ʻEnekini Carnot (ka hoʻohana ʻana o ke kānāwai ʻelua o ka thermodynamics) - nā pilikia a me nā hoʻonā

25 ʻenekini Carnot (ka hoʻohana ʻana i ke kānāwai ʻelua o ka thermodynamics) - nā pilikia a me nā hoʻonā

1. Hana kekahi ʻenekini ma waena o 1200 Kelvin a me 300 Kelvin. He aha ka pono o kēia ʻenekini?

ʻIke ʻia:

Mahana kiʻekiʻe (T _H ) = 1200 K

Haʻahaʻa ka mahana (T _L ) = 300 K

Makemake ʻia: Ka pono (e)

Lōlā:

2. Hana kekahi ʻenekini ma waena o 727 ^o C a me 127 ^o C. ʻO ka hoʻokomo wela o ka ʻenekini he 6000 Joules. He aha ka pono o ka ʻenekini a me ka hana i hana ʻia e ka ʻenekini i kēlā me kēia pōʻaiapuni?

ʻIke ʻia:

Mahana kiʻekiʻe (T _H ) = 727 ^o C + 273 = 1000 K

Haʻahaʻa ka mahana (T _L ) = 127 ^o C + 273 = 400 K

Ka hoʻokomo wela (Q _H ) = 6000 Joules

Makemake ʻia: Ka pono (e) a me ka hana i hana ʻia e ka ʻenekini (W)

Lōlā:

Ka pono o ka mīkini Carnot :

Hana ʻia ka hana e ka ʻenekini Carnot:

W = e Q _H

W = (0.6)(6000)

W = 3600 Joule

3. Hana kekahi ʻenekini ma waena o 527 ^o C a me 127 ^o C. ʻO ka hoʻokomo wela o ka ʻenekini he 10,000 Joules. ʻEhia ka nui o ka wela i hoʻokuʻu ʻia ma ke ʻano he wela ʻōpala mai kēia ʻenekini?

ʻIke ʻia:

Mahana kiʻekiʻe (T _H ) = 527 ^o C + 273 = 800 K

Haʻahaʻa ka mahana (T _L ) = 127 ^o C + 273 = 400 K

Ka hoʻokomo wela (Q _H ) = 10,000 Joules

Makemake ʻia: Ka hoʻopuka wela (Q _L )

Lōlā:

Ka pono o ka mīkini Carnot:

Hana ʻia ka hana e ka ʻenekini Carnot:

W = e Q ₁

W = (0.5)(10.000)

W = 5000 Joule

Ka hoʻopuka wela (Q _L ) = Ka hoʻokomo wela (Q _H ) – Hana (W)

Q _L = Q _H – W

Q _L = 10,000 – 5,000

QL = ₅₀₀₀ Joule

4. He aha ka pono o ka ʻenekini a me ka hana i hana ʻia e ka ʻenekini e like me ke kiʻikuhi ma lalo nei.

ʻIke ʻia:

Mahana kiʻekiʻe (T _H ) = 800 K

Haʻahaʻa ka mahana (T _L ) = 300 K

Ka hoʻokomo wela (Q _H ) = 1000 Joules

Makemake ʻia: Ka pono (e) a me ka hana (W) i hana ʻia e ka ʻenekini

Lōlā:

Ka pono o ka mīkini Carnot:

Hana ʻia ka hana e ka ʻenekini Carnot:

W = e Q _H

W = (0.625)(1000)

W = 625 Joule

5. Inā hana kahi ʻenekini Carnot ma waena o \( 500\,K \) a me \( 300\,K \), e helu i kona pono.
Hoʻonā: \( \eta = 1 – \frac{T_C}{T_H} = 1 – \frac{300}{500} = 0.4 = 40\% \)

6. E huli i ka pono o kahi pahu hau Carnot e hana ana ma waena o \( 300\,K \) a me \( 250\,K \).
Hoʻonā: \( \eta = \frac{T_C}{T_H – T_C} = \frac{250}{50} = 5 = 500\% \)

7. ʻO ka pono o kahi ʻenekini Carnot he \( 30\% \). Inā \( T_C = 300\,K \), e ʻimi \( T_H \).
Hoʻonā: \( T_H = \frac{T_C}{1 – \eta} = \frac{300}{0.7} \approx 428.57\,K \)

8. Inā hana kahi pamu wela Carnot ma waena o \( 270\,K \) a me \( 330\,K \), e ʻimi i ke koina o ka hana (COP).
Hoʻonā: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{330}{60} = 5.5 \)

9. E hoʻoholo i ka \( T_C \) no kahi ʻenekini Carnot me ka \( 50 \% \) pono a me \( T_H = 400 \,K \).
Hoʻonā: \( T_C = T_H \times (1 – \eta) = 400 \times 0.5 = 200\,K \)

10. E helu i ka pono o kahi ʻenekini Carnot e hana ana ma waena o \( 373\,K \) a me \( 273\,K \).
Hoʻonā: \( \eta = 1 – \frac{273}{373} \approx 0.268 = 26.8\% \)

11. E huli i ke COP o kahi pahu hau Carnot me \( T_C = 260\,K \) a me \( T_H = 300\,K \).
Hoʻonā: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{260}{40} = 6.5 \)

12. Loaʻa i kahi ʻenekini Carnot ka pono o \( 25\% \) a me \( T_C = 200\,K \). E huli \( T_H \).
Hoʻonā: \( T_H = \frac{T_C}{1 – \eta} = \frac{200}{0.75} \approx 266.67\,K \)

13. Inā hana kahi pamu wela Carnot ma waena o \( 220\,K \) a me \( 320\,K \), e ʻimi i ke COP.
Hoʻonā: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{320}{100} = 3.2 \)

14. E hoʻoholo i ka \( T_C \) no kahi ʻenekini Carnot me ka \( 60 \% \) pono a me \( T_H = 500 \,K \).
Hoʻonā: \( T_C = T_H \times (1 – \eta) = 500 \times 0.4 = 200\,K \)

15. E helu i ka pono o kahi ʻenekini Carnot e hana ana ma waena o \( 600\,K \) a me \( 400\,K \).
Hoʻonā: \( \eta = 1 – \frac{400}{600} \approx 0.333 = 33.3\% \)

16. E huli i ke COP o kahi pahu hau Carnot me \( T_C = 280\,K \) a me \( T_H = 330\,K \).
Hoʻonā: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{280}{50} = 5.6 \)

17. Loaʻa i kahi ʻenekini Carnot ka pono o \( 40\% \) a me \( T_C = 250\,K \). E huli \( T_H \).
Hoʻonā: \( T_H = \frac{T_C}{1 – \eta} = \frac{250}{0.6} \approx 416.67\,K \)

18. Inā hana kahi pamu wela Carnot ma waena o \( 270\,K \) a me \( 370\,K \), e ʻimi i ke COP.
Hoʻonā: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{370}{100} = 3.7 \)

15. E hoʻoholo i ka \( T_C \) no kahi ʻenekini Carnot me ka \( 75 \% \) pono a me \( T_H = 800 \,K \).
Hoʻonā: \( T_C = T_H \times (1 – \eta) = 800 \times 0.25 = 200\,K \)

16. E helu i ka pono o kahi ʻenekini Carnot e hana ana ma waena o \( 700\,K \) a me \( 300\,K \).
Hoʻonā: \( \eta = 1 – \frac{300}{700} \approx 0.571 = 57.1\% \)

17. E huli i ke COP o kahi pahu hau Carnot me \( T_C = 250\,K \) a me \( T_H = 350\,K \).
Hoʻonā: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{250}{100} = 2.5 \)

18. Loaʻa i kahi ʻenekini Carnot ka pono o \( 10\% \) a me \( T_C = 150\,K \). E huli \( T_H \).
Hoʻonā: \( T_H = \frac{T_C}{1 – \eta} = \frac{150}{0.9} \approx 166.67\,K \)

19. Inā hana kahi pamu wela Carnot ma waena o \( 200\,K \) a me \( 400\,K \), e ʻimi i ke COP.
Hoʻonā: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{400}{200} = 2 \)

20. E hoʻoholo i ka \( T_C \) no kahi ʻenekini Carnot me ka \( 80 \% \) pono a me \( T_H = 1000 \,K \).
Hoʻonā: \( T_C = T_H \times (1 – \eta) = 1000 \times 0.2 = 200\,K \)