25 Injini ye-Carnot (ukusetshenziswa komthetho wesibili we-thermodynamics) – izinkinga nezixazululo
1. Injini isebenza phakathi kuka-1200 Kelvin no-300 Kelvin. Ingakanani ukusebenza kahle kwale njini?
Kwaziwa:
Izinga lokushisa eliphakeme (TH ) = 1200 K
Izinga lokushisa eliphansi (T L ) = 300 K
Kufunwa: Ukusebenza kahle (e)
Isixazululo:
2. Injini isebenza phakathi kuka-727 o C no-127 o C. Ukufakwa kokushisa kwenjini kungama-Joules angu-6000. Kuyini ukusebenza kahle kwenjini kanye nomsebenzi owenziwa yinjini umjikelezo ngamunye?
Kwaziwa:
Izinga lokushisa eliphezulu (TH ) = 727 o C + 273 = 1000 K
Izinga lokushisa eliphansi (T L ) = 127 o C + 273 = 400 K
Okokufaka ukushisa (Q H ) = 6000 Joules
Okufunwayo: Ukusebenza kahle (e) kanye nomsebenzi owenziwe yinjini (W)
Isixazululo:
Ukusebenza kahle kwenjini yeCarnot :
Umsebenzi wenziwa yinjini yeCarnot:
W = e Q H
W = (0.6)(6000)
W = 3600 Joule
3. Injini isebenza phakathi kuka-527 o C no-127 o C. Ukufakwa kokushisa kwenjini kungama-Joules ayi-10,000. Kungakanani ukushisa okukhishwa njengokushisa okulahliwe kule njini?
Kwaziwa:
Izinga lokushisa eliphakeme (TH ) = 527 o C + 273 = 800 K
Izinga lokushisa eliphansi (T L ) = 127 o C + 273 = 400 K
Okokufaka ukushisa (Q H ) = 10,000 Joules
Okufunwayo: Ukushisa okukhiphayo (Q L )
Isixazululo:
Ukusebenza kahle kwenjini yeCarnot:
Umsebenzi wenziwa yinjini yeCarnot:
W = e Q 1
W = (0.5)(10.000)
W = 5000 Joule
Umphumela wokushisa (Q L ) = Ukufakwa kokushisa (Q H ) – Umsebenzi (W)
Q L = Q H – W
Q L = 10,000 – 5,000
Q L = 5000 Joule
4. Kuyini ukusebenza kahle kwenjini kanye nomsebenzi owenziwe yinjini ngokwesithombe esingezansi.
Kwaziwa:
Izinga lokushisa eliphakeme (TH ) = 800 K
Izinga lokushisa eliphansi (T L ) = 300 K
Okokufaka ukushisa (Q H ) = 1000 Joules
Okufunwayo: Ukusebenza kahle (e) kanye nomsebenzi (W) owenziwa yinjini
Isixazululo:
Ukusebenza kahle kwenjini yeCarnot:
Umsebenzi wenziwa yinjini yeCarnot:
W = e Q H
W = (0.625)(1000)
W = 625 Joule
5. Uma injini yeCarnot isebenza phakathi kuka-500, K no-300, K, bala ukusebenza kwayo kahle.
Isixazululo: \( \eta = 1 – \frac{T_C}{T_H} = 1 – \frac{300}{500} = 0.4 = 40\% \)
6. Thola ukusebenza kahle kwesiqandisi seCarnot esisebenza phakathi kuka-300, K) no-250, K.
Isixazululo: \( \eta = \frac{T_C}{T_H – T_C} = \frac{250}{50} = 5 = 500\% \)
7. Ukusebenza kahle kwenjini yeCarnot kungu-\( 30\% \). Uma \( T_C = 300\,K \), thola \( T_H \).
Isixazululo: \( T_H = \frac{T_C}{1 – \eta} = \frac{300}{0.7} \cishe 428.57\,K \)
8. Uma iphampu yokushisa yeCarnot isebenza phakathi kuka-270, K no-330, K, thola i-coefficient of performance (COP).
Isixazululo: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{330}{60} = 5.5 \)
9. Nquma \( T_C \) injini yeCarnot esebenza kahle ngo-\( 50\% \) kanye \( T_H = 400\,K \).
Isixazululo: \( T_C = T_H \izikhathi (1 – \eta) = 400 \izikhathi 0.5 = 200\,K \)
10. Bala ukusebenza kahle kwenjini yeCarnot esebenza phakathi kuka-\(373\,K \) no-\(273\,K \).
Isixazululo: \( \eta = 1 – \frac{273}{373} \cishe 0.268 = 26.8\% \)
11. Thola i-COP yesiqandisi se-Carnot esine-\( T_C = 260\,K \) kanye ne-\( T_H = 300\,K \).
Isixazululo: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{260}{40} = 6.5 \)
12. Injini yeCarnot inamandla okusebenza kahle angu-\( 25\% \) kanye no-\( T_C = 200\,K \). Thola \( T_H \).
Isixazululo: \( T_H = \frac{T_C}{1 – \eta} = \frac{200}{0.75} \cishe 266.67\,K \)
13. Uma iphampu yokushisa yeCarnot isebenza phakathi kuka-220, K no-320, K, thola i-COP.
Isixazululo: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{320}{100} = 3.2 \)
14. Nquma \( T_C \) injini yeCarnot esebenza kahle ngo-\( 60\% \) kanye \( T_H = 500\,K \).
Isixazululo: \( T_C = T_H \izikhathi (1 – \eta) = 500 \izikhathi 0.4 = 200\,K \)
15. Bala ukusebenza kahle kwenjini yeCarnot esebenza phakathi kuka-\(600\,K \) no-\(400\,K \).
Isixazululo: \( \eta = 1 – \frac{400}{600} \cishe 0.333 = 33.3\% \)
16. Thola i-COP yesiqandisi se-Carnot esine-\( T_C = 280\,K \) kanye ne-\( T_H = 330\,K \).
Isixazululo: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{280}{50} = 5.6 \)
17. Injini yeCarnot inamandla okusebenza kahle angu-\( 40\% \) kanye no-\( T_C = 250\,K \). Thola \( T_H \).
Isixazululo: \( T_H = \frac{T_C}{1 – \eta} = \frac{250}{0.6} \cishe 416.67\,K \)
18. Uma iphampu yokushisa yeCarnot isebenza phakathi kuka-270, K no-370, K, thola i-COP.
Isixazululo: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{370}{100} = 3.7 \)
15. Nquma \( T_C \) injini yeCarnot esebenza kahle ngo-\( 75\% \) kanye \( T_H = 800\,K \).
Isixazululo: \( T_C = T_H \izikhathi (1 – \eta) = 800 \izikhathi 0.25 = 200\,K \)
16. Bala ukusebenza kahle kwenjini yeCarnot esebenza phakathi kuka-\(700\,K \) no-\(300\,K \).
Isixazululo: \( \eta = 1 – \frac{300}{700} \cishe 0.571 = 57.1\% \)
17. Thola i-COP yesiqandisi se-Carnot esine-\( T_C = 250\,K \) kanye ne-\( T_H = 350\,K \).
Isixazululo: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{250}{100} = 2.5 \)
18. Injini yeCarnot inamandla okusebenza kahle angu-\( 10\% \) kanye no-\( T_C = 150\,K \). Thola \( T_H \).
Isixazululo: \( T_H = \frac{T_C}{1 – \eta} = \frac{150}{0.9} \cishe 166.67\,K \)
19. Uma iphampu yokushisa yeCarnot isebenza phakathi kuka-200, K no-400, K, thola i-COP.
Isixazululo: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{400}{200} = 2 \)
20. Nquma \( T_C \) injini yeCarnot esebenza kahle ngo-\( 80\% \) kanye \( T_H = 1000\,K \).
Isixazululo: \( T_C = T_H \izikhathi (1 – \eta) = 1000 \izikhathi 0.2 = 200\,K \)
