30 mau mīkini wela (ka hoʻohana ʻana i ke kānāwai ʻelua o ka thermodynamics) - nā pilikia a me nā hoʻonā
1. Hoʻokomo wela Q H = 3000 Joules a me ka hoʻopuka wela Q L = 1000 Joules. He aha ka pono o ka ʻenekini wela?
ʻIke ʻia:
Ka hoʻokomo wela (Q H ) = 3000 Joules
Ka hoʻopuka wela (Q L ) = 1000 Joules
Hana i hana ʻia e ka ʻenekini (W) = 3000 – 1000 = 2000 Joules
Makemake ʻia: Ka pono o ka mīkini wela (e)
Lōlā:
2. Hoʻopuka kahi ʻenekini wela i 2000 Joules o ka hana mechanical a hoʻokuʻu ka ʻenekini i ka wela i ke kaiapuni ma ka wikiwiki o 500 Joules. He aha ka pono o ka ʻenekini wela?
ʻIke ʻia:
Hana ʻia ka hana e ka ʻenekini (W) = 2000 Joules
Ka hoʻopuka wela (Q L ) = 5000 Joules
Ka hoʻokomo wela (Q H ) = 2000 + 5000 = 7000 Joules
Makemake ʻia: Ka pono (e)
Lōlā:
3. He 30% ka pono o kahi ʻenekini wela. Inā hana ka ʻenekini i 10,000 Joules o ka hana mechanical, ehia ka nui o ka wela i hoʻokuʻu ʻia ma ke ʻano he wela ʻōpala mai kēia ʻenekini?
ʻIke ʻia:
Ka pono (e) = 30% = 30/100 = 0.3
Hana ʻia ka hana e ka ʻenekini (W) = 3,000 Joules
Makemake ʻia : Ka hoʻopuka wela (Q L )
Lōlā:
Ka hoʻopuka wela (Q L ) = ka hoʻokomo wela (Q H ) - hana ʻia ka hana e ka ʻenekini (W)
Q L = 10,000 Joules – 3,000 Joules
QL = 7,000 Joule
4. E hoʻoholo i ka pono o kahi ʻenekini Carnot e hana ana ma waena o ʻelua mau waihona wai ma nā mahana o 500 K a me 300 K.
Hoʻonā: Ma ka hoʻohana ʻana i ke ʻano hana pono o Carnot, \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}}\), loaʻa iā mākou \(\eta = 1 – \frac{300}{500} = 0.4\) a i ʻole \(40\%\).
5. Hoʻopili kahi ʻenekini wela i 2000 J o ka wela mai kahi waihona wela a hoʻokuke aku i 1200 J i kahi waihona anu. E helu i ka hana i hana ʻia e ka ʻenekini.
Hoʻonā: Ma ka hoʻohana ʻana i ke kānāwai mua o ka thermodynamics, \(Q_{\text{hot}} = W + Q_{\text{cold}}\), ʻo ka hana i hana ʻia ʻo \(W = 2000 – 1200 = 800\ \text{J}\).
6. E helu i ka pono o kahi ʻenekini wela e omo ana i 1000 J mai kahi waihona wai wela a hana i 600 J o ka hana.
Hoʻonā: \(\eta = \frac{W}{Q_{\text{hot}}} = \frac{600}{1000} = 0.6\) a i ʻole \(60\%\).
7. Hana kahi ʻenekini wela ma waena o 400 K a me 200 K. E hoʻoholo i ka pono kūpono loa.
Hoʻonā: \(\eta_{\text{max}} = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{200}{400} = 0.5\) a i ʻole \(50\%\).
8. Hoʻolei kekahi ʻenekini wela i 300 J i ka waihona anu ʻoiai e hana ana i 200 J o ka hana. E helu i ka wela i omo ʻia mai ka waihona wela.
Hoʻonā: \(Q_{\text{wela}} = W + Q_{\text{anuanu}} = 200 + 300 = 500\ \text{J}\).
9. E hoʻoholo i ka pono o kahi pōʻaiapuni Otto me ka lakio compression o 8.
Hoʻonā: \(\eta = 1 – \frac{1}{r^{(\gamma – 1)}} = 1 – \frac{1}{8^{(1.4 – 1)}} \approx 0.564\) a i ʻole \(56.4\%\), kahi ʻo \(\gamma\) ka lakio o ka hiki ke wela.
10. Hana kahi ʻenekini wela i 150 J o ka hana a hōʻole i 100 J i ka waihona anu. E ʻimi i ka wela i omo ʻia mai ka waihona wela.
Hoʻonā: \(Q_{\text{wela}} = W + Q_{\text{anuanu}} = 150 + 100 = 250\ \text{J}\).
11. E hoʻoholo i ka pono o kahi ʻenekini Diesel me ka lakio compression o 18 a me ka lakio cutoff o 2.
Hoʻonā: \(\eta = 1 – \frac{1}{r^{(\gamma – 1)}} \left( \frac{r_c – 1}{r_c} \right) \approx 0.627\) a i ʻole \(62.7\%\), kahi ʻo \(r\) ka lakio compression, ʻo \(r_c\) ka lakio cutoff, a ʻo \(\gamma\) ka lakio hiki ke wela.
12. E helu i ka hana i hana ʻia e kahi ʻenekini wela e omo ana i 400 J a he 50% ka pono.
Hoʻonā: \(W = \eta \cdot Q_{\text{hot}} = 0.5 \cdot 400 = 200\ \text{J}\).
13. Hana kahi ʻenekini wela ma waena o 600 K a me 300 K. E huli i ka pono o Carnot.
Hoʻonā: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{300}{600} = 0.5\) a i ʻole \(50\%\).
14. Hoʻopili kahi ʻenekini wela i 3000 J a hōʻole i 1800 J i ka waihona anu. E helu i ka hana i hana ʻia.
Hoʻonā: \(W = Q_{\text{wela}} – Q_{\text{anuanu}} = 3000 – 1800 = 1200\ \text{J}\).
15. E hoʻoholo i ka pono o kahi ʻenekini Stirling e hana ana ma waena o nā waihona wai ʻelua ma 800 K a me 400 K.
Hoʻonā: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{400}{800} = 0.5\) a i ʻole \(50\%\).
16. Hoʻolei kekahi ʻenekini wela i 500 J i ka waihona anu ʻoiai e hana ana i 300 J o ka hana. E helu i ka wela i omo ʻia mai ka waihona wela.
Hoʻonā: \(Q_{\text{wela}} = W + Q_{\text{anuanu}} = 300 + 500 = 800\ \text{J}\).
17. E hoʻoholo i ka pono o kahi paikikala Ericsson me nā waihona wela a me ke anu ma 1000 K a me 250 K.
Hoʻonā: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{250}{1000} = 0.75\) a i ʻole \(75\%\).
18. Hana kahi ʻenekini wela i 700 J o ka hana a he 70% ka pono o ka hana. E helu i ka wela i hōʻole ʻia i ka waihona anu.
Hoʻonā: \(Q_{\text{anuanu}} = \frac{W}{\eta} – W = \frac{700}{0.7} – 700 \approx 1000 – 700 = 300\ \text{J}\).
19. E hoʻoholo i ka pono o kahi pōʻaiapuni Brayton me nā lakio kaomi o 6.5 a me \(\gamma = 1.4\).
Hoʻonā: \(\eta = 1 – \frac{1}{r_p^{(\gamma – 1)/\gamma}} \approx 0.433\) a i ʻole \(43.3\%\), kahi ʻo \(r_p\) ka lakio kaomi.
20. E helu i ka hana i hana ʻia e kahi ʻenekini wela e omo ana i 250 J a hōʻole i 100 J i ka waihona anu.
Hoʻonā: \(W = Q_{\text{wela}} – Q_{\text{anuanu}} = 250 – 100 = 150\ \text{J}\).
21. Hana kahi ʻenekini wela ma waena o 450 K a me 150 K. E huli i ka pono o Carnot.
Hoʻonā: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{150}{450} \approx 0.667\) a i ʻole \(66.7\%\).
22. E hoʻoholo i ka pono o kahi pōʻaiapuni Atkinson me ka lakio compression o 10.
Hoʻonā: \(\eta = 1 – \frac{1}{r^{(\gamma – 1)}} \approx 0.593\) a i ʻole \(59.3\%\),
kahi ʻo \(r\) ka lakio compression a ʻo \(\gamma\) ka lakio hiki ke wela.
20. Hoʻopili kahi ʻenekini wela i 180 J a he 40% ka pono o ka hana. E helu i ka hana i hana ʻia.
Hoʻonā: \(W = \eta \cdot Q_{\text{hot}} = 0.4 \cdot 180 = 72\ \text{J}\).
Nānā: No nā pilikia e pili ana i nā pōʻaiapuni wela kikoʻī (e like me Otto, Diesel, a pēlā aku), ua hoʻohana ʻia kekahi mau waiwai e like me ka lakio hiki ke wela \(\gamma\), he mea maʻamau no kekahi mau kinoea (e laʻa, \(\gamma = 1.4\) no ka ea). Hiki ke ʻokoʻa kēia mau waiwai ma muli o nā mea kikoʻī i hoʻohana ʻia i loko o ka ʻenekini.
