Karno dvigateli (termodinamikaning ikkinchi qonunining qo'llanilishi) – muammolar va yechimlar

25 Karno dvigateli (termodinamikaning ikkinchi qonunining qo'llanilishi) – muammolar va yechimlar

1. Dvigatel 1200 Kelvin va 300 Kelvin oralig'ida ishlaydi. Bu dvigatelning samaradorligi qancha?

Ma'lum:

Yuqori harorat (T _H ) = 1200 K

Past harorat (T _L ) = 300 K

Kerakli: Samaradorlik (e)

yechim:

2. Dvigatel 727 oralig'ida ishlaydi^oC va 127^oC. Dvigatelning issiqlik sarfi 6000 Joul. Dvigatelning samaradorligi va har bir siklda bajaradigan ishi qancha?

Ma'lum:

baland harorat (T_H) = 727^oC + 273 = 1000 K

Past harorat (T)_L) = 127^oC + 273 = 400 K

Issiqlik sarfi (QH ₎ = 6000 Joul

Kerakli: Samaradorlik (e) va dvigatel tomonidan bajarilgan ish (Vt)

yechim:

ning samaradorligi Carnot dvigateli :

Ish Carnot dvigateli tomonidan bajariladi:

W = e Q_H

W = (0.6)(6000)

W = 3600 Joul

3. Dvigatel 527 oralig'ida ishlaydi^oC va 127^oC. Dvigatelning issiqlik sarfi 10 000 Joulni tashkil qiladi. Bu dvigateldan qancha issiqlik chiqindi issiqlik sifatida chiqariladi?

Ma'lum:

Yuqori harorat (T _H ) = 527 ^o C + 273 = 800 K

Past harorat (T)_L) = 127^oC + 273 = 400 K

Issiqlik kiritish (QH ₎ = 10,000 Joul

Qidirilgan: Issiqlik chiqishi (Q)_L)

yechim:

Carnot dvigatelining samaradorligi:

Ish Carnot dvigateli tomonidan bajariladi:

W = e Q ₁

W = (0.5)(10.000)

W = 5000 Joul

Issiqlik chiqishi (Q)_L) = Issiqlik kiritish (Q_H) – Ish (W)

Q_L = Q_H - V

Q_L = 10,000 - 5,000

Q _L = 5000 Joul

4. Quyidagi diagrammaga muvofiq dvigatelning samaradorligi va dvigatel tomonidan bajarilgan ish qanday.

Ma'lum:

Yuqori harorat (T _H ) = 800 K

Past harorat (T _L ) = 300 K

Issiqlik sarfi (QH ₎ = 1000 Joul

Kerakli: Samaradorlik (e) va ish (W) dvigatel tomonidan bajarilgan

yechim:

Carnot dvigatelining samaradorligi:

Ish Carnot dvigateli tomonidan bajariladi:

W = e Q_H

W = (0.625)(1000)

W = 625 Joul

5. Agar Carnot dvigateli �(500\,K \) va �(300\,K \) oralig'ida ishlayotgan bo'lsa, uning samaradorligini hisoblang.
Yechim: \( \eta = 1 – \frac{T_C}{T_H} = 1 – \frac{300}{500} = 0.4 = 40\% \)

6. Carnot sovutgichining √(300,K) va √(250,K) oralig'ida ishlashining samarali samaradorligini toping.
Yechim: \( \eta = \frac{T_C}{T_H – T_C} = \frac{250}{50} = 5 = 500\% \)

7. Carnot dvigatelining samarali samaradorligi �(30% ga teng). Agar �(T_C = 300,K \) bo'lsa, �(T_H \) ni toping.
Yechim: \( T_H = \frac{T_C}{1 – \eta} = \frac{300}{0.7} \taxminan 428.57\,K \)

8. Agar Carnot issiqlik nasosi 270 K va 330 K oralig'ida ishlayotgan bo'lsa, unumdorlik koeffitsientini (COP) toping.
Yechim: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{330}{60} = 5.5 \)

9. 50% samaradorlikka va 400 K ga teng bo'lgan Carnot dvigateli uchun ni aniqlang.
Yechim: \( T_C = T_H \marta (1 – \eta) = 400 \marta 0.5 = 200\,K \)

10. \( 373\,K \) va \( 273\,K \) oralig'ida ishlaydigan Carnot dvigatelining samarali ish faoliyatini hisoblang.
Yechim: \( \eta = 1 – \frac{273}{373} \taxminan 0.268 = 26.8\% \)

11. Carnot sovutgichining mоslama qiymatini toping, bunda mоslama qiymati ...
Yechim: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{260}{40} = 6.5 \)

12. Carnot dvigateli 25% samaradorlikka va 200% samaradorlikka ega. (T_C = 200 K) ni toping.
Yechim: \( T_H = \frac{T_C}{1 – \eta} = \frac{200}{0.75} \taxminan 266.67\,K \)

13. Agar Carnot issiqlik nasosi 220K va 320K oralig'ida ishlayotgan bo'lsa, COP ni toping.
Yechim: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{320}{100} = 3.2 \)

14. 60% samaradorlikka va 500 K ga teng bo'lgan Carnot dvigateli uchun ni aniqlang.
Yechim: \( T_C = T_H \marta (1 – \eta) = 500 \marta 0.4 = 200\,K \)

15. \( 600\,K \) va \( 400\,K \) oralig'ida ishlaydigan Carnot dvigatelining samarali ish faoliyatini hisoblang.
Yechim: \( \eta = 1 – \frac{400}{600} \taxminan 0.333 = 33.3\% \)

16. Carnot sovutgichining mоslama qiymatini toping, bunda mоslama qiymati ...
Yechim: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{280}{50} = 5.6 \)

17. Carnot dvigateli 40% samaradorlikka va 250% samaradorlikka ega. (T_C = 200 K) ni toping.
Yechim: \( T_H = \frac{T_C}{1 – \eta} = \frac{250}{0.6} \taxminan 416.67\,K \)

18. Agar Carnot issiqlik nasosi 270K va 370K oralig'ida ishlayotgan bo'lsa, COP ni toping.
Yechim: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{370}{100} = 3.7 \)

15. 75% samaradorlikka va 800 K ga teng bo'lgan Carnot dvigateli uchun ni aniqlang.
Yechim: \( T_C = T_H \marta (1 – \eta) = 800 \marta 0.25 = 200\,K \)

16. \( 700\,K \) va \( 300\,K \) oralig'ida ishlaydigan Carnot dvigatelining samarali ish faoliyatini hisoblang.
Yechim: \( \eta = 1 – \frac{300}{700} \taxminan 0.571 = 57.1\% \)

17. Carnot sovutgichining mоslama qiymatini toping, bunda mоslama qiymati ...
Yechim: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{250}{100} = 2.5 \)

18. Carnot dvigateli 10% samaradorlikka va 150% samaradorlikka ega. (T_C = 200 K) ni toping.
Yechim: \( T_H = \frac{T_C}{1 – \eta} = \frac{150}{0.9} \taxminan 166.67\,K \)

19. Agar Carnot issiqlik nasosi 200K va 400K oralig'ida ishlayotgan bo'lsa, COP ni toping.
Yechim: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{400}{200} = 2 \)

20. 80% samaradorlikka va 1000 K ga teng bo'lgan Carnot dvigateli uchun ni aniqlang.
Yechim: \( T_C = T_H \marta (1 – \eta) = 1000 \marta 0.2 = 200\,K \)