25 Injini yeCarnot (kushandiswa kwemutemo wechipiri wethermodynamics) - matambudziko nemhinduro
1. Injini inoshanda pakati pe1200 Kelvin ne300 Kelvin. Injini iyi inoshanda sei?
Zvinozivikanwa:
Kupisa kwakanyanya (TH ) = 1200 K
Tembiricha yakaderera (T L ) = 300 K
Zvinodiwa: Kushanda zvakanaka (e)
Solution:
2. Injini inoshanda pakati pe727 o C ne127 o C. Kupisa kweinjini i6000 Joules. Injini inoshanda sei uye basa rinoitwa neinjini painotenderera yega yega?
Zvinozivikanwa:
Kupisa kwakanyanya (TH ) = 727 o C + 273 = 1000 K
Tembiricha yakaderera (T L ) = 127 o C + 273 = 400 K
Kupinza kupisa (Q H ) = 6000 Joules
Zvinodiwa: Kushanda zvakanaka (e) uye basa rinoitwa neinjini (W)
Solution:
Kushanda zvakanaka kweinjini yeCarnot :
Basa rinoitwa neinjini yeCarnot:
W = e Q H
W = (0.6)(6000)
W = 3600 Joule
3. Injini inoshanda pakati pe527 o C ne127 o C. Kupisa kweinjini i10,000 Joules. Kupisa kwakadini kunoburitswa sekupisa kwemarara kubva muinjini iyi?
Zvinozivikanwa:
Kupisa kwakanyanya (TH ) = 527 o C + 273 = 800 K
Tembiricha yakaderera (T L ) = 127 o C + 273 = 400 K
Kupinza kupisa (Q H ) = 10,000 Joules
Zvinodiwa: Kupisa kunobuda (Q L )
Solution:
Kushanda zvakanaka kweinjini yeCarnot:
Basa rinoitwa neinjini yeCarnot:
W = e Mubvunzo 1
W = (0.5)(10.000)
W = 5000 Joule
Kupisa kunobuda (Q L ) = Kupisa kunoiswa (Q H ) – Basa (W)
Q L = Q H – W
Q L = 10,000 – 5,000
Q L = 5000 Joule
4. Chii chinoshanda zvakanaka uye basa rinoitwa neinjini zvichienderana nedhayagiramu iri pazasi?
Zvinozivikanwa:
Kupisa kwakanyanya (TH ) = 800 K
Tembiricha yakaderera (T L ) = 300 K
Kupinza kupisa (Q H ) = 1000 Joules
Zvinodiwa: Kushanda zvakanaka (e) uye basa (W) rinoitwa neinjini
Solution:
Kushanda zvakanaka kweinjini yeCarnot:
Basa rinoitwa neinjini yeCarnot:
W = e Q H
W = (0.625)(1000)
W = 625 Joule
5. Kana injini yeCarnot ichishanda pakati pe500,K) ne300,K), verenga mashandiro ayo.
Mhinduro: \( \eta = 1 – \frac{T_C}{T_H} = 1 – \frac{300}{500} = 0.4 = 40\% \)
6. Tsvaga mashandiro anoita firiji yeCarnot iri pakati pe 300,K ne 250,K.
Mhinduro: \( \eta = \frac{T_C}{T_H – T_C} = \frac{250}{50} = 5 = 500\% \)
7. Kushanda zvakanaka kweinjini yeCarnot kuri \( 30\% \). Kana \( T_C = 300\,K \), tsvaga \( T_H \).
Mhinduro: \( T_H = \frac{T_C}{1 – \eta} = \frac{300}{0.7} \approx 428.57\,K \)
8. Kana pombi yekupisa yeCarnot ichishanda pakati pe \(270\,K \) uye \(330\,K \), tsvaga coefficient of performance (COP).
Mhinduro: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{330}{60} = 5.5 \)
9. Sarudza \( T_C \) injini yeCarnot ine \( 50\% \) kushanda zvakanaka uye \( T_H = 400\,K \).
Mhinduro: \( T_C = T_H \nguva (1 – \eta) = 400 \nguva 0.5 = 200\,K \)
10. Verenga kushanda zvakanaka kweinjini yeCarnot inoshanda pakati pe \(373\,K \) uye \(273\,K \).
Mhinduro: \( \eta = 1 – \frac{273}{373} \inenge 0.268 = 26.8\% \)
11. Tsvaga COP yefiriji yeCarnot ine \( T_C = 260\,K \) uye \( T_H = 300\,K \).
Mhinduro: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{260}{40} = 6.5 \)
12. Injini yeCarnot ine \(25\% \) kushanda zvakanaka uye \( T_C = 200\,K \). Tsvaga \( T_H \).
Mhinduro: \( T_H = \frac{T_C}{1 – \eta} = \frac{200}{0.75} \approx 266.67\,K \)
13. Kana pombi yekupisa yeCarnot ichishanda pakati pe 220,K ne 320,K, tsvaga COP.
Mhinduro: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{320}{100} = 3.2 \)
14. Sarudza \( T_C \) injini yeCarnot ine \( 60\% \) kushanda zvakanaka uye \( T_H = 500\,K \).
Mhinduro: \( T_C = T_H \nguva (1 – \eta) = 500 \nguva 0.4 = 200\,K \)
15. Verenga kushanda zvakanaka kweinjini yeCarnot inoshanda pakati pe \(600\,K \) uye \(400\,K \).
Mhinduro: \( \eta = 1 – \frac{400}{600} \inenge 0.333 = 33.3\% \)
16. Tsvaga COP yefiriji yeCarnot ine \( T_C = 280\,K \) uye \( T_H = 330\,K \).
Mhinduro: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{280}{50} = 5.6 \)
17. Injini yeCarnot ine \(40\% \) kushanda zvakanaka uye \( T_C = 250\,K \). Tsvaga \( T_H \).
Mhinduro: \( T_H = \frac{T_C}{1 – \eta} = \frac{250}{0.6} \approx 416.67\,K \)
18. Kana pombi yekupisa yeCarnot ichishanda pakati pe 270,K ne 370,K, tsvaga COP.
Mhinduro: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{370}{100} = 3.7 \)
15. Sarudza \( T_C \) injini yeCarnot ine \( 75\% \) kushanda zvakanaka uye \( T_H = 800\,K \).
Mhinduro: \( T_C = T_H \nguva (1 – \eta) = 800 \nguva 0.25 = 200\,K \)
16. Verenga kushanda zvakanaka kweinjini yeCarnot inoshanda pakati pe \(700\,K \) uye \(300\,K \).
Mhinduro: \( \eta = 1 – \frac{300}{700} \inenge 0.571 = 57.1\% \)
17. Tsvaga COP yefiriji yeCarnot ine \( T_C = 250\,K \) uye \( T_H = 350\,K \).
Mhinduro: \( \text{COP} = \frac{T_C}{T_H – T_C} = \frac{250}{100} = 2.5 \)
18. Injini yeCarnot ine \(10\% \) kushanda zvakanaka uye \( T_C = 150\,K \). Tsvaga \( T_H \).
Mhinduro: \( T_H = \frac{T_C}{1 – \eta} = \frac{150}{0.9} \approx 166.67\,K \)
19. Kana pombi yekupisa yeCarnot ichishanda pakati pe 200,K ne 400,K, tsvaga COP.
Mhinduro: \( \text{COP} = \frac{T_H}{T_H – T_C} = \frac{400}{200} = 2 \)
20. Sarudza \( T_C \) injini yeCarnot ine \( 80\% \) kushanda zvakanaka uye \( T_H = 1000\,K \).
Mhinduro: \( T_C = T_H \nguva (1 – \eta) = 1000 \nguva 0.2 = 200\,K \)
