30 Matoorada kulaylka (isticmaalka sharciga labaad ee thermodynamics) - dhibaatooyinka iyo xalalka
1. Kuleylka la geliyo Q H = 3000 Joules iyo wax soo saarka kulaylka Q L = 1000 Joules. Waa maxay waxtarka matoorka kulaylka?
La yaqaan:
Kuleylka la geliyo (Q H ) = 3000 Joules
Soo saarista kulaylka (QL ) = 1000 Joules
Shaqada uu sameeyo matoorku (W) = 3000 – 1000 = 2000 Joules
La Doonayo: Hufnaanta matoorka kulaylka (e)
Xalka:
2. Matoorka kuleylku wuxuu soo saaraa 2000 Joules oo shaqo farsamo ah, matoorkuna wuxuu kulaylka u daayaa deegaanka heer dhan 500 Joules. Waa maxay waxtarka matoorka kuleylku?
La yaqaan:
Shaqada waxaa qabta matoorka (W) = 2000 Joules
Soo saarista kulaylka (QL ) = 5000 Joules
Kuleylka la geliyo (QH ) = 2000 + 5000 = 7000 Joules
La Doonayo: Waxtar (e)
Xalka:
3. Matoorka kuleylku wuxuu leeyahay hufnaan dhan 30%. Haddii matoorku soo saaro 10,000 oo Joule oo shaqo farsamo ah, intee le'eg ayaa kuleyl qashin ah laga saaraa matoorkan?
La yaqaan:
Hufnaan (e) = 30% = 30/100 = 0.3
Shaqada waxaa lagu sameeyaa matoor (W) = 3,000 Joules
La Doonayo : Wax soo saarka kulaylka (Q L )
Xalka:
Wax soo saarka kulaylka (QL ) = gelinta kulaylka (QH ) - shaqada waxaa qabta matoorka (W)
Q L = 10,000 Joules - 3,000 Joules
Q L = 7,000 Joule
4. Go'aami waxtarka matoorka Carnot ee ka shaqeeya laba kayd oo heerkulkoodu yahay 500 K iyo 300 K.
Xalka: Adigoo isticmaalaya qaacidada waxtarka Carnot, \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}}\), waxaan helnaa \(\eta = 1 – \frac{300}{500} = 0.4\) ama \(40\%\).
5. Matoorka kuleylku wuxuu nuugaa 2000 J oo kuleyl ah oo ka yimaada kayd kulul wuxuuna 1200 J u saaraa kayd qabow. Xisaabi shaqada uu matoorku qabtay.
Xalka: Iyada oo la adeegsanayo sharciga ugu horreeya ee thermodynamics, \(Q_{\text{hot}} = W + Q_{\text{cold}}\), shaqada la qabtay waa \(W = 2000 – 1200 = 800\ \text{J}\).
6. Xisaabi waxtarka matoorka kulaylka ee nuuga 1000 J kaydka kulul oo qabta 600 J oo shaqo ah.
Xalka: \(\eta = \frac{W}{Q_{\text{hot}}} = \frac{600}{1000} = 0.6\) ama \(60\%\).
7. Matoorka kuleylku wuxuu shaqeeyaa inta u dhaxaysa 400 K iyo 200 K. Go'aami waxtarka ugu badan ee suurtogalka ah.
Xalka: \(\eta_{\text{max}} = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{200}{400} = 0.5\) ama \(50\%\).
8. Matoorka kuleylku wuxuu diidaa 300 J kaydka qabow isagoo qabanaya 200 J oo shaqo ah. Xisaabi kulaylka ka soo nuugaya kaydka kulul.
Xalka: \(Q_{\text{hot}} = W + Q_{\text{cold}} = 200 + 300 = 500\ \text{J}\).
9. Go'aami waxtarka wareegga Otto oo leh saamiga cadaadiska oo ah 8.
Xalka: \(\eta = 1 – \frac{1}{r^{(\gamma – 1)}} = 1 – \frac{1}{8^{(1.4 – 1)}} \approx 0.564\) ama \(56.4\%\), halkaas oo \(\gamma\) uu yahay saamiga awoodda kulaylka.
10. Matoorka kuleylku wuxuu qabtaa 150 J oo shaqo ah wuxuuna 100 J u diidaa kaydka qabow. Soo hel kulaylka ka soo nuugaya kaydka kulul.
Xalka: \(Q_{\text{hot}} = W + Q_{\text{cold}} = 150 + 100 = 250\ \text{J}\).
11. Go'aami waxtarka matoorka naaftada oo leh saamiga cadaadiska oo ah 18 iyo saamiga goynta oo ah 2.
Xalka: \(\eta = 1 – \frac{1}{r^{(\gamma – 1)}} \left( \frac{r_c – 1}{r_c} \right) \approx 0.627\) ama \(62.7\%\), halkaas oo \(r\) uu yahay saamiga cadaadiska, \(r_c\) uu yahay saamiga goynta, iyo \(\gamma\) uu yahay saamiga awoodda kulaylka.
12. Xisaabi shaqada uu qabto matoorka kulaylka kaas oo nuuga 400 J isla markaana leh hufnaan dhan 50%.
Xalka: \(W = \eta \cdot Q_{\text{hot}} = 0.5 \cdot 400 = 200\ \text{J}\).
13. Matoorka kuleylku wuxuu shaqeeyaa inta u dhaxaysa 600 K iyo 300 K. Soo hel waxtarka Carnot.
Xalka: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{300}{600} = 0.5\) ama \(50\%\).
14. Matoorka kuleylku wuxuu nuugaa 3000 J wuxuuna 1800 J u diidaa kaydka qabow. Xisaabi shaqada la qabtay.
Xalka: \(W = Q_{\text{hot}} – Q_{\text{cold}} = 3000 – 1800 = 1200\ \text{J}\).
15. Go'aami hufnaanta matoorka Stirling ee ka shaqeeya laba kayd oo leh 800 K iyo 400 K.
Xalka: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{400}{800} = 0.5\) ama \(50\%\).
16. Matoorka kuleylku wuxuu diidaa 500 J kaydka qabow isagoo qabanaya 300 J oo shaqo ah. Xisaabi kulaylka ka soo nuugaya kaydka kulul.
Xalka: \(Q_{\text{hot}} = W + Q_{\text{cold}} = 300 + 500 = 800\ \text{J}\).
17. Go'aami waxtarka wareegga Ericsson oo leh kayd biyood kulul iyo qabow oo ah 1000 K iyo 250 K.
Xalka: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{250}{1000} = 0.75\) ama \(75\%\).
18. Matoorka kuleylku wuxuu qabtaa 700 J oo shaqo ah wuxuuna leeyahay hufnaan dhan 70%. Xisaabi kulaylka loo diiday kaydka qabow.
Xalka: \(Q_{\text{cold}} = \frac{W}{\eta} – W = \frac{700}{0.7} – 700 \qiyaastii 1000 – 700 = 300\ \text{J}\).
19. Go'aami waxtarka wareegga Brayton oo leh saamiga cadaadiska ee 6.5 iyo \(\gamma = 1.4\).
Xalka: \(\eta = 1 – \frac{1}{r_p^{(\gamma – 1)/\gamma}} \approx 0.433\) ama \(43.3\%\), halkaasoo \(r_p\) uu yahay saamiga cadaadiska.
20. Xisaabi shaqada uu qabtay matoorka kulaylka kaas oo nuugaya 250 J isla markaana 100 J u diidaya kaydka qabow.
Xalka: \(W = Q_{\text{hot}} – Q_{\text{cold}} = 250 – 100 = 150\ \text{J}\).
21. Matoorka kuleylku wuxuu shaqeeyaa inta u dhaxaysa 450 K iyo 150 K. Soo hel waxtarka Carnot.
Xalka: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{150}{450} \approx 0.667\) ama \(66.7\%\).
22. Go'aami waxtarka wareegga Atkinson oo leh saamiga cadaadiska oo ah 10.
Xalka: \(\eta = 1 – \frac{1}{r^{(\gamma – 1)}} \qiyaastii 0.593\) ama \(59.3\%\),
halkaas oo \(r\) uu yahay saamiga cadaadiska iyo \(\gamma\) uu yahay saamiga awoodda kulaylka.
20. Matoorka kuleylku wuxuu nuugaa 180 J wuxuuna leeyahay hufnaan dhan 40%. Xisaabi shaqada la qabtay.
Xalka: \(W = \eta \cdot Q_{\text{hot}} = 0.4 \cdot 180 = 72\ \text{J}\).
Fiiro gaar ah: Dhibaatooyinka ku lug leh wareegyada kulaylka gaarka ah (sida Otto, Diesel, iwm.), qiimayaal gaar ah sida saamiga awoodda kulaylka \(\gamma\) ayaa la isticmaalay, kuwaas oo caadi u ah gaasaska qaarkood (tusaale ahaan, \(\gamma = 1.4\) hawada). Qiimayaashani way kala duwanaan karaan iyadoo ku xiran walxaha gaarka ah ee loo isticmaalo matoorka.
