Njira 30 za Isothermal thermodynamic - mavuto ndi mayankho
1. Chithunzi cha PV chomwe chili pansipa chikuwonetsa mpweya wabwino womwe umadutsa mu njira ya isothermal . Werengani ntchito yomwe yachitika ndi mpweya mu ndondomeko ya AB.
Anakonza
ntchito Chopangidwa ndi mpweya ndi chofanana ndi malo omwe ali pansi pa PV curve
AB = dera la katatu + dera la rectangle
W = [½ (8 x 10 5 –4 x 10 5 )(3-1)] + [4 x 10 5 (3-1)]
W = [½ (4 x 10 5 )(2)] + [4 x 10 5 (2)]
W = [4 x 10 5 ] + [8 x 10 5 ]
W = 12 x 105 Joules
Ntchitoyi imachitika ndi mpweya womwe umagwiritsidwa ntchito AB = 12 x 10 5 Joules
2. Werengani ntchito yomwe yachitika ndi mpweya wabwino kwambiri mu ndondomeko ya ABC.
Ntchitoyi imachitidwa ndi mpweya wabwino kwambiri mu ndondomekoyi ABC = dera lomwe lili pansi pa PV curve
AB = dera la katatu + dera la rectangle
W = [½(10×10 5 –5×10 5 )(30-10)]+[5×10 5 (30-10)]
W = [½ (5 x 10 5 )(20)] + [5 x 10 5 (20)]
W = [(5 x 10 5 )(10)] + [100 x 10 5 ]
W = [50 x 10 5 ] + [100 x 10 5 ]
W = 150 x 105 Joules
W = 1.5 x 105 Joules
3. Mpweya wabwino kwambiri womwe umachitika mu njira za isothermal. Kutentha komwe kumawonjezeredwa kumayikidwa mu mpweya kotero kuti mpweyawo umagwira ntchito ya ma Joules 5000 pa chilengedwe.
Zodziwika:
Ntchito (W) = 5000 Joule
Kufunidwa: Kutentha kumawonjezedwa ku mpweya (Q)
Yankho:
Njira ya isothermal ndi njira ya thermodynamic yomwe imachitika pa kutentha kosasintha.
ΔU = 3/2 n R ΔT
ΔU = kusintha kwa mphamvu yamkati, n = chiwerengero cha ma moles, R = mpweya wosasinthika wa chilengedwe chonse, ΔT = Kusintha kwa kutentha.
Malinga ndi equation yomwe ili pamwambapa, ngati ΔT = 0 ndiye kuti ΔU = 0.
Kuyerekeza kwa lamulo loyamba la thermodynamics:
ΔU = Q – W
0 = Q – W
Q = W
Q = 5000 Joules.
4. Chithunzi cha PV cha mpweya wabwino kwambiri womwe ukudutsa mu njira ya isothermal yomwe yawonetsedwa pachithunzi chili pansipa. Werengani kutentha komwe kumawonjezedwa ndi mpweya womwe ukuyendetsedwa mu njira ya AB.
Zodziwika:
Kupanikizika 1 (P 1 ) = 5 atm = 5 x 10 5 Pa
Kupanikizika 2 (P 2 ) = 10 atm = 10 x 10 5 Pa
Voliyumu 1 (V 1 ) = 2 m 3
Voliyumu 2 (V 2 ) = 6 m 3
Kufunidwa : Kutentha kumawonjezedwa mu ndondomeko AB.
Yankho:
Isothermal = kutentha kosasintha. Malinga ndi equation yomwe ili pansipa, ngati ΔT = 0 ndiye kuti ΔU = 0.
ΔU = 3/2 n R ΔT
ΔU = 3/2 n R (0)
ΔU = 0
Gwiritsani ntchito lamulo loyamba la thermodynamics :
ΔU = QW
0 = QW
Q=W
Ntchitoyi imachitika ndi mpweya wabwino = malo omwe ali pansi pa PV curve = malo a makona atatu + malo amakona anayi
W = ½ (P 2 – P 1 )(V 2 – V 1 ) + P 1 (V 2 – V 1 )
W = ½ (10 x 10 5 – 5 x 10 5 )(6-2) + (5 x 10 5 )(6-2)
W = ½ (5 x 10 5 )(4) + (5 x 10 5 )(4)
W = ½ (20 x 10 5 ) + (20 x 10 5 )
W = (10 x 10 5 ) + (20 x 10 5 )
W = 30 x 10 5 Joule
5. Werengerani ntchito yomwe yachitika pa 1 mol ya mpweya wabwino womwe ukufutukuka kuchokera pa 2 L mpaka 4 L pa 300 K.
Yankho: \( W = nRT \ln\left(\frac{V_2}{V_1}\right) = 1 \times 8.314 \times 300 \times \ln(2) \approx 1724 \, \text{J} \)
6. Dziwani momwe kutentha kumayendera pa vuto lomwe lili pamwambapa.
Yankho: \( Q = W = 1724 \, \text{J} \)
7. Werengani kusintha kwa mphamvu yamkati pa ndondomeko yomwe ili pamwambapa.
Yankho: \( \Delta U = 0 \, \text{J} \) (popeza njira imeneyi ndi ya isothermal)
8. Kuti mpweya wabwino ukhale wokwanira kuyambira 10 L mpaka 5 L pa 300 K, pezani ntchito yomwe yachitika.
Yankho: \( W = 8.314 \times 300 \times \ln\left(\frac{5}{10}\right) \approx -862 \, \text{J} \)
9. Werengani kusintha kwa entropy kwa expansion ya isothermal mu Vuto 1.
Yankho: \( \Delta S = nR\ln\left(\frac{V_2}{V_1}\right) = 8.314 \times \ln(2) \approx 5.76 \, \text{J/K} \)
10. Pezani njira yosinthira kutentha kuti mupeze kupsinjika kwa isothermal kwa 2 mol ya mpweya wabwino kuyambira 4 L mpaka 2 L pa 200 K.
Yankho: \( Q = 2 \nthawi 8.314 \nthawi 200 \nthawi \ln\left(\frac{2}{4}\right) \pafupifupi -1152 \, \text{J} \)
11. Werengani kusintha kwa mphamvu ya Gibbs yaulere pa njira ya isothermal.
Yankho: \( \Delta G = 0 \) (Pa njira yosinthira ya isothermal mu dongosolo lotsekedwa, \( \Delta G = 0 \))
12. Dziwani kusintha kwa entropy kwa kupsinjika kwa isothermal kwa 3 mol ya mpweya wabwino kuyambira 6 L mpaka 3 L pa 400 K.
Yankho: \( \Delta S = 3 \times 8.314 \times \ln\left(\frac{3}{6}\right) \approx -17.29 \, \text{J/K} \)
13. Pezani ntchito yomwe yachitika ndi mpweya wabwino kwambiri womwe umakula kuchokera pa malita atatu mpaka 6 pa 250 K pa malita awiri.
Yankho: \( W = 2 \nthawi 8.314 \nthawi 250 \nthawi \ln(2) \pafupifupi 2874 \, \malemba{J} \)
14. Dziwani momwe kutentha kudzasamutsidwira pa ndondomeko yomwe ili pamwambapa.
Yankho: \( Q = W = 2874 \, \text{J} \)
15. Werengani kusintha kwa mphamvu yamkati pakukula kwa isothermal komwe kwatchulidwa pamwambapa.
Yankho: \( \Delta U = 0 \, \text{J} \)
16. Werengani kusintha kwa entropy kwa expansion ya isothermal ya 4 mol ya mpweya wabwino kuyambira 5 L mpaka 10 L pa 500 K.
Yankho: \( \Delta S = 4 \nthawi 8.314 \nthawi \ln(2) \pafupifupi 23.03 \, \malemba{J/K} \)
17. Dziwani momwe kutentha kumayendera kuti mpweya wabwino ukhale wochepa kwambiri (isothermal compression) wa 1 mol wa mpweya wabwino kwambiri (better gas) kuyambira 8 L mpaka 4 L pa 300 K.
Yankho: \( Q = 8.314 \nthawi 300 \nthawi \ln\left(\frac{4}{8}\right) \pafupifupi -862 \, \text{J} \)
18. Pezani ntchito yochitidwa ndi 3 mol ya mpweya wabwino womwe ukufutukuka kuchokera pa 3 L mpaka 9 L pa 350 K.
Yankho: \( W = 3 \nthawi 8.314 \nthawi 350 \nthawi \ln(3) \pafupifupi 5362 \, \malemba{J} \)
19. Werengani kusintha kwa entropy kwa njira yomwe ili pamwambapa.
Yankho: \( \Delta S = 3 \nthawi 8.314 \nthawi \ln(3) \pafupifupi 14.88 \, \malemba{J/K} \)
20. Dziwani momwe kutentha kumayendera kuti pakhale kufalikira kwa 2 mol ya mpweya wabwino kwambiri kuchokera pa 2 L mpaka 8 L pa 200 K.
Yankho: \( Q = 2 \nthawi 8.314 \nthawi 200 \nthawi \ln(4) \pafupifupi 2304 \, \malemba{J} \)
21. Werengani kusintha kwa mphamvu yamkati ya kupsinjika kwa isothermal kwa 4 mol ya mpweya wabwino kuyambira 10 L mpaka 5 L pa 500 K.
Yankho: \( \Delta U = 0 \, \text{J} \)
22. Dziwani kusintha kwa entropy kwa kufalikira kwa isothermal kwa 5 mol ya mpweya wabwino kuyambira 5 L mpaka 15 L pa 300 K.
Yankho: \( \Delta S = 5 \nthawi 8.314 \nthawi \ln(3) \pafupifupi 24.81 \, \malemba{J/K} \)
23. Pezani ntchito yochitidwa ndi 2 mol ya mpweya woyenera kukanikiza mpweya kuchokera pa 6 L mpaka 2 L pa 400 K.
Yankho: \( W = 2 \nthawi 8.314 \nthawi 400 \nthawi \ln\left(\frac{2}{6}\right) \pafupifupi -2874 \, \text{J} \)
24. Werengani kusintha kwa entropy kwa kupsinjika kwa isothermal kwa 3 mol ya mpweya wabwino kuyambira 9 L mpaka 3 L pa 250 K.
Yankho: \( \Delta S = 3 \times 8.314 \times \ln\left(\frac{3}{9}\right) \approx -14.88 \, \text{J/K} \)
25. Dziwani momwe kutentha kumayendera kuti pakhale kufalikira kwa 1 mol ya mpweya wabwino kwambiri kuchokera pa 4 L mpaka 12 L pa 350 K.
Yankho: \( Q = 8.314 \nthawi 350 \nthawi \ln(3) \pafupifupi 1791 \, \malemba{J} \)
26. Pezani ntchito yochitidwa ndi 4 mol ya mpweya wabwino womwe ukufutukuka kuchokera pa 4 L mpaka 8 L pa 500 K.
Yankho: \( W = 4 \nthawi 8.314 \nthawi 500 \nthawi \ln(2) \pafupifupi 5749 \, \malemba{J} \)
27. Dziwani kusintha kwa entropy kwa kupsinjika kwa isothermal kwa 2 mol ya mpweya wabwino kuyambira 10 L mpaka 5 L pa 200 K.
Yankho: \( \Delta S = 2 \times 8.314 \times \ln\left(\frac{5}{10}\right) \approx -5.76 \, \text{J/K} \)
24. Pezani ntchito yochitidwa ndi 3 mol ya mpweya woyenera kukanikiza mpweya kuchokera pa 9 L mpaka 3 L pa 450 K.
Yankho: \( W = 3 \nthawi 8.314 \nthawi 450 \nthawi \ln\left(\frac{3}{9}\right) \pafupifupi -4310 \, \text{J} \)
25. Werengani kusintha kwa mphamvu yamkati kuti pakhale kufalikira kwa 5 mol ya mpweya wabwino kwambiri kuchokera pa 5 L mpaka 10 L pa 400 K.
Yankho: \( \Delta U = 0 \, \text{J} \)
26. Dziwani kusintha kwa entropy kwa kufalikira kwa isothermal kwa 4 mol ya mpweya wabwino kuyambira 6 L mpaka 18 L pa 300 K.
Yankho: \( \Delta S = 4 \nthawi 8.314 \nthawi \ln(3) \pafupifupi 19.85 \, \malemba{J/K} \)
Mavutowa akuphatikizapo mbali zosiyanasiyana za njira zosinthira kutentha, kuphatikizapo ntchito yomwe yachitika, kusamutsa kutentha, kusintha kwa mphamvu zamkati, ndi kusintha kwa entropy.
