25 Matoorka Carnot (isticmaalka sharciga labaad ee thermodynamics) - dhibaatooyinka iyo xalalka
1. Matoorku wuxuu shaqeeyaa inta u dhaxaysa 1200 Kelvin iyo 300 Kelvin. Waa maxay waxtarka matoorkani?
La yaqaan:
Heerkul sare (T H ) = 1200 K
Heerkul hoose (T L ) = 300 K
La Doonayo: Waxtar (e)
Xalka:
2. Matoorku wuxuu shaqeeyaa inta u dhaxaysa 727 o C iyo 127 o C. Kuleylka matoorku waa 6000 Joules. Waa maxay hufnaanta matoorka iyo shaqada uu matoorku qabto wareeg kasta?
La yaqaan:
Heerkulka sare (T H ) = 727 o C + 273 = 1000 K
Heerkulka hoose (T L ) = 127 o C + 273 = 400 K
Kuleylka la geliyo (Q H ) = 6000 Joules
La Doonayo: Hufnaan (e) iyo shaqada uu sameeyo matoorku (W)
Xalka:
Waxtarka matoorka Carnot :
Shaqada waxaa qabta matoorka Carnot:
W = e Q H
W = (0.6)(6000)
W = 3600 Joule
3. Matoorku wuxuu shaqeeyaa inta u dhaxaysa 527 o C iyo 127 o C. Kuleylka matoorku waa 10,000 Joules. Immisa kulayl ayaa laga saaraa kulaylka qashinka ah ee matoorkan?
La yaqaan:
Heerkulka sare (T H ) = 527 o C + 273 = 800 K
Heerkulka hoose (T L ) = 127 o C + 273 = 400 K
Kuleylka la geliyo (Q H ) = 10,000 Joules
La Doonayo: Wax soo saarka kulaylka (Q L )
Xalka:
Hufnaanta matoorka Carnot:
Shaqada waxaa qabta matoorka Carnot:
W = e Q 1
W = (0.5)(10.000)
W = 5000 Joule
Wax soo saarka kulaylka (Q L ) = gelinta kulaylka (Q H ) - Shaqada (W)
Q L = Q H – W
Q L = 10,000 – 5,000
Q L = 5000 Joule
4. Waa maxay hufnaanta matoorka iyo shaqada uu matoorku qabto sida ku cad jaantuska hoose.
La yaqaan:
Heerkul sare (T H ) = 800 K
Heerkul hoose (T L ) = 300 K
Kuleylka la geliyo (Q H ) = 1000 Joules
La Doonayo: Hufnaan (e) iyo shaqo (W) oo uu sameeyo matoorku
Xalka:
Waxtarka matoorka Carnot:
Shaqada waxaa qabta matoorka Carnot:
W = e Q H
W = (0.625)(1000)
W = 625 Joule
5. Haddii matoorka Carnot uu shaqeeyo inta u dhaxaysa \( 500 \,K \) iyo \( 300 \,K \), xisaabi waxtarkiisa.
Xalka: \( \eta = 1 – \frac{T_C}{T_H} = 1 – \frac{300}{500} = 0.4 = 40% \)
6. Soo hel waxtarka qaboojiyaha Carnot ee u shaqeeya inta u dhaxaysa \(300\,K\) iyo \(250\,K\).
Xalka: \( \eta = \frac{T_C}{T_H – T_C} = \frac{250}{50} = 5 = 500\% \)
7. Waxtarka matoorka Carnot waa \( 30% \). Haddii \( T_C = 300\,K \), raadi \( T_H \).
Xalka: \( T_H = \frac{T_C}{1 – \eta} = \frac{300}{0.7} \qiyaastii 428.57\,K \)
8. Haddii bamka kulaylka Carnot uu shaqeeyo inta u dhaxaysa \( 270 \,K \) iyo \( 330 \,K \), hel isku-dhafka waxqabadka (COP).
Xalka: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{330}{60} = 5.5 \)
9. Go'aami \(T_C \) matoorka Carnot oo leh hufnaan \(50% \) iyo \(T_H = 400\,K \).
Xalka: \( T_C = T_H \times (1 – \eta) = 400 \times 0.5 = 200\,K \)
10. Xisaabi waxtarka matoorka Carnot ee u shaqeeya inta u dhaxaysa \( 373 \,K \) iyo \( 273 \,K \).
Xalka: \( \eta = 1 – \frac{273}{373} \qiyaastii 0.268 = 26.8\% \)
11. Soo hel COP-ga qaboojiyaha Carnot oo leh \( T_C = 260\,K \) iyo \( T_H = 300\,K \).
Xalka: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{260}{40} = 6.5 \)
12. Matoorka Carnot wuxuu leeyahay hufnaan 25% ah iyo ( T_C = 200\,K \). Soo hel \( T_H \).
Xalka: \( T_H = \frac{T_C}{1 – \eta} = \frac{200}{0.75} \qiyaastii 266.67\,K \)
13. Haddii bamka kulaylka Carnot uu shaqeeyo inta u dhaxaysa \( 220 \,K \) iyo \( 320 \,K \), hel COP.
Xalka: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{320}{100} = 3.2 \)
14. Go'aami \(T_C \) matoorka Carnot oo leh hufnaan \(60% \) iyo \(T_H = 500\,K \).
Xalka: \( T_C = T_H \times (1 – \eta) = 500 \times 0.4 = 200\,K \)
15. Xisaabi waxtarka matoorka Carnot ee u shaqeeya inta u dhaxaysa \( 600 \,K \) iyo \( 400 \,K \).
Xalka: \( \eta = 1 – \frac{400}{600} \qiyaastii 0.333 = 33.3\% \)
16. Soo hel COP-ga qaboojiyaha Carnot oo leh \( T_C = 280\,K \) iyo \( T_H = 330\,K \).
Xalka: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{280}{50} = 5.6 \)
17. Matoorka Carnot wuxuu leeyahay hufnaan 40% ah iyo ( T_C = 250\,K \). Soo hel \( T_H \).
Xalka: \( T_H = \frac{T_C}{1 – \eta} = \frac{250}{0.6} \qiyaastii 416.67\,K \)
18. Haddii bamka kulaylka Carnot uu shaqeeyo inta u dhaxaysa \( 270 \,K \) iyo \( 370 \,K \), hel COP.
Xalka: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{370}{100} = 3.7 \)
15. Go'aami \(T_C \) matoorka Carnot oo leh hufnaan \(75% \) iyo \(T_H = 800\,K \).
Xalka: \( T_C = T_H \times (1 – \eta) = 800 \times 0.25 = 200\,K \)
16. Xisaabi waxtarka matoorka Carnot ee u shaqeeya inta u dhaxaysa \( 700 \,K \) iyo \( 300 \,K \).
Xalka: \( \eta = 1 – \frac{300}{700} \qiyaastii 0.571 = 57.1\% \)
17. Soo hel COP-ga qaboojiyaha Carnot oo leh \( T_C = 250\,K \) iyo \( T_H = 350\,K \).
Xalka: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{250}{100} = 2.5 \)
18. Matoorka Carnot wuxuu leeyahay hufnaan 10% ah iyo ( T_C = 150\,K \). Soo hel \( T_H \).
Xalka: \( T_H = \frac{T_C}{1 – \eta} = \frac{150}{0.9} \qiyaastii 166.67\,K \)
19. Haddii bamka kulaylka Carnot uu shaqeeyo inta u dhaxaysa \( 200 \,K \) iyo \( 400 \,K \), hel COP.
Xalka: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{400}{200} = 2 \)
20. Go'aami \(T_C \) matoorka Carnot oo leh hufnaan \(80% \) iyo \(T_H = 1000\,K \).
Xalka: \( T_C = T_H \times (1 – \eta) = 1000 \times 0.2 = 200\,K \)
