30 Injini dzinopisa (kushandiswa kwemutemo wechipiri wethermodynamics) - matambudziko nemhinduro
1. Kupisa kweQH = 3000 Joules uye kupisa kunobuda QL = 1000 Joules. Chii chinoshanda zvakanaka che injini yekupisa?
Zvinozivikanwa:
Heat chinhu chinopinzwa (Q)H) = 3000 Joule
Kupisa kunobuda (Q)L) = 1000 Joule
basa zvinoitwa neinjini (W) = 3000 – 1000 = 2000 Joules
Kuda: Kushanda zvakanaka kweinjini yekupisa (e)
Solution:
2. Injini yekupisa inogadzira maJoules maviri ebasa remakanika uye injini inoburitsa kupisa kunzvimbo yakapoteredza nechiyero cheMajoules mazana mashanu. Injini yekupisa inoshanda sei?
Zvinozivikanwa:
Basa rinoitwa neinjini (W) = 2000 Joules
Kupisa kunobuda (Q)L) = 5000 Joule
Kupinza kupisa (Q)H) = 2000 + 5000 = 7000 Joule
Kuda: Kushanda zvakanaka (e)
Solution:
3. Injini yekupisa ine simba re30%. Kana injini ikagadzira maJoules zviuru gumi ebasa remakanika, kupisa kwakadini kunoburitswa sekupisa kwemarara kubva muinjini iyi?
Zvinozivikanwa:
Kushanda zvakanaka (e) = 30% = 30/100 = 0.3
Basa rinoitwa neinjini (W) = 3,000 Joules
Wanted : Kupisa kunobuda (Q)L)
Solution:
Kupisa kunobuda (Q)L) = kupisa (Q)H) – basa rinoitwa neinjini (W)
QL = MaJoules 10,000 – MaJoules 3,000
QL = 7,000 Joule
4. Kuziva kushanda zvakanaka kweinjini yeCarnot inoshanda pakati pematangi maviri patembiricha ye500 K ne300 K.
Mhinduro: Tichishandisa fomura yekushanda zvakanaka kweCarnot, \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}}\), tinowana \(\eta = 1 – \frac{300}{500} = 0.4\) kana \(40\%\).
5. Injini yekupisa inotora 2000 J yekupisa kubva mudura rinopisa uye inoburitsa 1200 J mudura rinotonhora. Verenga basa rinoitwa neinjini.
Mhinduro: Uchishandisa mutemo wekutanga wethermodynamics, \(Q_{\text{hot}} = W + Q_{\text{cold}}\), basa raitwa ndiro \(W = 2000 – 1200 = 800\ \text{J}\).
6. Verenga kushanda zvakanaka kweinjini yekupisa inotora 1000 J kubva mudura rinopisa uye inoita 600 J yebasa.
Mhinduro: \(\eta = \frac{W}{Q_{\text{hot}}} = \frac{600}{1000} = 0.6\) kana \(60\%\).
7. Injini yekupisa inoshanda pakati pe400 K ne200 K. Sarudza kushanda kwakanyanya kunogoneka.
Mhinduro: \(\eta_{\text{max}} = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{200}{400} = 0.5\) kana \(50\%\).
8. Injini yekupisa inoramba 300 J kuenda kudhamu rinotonhora uku ichiita 200 J yebasa. Verenga kupisa kunotorwa kubva mudhamu rinopisa.
Mhinduro: \(Q_{\text{hot}} = W + Q_{\text{cold}} = 200 + 300 = 500\ \text{J}\).
9. Tsvaga kushanda zvakanaka kweOtto cycle ine chiyero chekudzvanywa kwe8.
Mhinduro: \(\eta = 1 – \frac{1}{r^{(\gamma – 1)}} = 1 – \frac{1}{8^{(1.4 – 1)}} \inenge 0.564\) kana \(56.4\%\), apo \(\gamma\) iri chiyero chekupisa.
10. Injini yekupisa inoita basa re 150 J uye inoramba 100 J mudura rinotonhora. Tsvaga kupisa kunotorwa kubva mudura rinopisa.
Mhinduro: \(Q_{\text{hot}} = W + Q_{\text{cold}} = 150 + 100 = 250\ \text{J}\).
11. Sarudza kushanda zvakanaka kweinjini yedhiziri ine chiyero chekudzvanywa kwe18 uye chiyero che cutoff che2.
Mhinduro: \(\eta = 1 – \frac{1}{r^{(\gamma – 1)}} \left( \frac{r_c – 1}{r_c} \right) \approx 0.627\) kana \(62.7\%\), apo \(r\) iri chiyero chekumanikidzwa, \(r_c\) iri chiyero che cutoff, uye \(\gamma\) iri chiyero chekukwanisa kupisa.
12. Verenga basa rinoitwa neinjini yekupisa inotora 400 J uye ine simba re50%.
Mhinduro: \(W = \eta \cdot Q_{\text{hot}} = 0.5 \cdot 400 = 200\ \text{J}\).
13. Injini yekupisa inoshanda pakati pe600 K ne300 K. Tsvaga kushanda zvakanaka kweCarnot.
Mhinduro: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{300}{600} = 0.5\) kana \(50\%\).
14. Injini yekupisa inotora 3000 J yoramba 1800 J mudura rinotonhora. Verenga basa raitwa.
Mhinduro: \(W = Q_{\text{hot}} – Q_{\text{cold}} = 3000 – 1800 = 1200\ \text{J}\).
15. Tsvaga kuti injini yeStirling inoshanda zvakanaka here pakati pematangi maviri emvura pa800 K ne400 K.
Mhinduro: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{400}{800} = 0.5\) kana \(50\%\).
16. Injini yekupisa inoramba 500 J kuenda kudhamu rinotonhora uku ichiita 300 J yebasa. Verenga kupisa kunotorwa kubva mudhamu rinopisa.
Mhinduro: \(Q_{\text{hot}} = W + Q_{\text{cold}} = 300 + 500 = 800\ \text{J}\).
17. Sarudza kushanda zvakanaka kweEricsson cycle ine matangi anopisa neanopisa pa1000 K ne250 K.
Mhinduro: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{250}{1000} = 0.75\) kana \(75\%\).
18. Injini yekupisa inoita basa re700 J uye inoshanda zvakanaka ne70%. Verenga kupisa kwakarambwa kusvika kunzvimbo inotonhora.
Mhinduro: \(Q_{\text{cold}} = \frac{W}{\eta} – W = \frac{700}{0.7} – 700 \approx 1000 – 700 = 300\ \text{J}\).
19. Sarudza kushanda zvakanaka kweBrayton cycle ne pressure ratios ye6.5 uye \(\gamma = 1.4\).
Mhinduro: \(\eta = 1 – \frac{1}{r_p^{(\gamma – 1)/\gamma}} \approx 0.433\) kana \(43.3\%\), apo \(r_p\) iri chiyero chekumanikidzwa.
20. Verenga basa rinoitwa neinjini yekupisa inotora 250 J yoramba 100 J mudura rinotonhora.
Mhinduro: \(W = Q_{\text{hot}} – Q_{\text{cold}} = 250 – 100 = 150\ \text{J}\).
21. Injini yekupisa inoshanda pakati pe450 K ne150 K. Tsvaga kushanda zvakanaka kweCarnot.
Mhinduro: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{150}{450} \inenge 0.667\) kana \(66.7\%\).
22. Sarudza kushanda zvakanaka kweAtkinson cycle ine chiyero chekudzvanywa kwe10.
Mhinduro: \(\eta = 1 – \frac{1}{r^{(\gamma – 1)}} \inenge 0.593\) kana \(59.3\%\),
apo \(r\) iri chiyero chekumanikidzwa uye \(\gamma\) iri chiyero chekukwanisa kupisa.
20. Injini yekupisa inotora 180 J uye ine simba re40%. Verenga basa raitwa.
Mhinduro: \(W = \eta \cdot Q_{\text{hot}} = 0.4 \cdot 180 = 72\ \text{J}\).
Cherechedza: Pamatambudziko ane chekuita nekupisa kwakati (senge Otto, Diesel, nezvimwewo), mamwe mavalue akadai se heat capacity ratio \(\gamma\) akashandiswa, ayo anowanzo shandiswa kune mamwe magasi (semuenzaniso, \(\gamma = 1.4\) yemhepo). Mavalue aya anogona kusiyana zvichienderana nezvinhu zvakati zvinoshandiswa muinjini.
