echibini elibandayo ngenkathi yenza umsebenzi wama-J angu-200. Bala ukushisa okumuncwe yichibi elishisayo.
Isixazululo: \(Q_{\text{hot}} = W + Q_{\text{cold}} = 200 + 300 = 500\ \text{J}\).
9. Nquma ukusebenza kahle komjikelezo we-Otto onesilinganiso sokucindezela esingu-8.
Isixazululo: \(\eta = 1 – \frac{1}{r^{(\gamma – 1)}} = 1 – \frac{1}{8^{(1.4 – 1)}} \cishe 0.564\) noma \(56.4\%\), lapho \(\gamma\) kuyisilinganiso samandla okushisa.
10. Injini yokushisa yenza umsebenzi ongu-150 J bese yenqaba u-100 J endaweni ebandayo yokugcina amanzi. Thola ukushisa okumuncwe yi-hot reservoir.
Isixazululo: \(Q_{\text{hot}} = W + Q_{\text{cold}} = 150 + 100 = 250\ \text{J}\).
11. Nquma ukusebenza kahle kwenjini yedizili enesilinganiso sokucindezela esingu-18 kanye nesilinganiso sokuvala esingu-2.
Isixazululo: \(\eta = 1 – \frac{1}{r^{(\gamma – 1)}} \left( \frac{r_c – 1}{r_c} \right) \approx 0.627\) noma \(62.7\%\), lapho \(r\) kuyisilinganiso sokucindezela, \(r_c\) kuyisilinganiso sokunqunywa, kanye \(\gamma\) kuyisilinganiso samandla okushisa.
12. Bala umsebenzi owenziwe yinjini yokushisa emunca ama-J angu-400 futhi esebenza kahle ngo-50%.
Isixazululo: \(W = \eta \cdot Q_{\text{hot}} = 0.5 \cdot 400 = 200\ \text{J}\).
13. Injini yokushisa isebenza phakathi kuka-600 K no-300 K. Thola ukusebenza kahle kweCarnot.
Isixazululo: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{300}{600} = 0.5\) noma \(50\%\).
14. Injini yokushisa imunca ama-J angu-3000 bese yenqaba ama-J angu-1800 endaweni yokugcina amanzi ebandayo. Bala umsebenzi owenziwe.
Isixazululo: \(W = Q_{\text{hot}} – Q_{\text{cold}} = 3000 – 1800 = 1200\ \text{J}\).
15. Nquma ukusebenza kahle kwenjini ye-Stirling esebenza phakathi kwamachibi amabili ku-800 K kanye no-400 K.
Isixazululo: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{400}{800} = 0.5\) noma \(50\%\).
16. Injini yokushisa yenqaba ama-J angu-500 iye echibini elibandayo ngenkathi yenza umsebenzi wama-J angu-300. Bala ukushisa okumuncwe yichibi elishisayo.
Isixazululo: \(Q_{\text{hot}} = W + Q_{\text{cold}} = 300 + 500 = 800\ \text{J}\).
17. Nquma ukusebenza kahle komjikelezo we-Ericsson ngama-reservoirs ashisayo nabandayo ku-1000 K kanye no-250 K.
Isixazululo: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{250}{1000} = 0.75\) noma \(75\%\).
18. Injini yokushisa yenza umsebenzi ongu-700 J futhi isebenza kahle ngo-70%. Bala ukushisa okwenqatshiwe endaweni ebandayo.
Isixazululo: \(Q_{\text{cold}} = \frac{W}{\eta} – W = \frac{700}{0.7} – 700 \cishe 1000 – 700 = 300\ \text{J}\).
19. Nquma ukusebenza kahle komjikelezo we-Brayton ngezilinganiso zokucindezela ezingu-6.5 kanye no-\(\gamma = 1.4\).
Isixazululo: \(\eta = 1 – \frac{1}{r_p^{(\gamma – 1)/\gamma}} \cishe kube ngu-0.433\) noma \(43.3\%\), lapho \(r_p\) kuyisilinganiso sokucindezela.
20. Bala umsebenzi owenziwe yinjini yokushisa emunca ama-J angu-250 bese yenqaba ama-J angu-100 endaweni yokugcina amanzi ebandayo.
Isixazululo: \(W = Q_{\text{hot}} – Q_{\text{cold}} = 250 – 100 = 150\ \text{J}\).
21. Injini yokushisa isebenza phakathi kuka-450 K no-150 K. Thola ukusebenza kahle kweCarnot.
Isixazululo: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{150}{450} \cishe kube ngu-0.667\) noma \(66.7\%\).
22. Nquma ukusebenza kahle komjikelezo we-Atkinson onesilinganiso sokucindezela esingu-10.
Isixazululo: \(\eta = 1 – \frac{1}{r^{(\gamma – 1)}} \cishe 0.593\) noma \(59.3\%\),
lapho \(r\) kuyisilinganiso sokucindezela kanye \(\gamma\) kuyisilinganiso samandla okushisa.
20. Injini yokushisa imunca ama-J angu-180 futhi inamandla okusebenza angu-40%. Bala umsebenzi owenziwe.
Isixazululo: \(W = \eta \cdot Q_{\text{hot}} = 0.4 \cdot 180 = 72\ \text{J}\).
Qaphela: Ngezinkinga ezihilela imijikelezo ethile yokushisa (njenge-Otto, i-Diesel, njll.), kwasetshenziswa amanani athile afana nesilinganiso somthamo wokushisa \(\gamma\), ajwayelekile kumagesi athile (isb., \(\gamma = 1.4\) emoyeni). Lawa manani angahluka kuye ngezinto ezithile ezisetshenziswa enjinini.
