30 Injinan zafi (amfani da dokar thermodynamics ta biyu) - matsaloli da mafita
1. Shigar da zafi Q H = Joules 3000 da fitowar zafi Q L = Joules 1000. Menene ingancin injin zafi?
An sani:
Shigar da zafi (Q H ) = Joules 3000
Fitar da zafi (Q L ) = Joules 1000
Aikin da injin ya yi (W) = 3000 – 1000 = Joules 2000
Ana so: Ingancin injin zafi (e)
Magani:
2. Injin zafi yana samar da joules 2000 na aikin injiniya kuma injin yana fitar da zafi zuwa muhalli akan saurin joules 500. Menene ingancin injin zafi?
An sani:
Injin (W) = Joules 2000 ne ke yin aikin.
Fitar da zafi (Q L ) = Joules 5000
Shigar da zafi (QH ) = 2000 + 5000 = Joules 7000
Ana so: Inganci (e)
Magani:
3. Injin zafi yana da inganci na 30%. Idan injin yana samar da joules 10,000 na aikin injiniya, nawa ne zafi ake fitarwa a matsayin zafi na sharar gida daga wannan injin?
An sani:
Inganci (e) = 30% = 30/100 = 0.3
Ana yin aikin ta hanyar injin (W) = Joules 3,000
Ana so : Fitar da zafi ( QL )
Magani:
Fitowar zafi (Q L ) = shigar da zafi (Q H ) - injin (W) ne ke yin aikin
Q L = Joules 10,000 - Joules 3,000
QL = Joule 7,000
4. Kayyade ingancin injin Carnot da ke aiki tsakanin ma'ajiyar ruwa guda biyu a yanayin zafi na 500 K da 300 K.
Magani: Ta amfani da dabarar ingancin Carnot, \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}}\), mun sami \(\eta = 1 – \frac{300}{500} = 0.4\) ko \(40\%\).
5. Injin zafi yana shan zafi 2000 J daga wani wurin adana zafi sannan ya fitar da 1200 J zuwa wurin adana sanyi. A lissafta aikin da injin ya yi.
Magani: Ta amfani da dokar thermodynamics ta farko, \(Q_{\text{hot}} = W + Q_{\text{cold}}\), aikin da aka yi shine \(W = 2000 – 1200 = 800\ \text{J}\).
6. Lissafa ingancin injin zafi wanda ke shan 1000 J daga wurin ajiyar zafi kuma yana yin aikin 600 J.
Magani: \(\eta = \frac{W}{Q_{\text{hot}}} = \frac{600}{1000} = 0.6\) ko \(60\%\).
7. Injin zafi yana aiki tsakanin 400 K da 200 K. Kayyade matsakaicin ƙarfin aiki.
Magani: \(\eta_{\text{max}} = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{200}{400} = 0.5\) ko \(50\%\).
8. Injin zafi yana hana 300 J zuwa wurin ajiyar ruwan sanyi yayin da yake yin aikin J 200. A lissafta zafin da ke sha daga wurin ajiyar ruwan zafi.
Magani: \(Q_{\text{hot}} = W + Q_{\text{cold}} = 200 + 300 = 500\ \text{J}\).
9. Kayyade ingancin zagayowar Otto tare da rabon matsi na 8.
Magani: \(\eta = 1 – \frac{1}{r^{(\gamma – 1)}} = 1 – \frac{1}{8^{(1.4 – 1)}} \approx 0.564\) ko \(56.4\%\), inda \(\gamma\) shine rabon ƙarfin zafi.
10. Injin zafi yana yin aiki 150 J kuma yana ƙin 100 J zuwa wurin ajiyar ruwan sanyi. Nemo zafin da ke sha daga wurin ajiyar ruwan zafi.
Magani: \(Q_{\text{hot}} = W + Q_{\text{cold}} = 150 + 100 = 250\ \text{J}\).
11. Kayyade ingancin injin dizal mai rabon matsi na 18 da rabon yankewa na 2.
Magani: \(\eta = 1 – \frac{1}{r^{(\gamma – 1)}} \left( \frac{r_c – 1}{r_c} \right) \approx 0.627\) ko \(62.7\%\), inda \(r\) shine rabon matsi, \(r_c\) shine rabon yankewa, kuma \(\gamma\) shine rabon ƙarfin zafi.
12. Lissafa aikin da injin zafi ke yi wanda ke shan 400 J kuma yana da inganci na 50%.
Magani: \(W = \eta \cdot Q_{\text{hot}} = 0.5 \cdot 400 = 200\ \text{J}\).
13. Injin zafi yana aiki tsakanin 600 K da 300 K. Nemo ingancin Carnot.
Magani: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{300}{600} = 0.5\) ko \(50\%\).
14. Injin zafi yana shan 3000 J kuma yana ƙin 1800 J zuwa wurin ajiyar sanyi. A ƙididdige aikin da aka yi.
Magani: \(W = Q_{\text{hot}} – Q_{\text{cold}} = 3000 – 1800 = 1200\ \text{J}\).
15. Kayyade ingancin injin Stirling da ke aiki tsakanin ma'ajiyar ruwa guda biyu a 800 K da 400 K.
Magani: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{400}{800} = 0.5\) ko \(50\%\).
16. Injin zafi yana hana 500 J zuwa wurin ajiyar ruwan sanyi yayin da yake yin aikin J 300. A lissafta zafin da ke sha daga wurin ajiyar ruwan zafi.
Magani: \(Q_{\text{hot}} = W + Q_{\text{cold}} = 300 + 500 = 800\ \text{J}\).
17. Kayyade ingancin zagayowar Ericsson tare da ma'ajiyar ruwa mai zafi da sanyi a 1000 K da 250 K.
Magani: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{250}{1000} = 0.75\) ko \(75\%\).
18. Injin zafi yana yin aikin J 700 kuma yana da inganci na 70%. A ƙididdige zafin da aka ƙi zuwa wurin ajiyar sanyi.
Magani: \(Q_{\text{cold}} = \frac{W}{\eta} – W = \frac{700}{0.7} – 700 \approx 1000 – 700 = 300\ \text{J}\).
19. Kayyade ingancin zagayowar Brayton tare da rabon matsi na 6.5 da \(\gamma = 1.4\).
Magani: \(\eta = 1 – \frac{1}{r_p^{(\gamma – 1)/\gamma}} \approx 0.433\) ko \(43.3\%\), inda \(r_p\) shine rabon matsin lamba.
20. Lissafa aikin da injin zafi ke yi wanda ke shan 250 J kuma yana ƙin 100 J zuwa wurin ajiyar sanyi.
Magani: \(W = Q_{\text{hot}} – Q_{\text{cold}} = 250 – 100 = 150\ \text{J}\).
21. Injin zafi yana aiki tsakanin 450 K da 150 K. Nemo ingancin Carnot.
Magani: \(\eta = 1 – \frac{T_{\text{cold}}}{T_{\text{hot}}} = 1 – \frac{150}{450} \approx 0.667\) ko \(66.7\%\).
22. Kayyade ingancin zagayowar Atkinson tare da rabon matsi na 10.
Magani: \(\eta = 1 – \frac{1}{r^{(\gamma – 1)}} \approx 0.593\) ko \(59.3\%\),
inda \(r\) shine rabon matsi da kuma \(\gamma\) shine rabon ƙarfin zafi.
20. Injin zafi yana shan 180 J kuma yana da inganci na 40%. A ƙididdige aikin da aka yi.
Magani: \(W = \eta \cdot Q_{\text{hot}} = 0.4 \cdot 180 = 72\ \text{J}\).
Lura: Ga matsalolin da suka shafi takamaiman zagayowar zafi (kamar Otto, Diesel, da sauransu), an yi amfani da wasu ƙima kamar rabon ƙarfin zafi \(\gamma\), waɗanda suka zama ruwan dare ga wasu iskar gas (misali, \(\gamma = 1.4\) ga iska). Waɗannan ƙima na iya bambanta dangane da takamaiman abubuwan da ake amfani da su a cikin injin.
