Enjene ea Carnot (ts'ebeliso ea molao oa bobeli oa thermodynamics) - mathata le litharollo

25 Enjene ea Carnot (ts'ebeliso ea molao oa bobeli oa thermodynamics) - mathata le litharollo

1. Enjene e sebetsa pakeng tsa 1200 Kelvin le 300 Kelvin. Bokgoni ba enjene ena ke bofe?

Tse tsejoang:

Mocheso o phahameng (T)_H) = 1200 K

Mocheso o tlase (T)_L) = 300 K

Ho Batloa: Bokgoni (e)

Tharollo:

Enjene ea Carnot (ts'ebeliso ea molao oa bobeli oa thermodynamics) - mathata le litharollo 1

2. Enjene e sebetsa pakeng tsa 727^oC le 127^oC. Mocheso o kenang ka enjene ke dijoule tse 6000. Bokgoni ba enjene le mosebetsi o etswang ke enjene potolohong ka nngwe ke bofe?

Tse tsejoang:

High mocheso (T_H= 727^oC + 273 = 1000 K

Mocheso o tlase (T)_L= 127^oC + 273 = 400 K

Kenyelletso ea mocheso (Q)_H) = 6000 Joule

Oa Batla: Bokgoni (e) le mosebetsi o etswang ke enjene (W)

Tharollo:

Katleho ea Enjene ea Carnot :

Enjene ea Carnot (ts'ebeliso ea molao oa bobeli oa thermodynamics) - mathata le litharollo 2

Mosebetsi o etsoa ke enjene ea Carnot:

W = e Q_H

W = (0.6)(6000)

W = 3600 Joule

3. Enjene e sebetsa pakeng tsa 527^oC le 127^oC. Mocheso o kenang ka enjene ke dijoule tse 10,000. Ke mocheso o mokae o ntshwang e le mocheso o lahlilweng ho tswa enjeneng ena?

Tse tsejoang:

Mocheso o phahameng (T)_H= 527^oC + 273 = 800 K

Mocheso o tlase (T)_L= 127^oC + 273 = 400 K

Heat ho kenya (Q_H) = 10,000 Joule

Ho batloa: Mocheso o hlahang (Q)_L)

Tharollo:

Bokgoni ba enjene ea Carnot:

Enjene ea Carnot (ts'ebeliso ea molao oa bobeli oa thermodynamics) - mathata le litharollo 3

Mosebetsi o etsoa ka enjene ea Carnot:

W = e Q₁

W = (0.5)(10.000)

W = 5000 Joule

Mocheso o hlahang (Q)_L) = Kenyelletso ea mocheso (Q_H) – Mosebetsi (W)

Q_L =Q_H - W

Q_L = 10,000 - 5,000

Q_L = 5000 Joule

4. Bokgoni ba enjene le mosebetsi o etswang ke enjene ke bofe ho ya ka setshwantsho se ka tlase.

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Enjene ea Carnot (ts'ebeliso ea molao oa bobeli oa thermodynamics) - mathata le litharollo 4 Tse tsejoang:

Mocheso o phahameng (T)_H) = 800 K

Mocheso o tlase (T)_L) = 300 K

Kenyelletso ea mocheso (Q)_H) = 1000 Joule

Ho Batloa: Bokgoni (e) le mosebetsi (W) e entsoe ke enjene

Tharollo:

Bokgoni ba enjene ea Carnot:

Enjene ea Carnot (ts'ebeliso ea molao oa bobeli oa thermodynamics) - mathata le litharollo 5

Mosebetsi o etsoa ke enjene ea Carnot:

W = e Q_H

W = (0.625)(1000)

W = 625 Joule

5. Haeba enjene ea Carnot e sebetsa pakeng tsa 500, K) le 300, K, bala katleho ea eona.
Tharollo: \( \eta = 1 – \frac{T_C}{T_H} = 1 – \frac{300}{500} = 0.4 = 40\% \)

6. Fumana bokgoni ba sehatsetsi sa Carnot se sebetsang pakeng tsa 300,K le 250,K.
Tharollo: \( \eta = \frac{T_C}{T_H – T_C} = \frac{250}{50} = 5 = 500\% \)

7. Bokgoni ba enjene ya Carnot ke \( 30\% \). Haeba \( T_C = 300\,K \), fumana \( T_H \).
Tharollo: \( T_H = \frac{T_C}{1 – \eta} = \frac{300}{0.7} \hoo e ka bang 428.57\,K \)

8. Haeba pompo ea mocheso ea Carnot e sebetsa pakeng tsa 270, K) le 330, K), fumana coefficient ea ts'ebetso (COP).
Tharollo: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{330}{60} = 5.5 \)

9. Fumana \( T_C \) bakeng sa enjene ea Carnot e nang le bokhoni ba \( 50\% \) le \( T_H = 400\,K \).
Tharollo: \( T_C = T_H \times (1 – \eta) = 400 \times 0.5 = 200\,K \)

10. Bala bokgoni ba enjene ya Carnot e sebetsang pakeng tsa \(373\,K \) le \(273\,K \).
Tharollo: \( \eta = 1 – \frac{273}{373} \hoo e ka bang 0.268 = 26.8\% \)

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11. Fumana COP ea sehatsetsi sa Carnot se nang le \( T_C = 260\,K \) le \( T_H = 300\,K \).
Tharollo: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{260}{40} = 6.5 \)

12. Enjene ea Carnot e na le bokhoni ba \(25\% \) le \( T_C = 200\,K \). Fumana \( T_H \).
Tharollo: \( T_H = \frac{T_C}{1 – \eta} = \frac{200}{0.75} \hoo e ka bang 266.67\,K \)

13. Haeba pompo ea mocheso ea Carnot e sebetsa pakeng tsa 220, K) le 320, K, fumana COP.
Tharollo: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{320}{100} = 3.2 \)

14. Fumana \( T_C \) bakeng sa enjene ea Carnot e nang le bokhoni ba \( 60\% \) le \( T_H = 500\,K \).
Tharollo: \( T_C = T_H \times (1 – \eta) = 500 \times 0.4 = 200\,K \)

15. Bala bokgoni ba enjene ya Carnot e sebetsang pakeng tsa \(600\,K \) le \(400\,K \).
Tharollo: \( \eta = 1 – \frac{400}{600} \hoo e ka bang 0.333 = 33.3\% \)

16. Fumana COP ea sehatsetsi sa Carnot se nang le \( T_C = 280\,K \) le \( T_H = 330\,K \).
Tharollo: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{280}{50} = 5.6 \)

17. Enjene ea Carnot e na le bokhoni ba \(40\% \) le \( T_C = 250\,K \). Fumana \( T_H \).
Tharollo: \( T_H = \frac{T_C}{1 – \eta} = \frac{250}{0.6} \hoo e ka bang 416.67\,K \)

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18. Haeba pompo ea mocheso ea Carnot e sebetsa pakeng tsa 270, K) le 370, K, fumana COP.
Tharollo: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{370}{100} = 3.7 \)

15. Fumana \( T_C \) bakeng sa enjene ea Carnot e nang le bokhoni ba \( 75\% \) le \( T_H = 800\,K \).
Tharollo: \( T_C = T_H \times (1 – \eta) = 800 \times 0.25 = 200\,K \)

16. Bala bokgoni ba enjene ya Carnot e sebetsang pakeng tsa \(700\,K \) le \(300\,K \).
Tharollo: \( \eta = 1 – \frac{300}{700} \hoo e ka bang 0.571 = 57.1\% \)

17. Fumana COP ea sehatsetsi sa Carnot se nang le \( T_C = 250\,K \) le \( T_H = 350\,K \).
Tharollo: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{250}{100} = 2.5 \)

18. Enjene ea Carnot e na le bokhoni ba \(10\% \) le \( T_C = 150\,K \). Fumana \( T_H \).
Tharollo: \( T_H = \frac{T_C}{1 – \eta} = \frac{150}{0.9} \hoo e ka bang 166.67\,K \)

19. Haeba pompo ea mocheso ea Carnot e sebetsa pakeng tsa 200, K) le 400, K, fumana COP.
Tharollo: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{400}{200} = 2 \)

20. Fumana \( T_C \) bakeng sa enjene ea Carnot e nang le bokhoni ba \( 80\% \) le \( T_H = 1000\,K \).
Tharollo: \( T_C = T_H \times (1 – \eta) = 1000 \times 0.2 = 200\,K \)