Matambudziko makumi matatu eIsothermal thermodynamic - matambudziko nemhinduro
1. Dhayagiramu yePV pazasi inoratidza gasi rakanaka underes an maitiro e-isothermalVerengai kuti gasi rinoitwa sei mukuita kwe AB.
mhinduro
basa zvakaitwa negasi zvakaenzana nenzvimbo iri pasi pePV curve
AB = nzvimbo yetriangle + nzvimbo yetriangle
W = [½ (8 x 10)5–4 x 105)(3-1)] + [4 x 105 (3-1)]
W = [½ (4 x 10)5)(2)] + [4 x 105 (2)]
W = [4 x 10]5] + [8 x 105]
W = 12 x 105 Joule
Basa rinoitwa negasi mukuita AB = 12 X 105 Joule
2. Verenga kuti basa rinoitwa negasi rakakodzera mukuita ABC.
Basa rinoitwa negasi rakakodzera mukuita ABC = nzvimbo iri pasi pePV curve
AB = nzvimbo yetriangle + nzvimbo yetriangle
W = [½(10×10)5–5×105)(30-10)]+[5×105(30-10)]
W = [½ (5 x 10)5)(20)] + [5 x 105 (20)]
W = [(5 x 10)5)(10)] + [100 x 105]
W = [50 x 10]5] + [100 x 105]
W = 150 x 105 Joule
W = 1.5 x 107 Joule
3. An gasi rakakodzera riri kushandiswa mumaitiro ekupisa kwemuviri. Chii chinonzi huwandu hwe kupisa inowedzerwa kugasi saka gasi rinoita basa re5000 Joules pane zvakatipoteredza.
Zvinozivikanwa:
Basa (W) = 5000 Joule
Kuda: Kupisa kunowedzerwa kugasi (Q)
Solution:
Maitiro e-isothermal a maitiro e thermodynamic anoitika panguva imwe chete tembiricha.
ΔU = 3/2 n R ΔT
ΔU = shanduko yesimba remukati, n = nhamba yemamota, R = gasi risingaperi repasi rose, ΔT = Kuchinja kwekupisa.
Zvichienderana ne equation iri pamusoro apa, kana ΔT = 0 saka ΔU = 0.
Kuenzanisa kwemutemo wekutanga wethermodynamics:
ΔU = Q - W
0 = Q – W
Q = W
Q = 5000 Joules.
4. Dhayagiramu yePV yegasi rakakodzera riri kushandiswa muchikamu che isothermal rinoratidzwa mumufananidzo uri pazasi. Verenga kupisa kunowedzerwa negasi riri muchikamu che AB.
Zvinozivikanwa:
Kumanikidzwa 1 (P)1) = 5 atm = 5 x 105 Pa
Kumanikidzwa 2 (P)2) = 10 atm = 10 x 105 Pa
Vhoriyamu 1 (V)1) = 2 m3
Vhoriyamu 2 (V)2) = 6 m3
Wanted : Kupisa kunowedzerwa mukuita AB.
Solution:
Isothermal = tembiricha isingachinji. Zvichienderana ne equation iri pazasi, kana ΔT = 0 saka ΔU = 0.
ΔU = 3/2 n R ΔT
ΔU = 3/2 n R (0)
ΔU = 0
Nyorera kuna mutemo wekutanga wethermodynamics :
ΔU = QW
0 = QW
Q=W
Basa rinoitwa negasi rakakodzera = nzvimbo iri pasi pePV curve = nzvimbo yetriangle + nzvimbo yerectangle
W = ½ (P)2 - P1)(V)2 - V1) + P1 (V2 - V1)
W = ½ (10 x 10)5 - 5 x 105)(6-2) + (5 x 105(6-2)
W = ½ (5 x 10)5)(4) + (5 x 105)(4)
W = ½ (20 x 10)5) + (20 x 105)
W = (10 x 10)5) + (20 x 105)
W = 30 x 105 Joule
5. Verenga basa rakaitwa pa 1 mol yegasi rakanaka riri kuwedzera kubva pa 2 L kusvika 4 L pa 300 K.
Mhinduro: \( W = nRT \ln\left(\frac{V_2}{V_1}\right) = 1 \times 8.314 \times 300 \times \ln(2) \approx 1724 \, \text{J} \)
6. Sarudza kuti chii chinotamisirwa kupisa kwedambudziko riri pamusoro apa.
Mhinduro: \( Q = W = 1724 \, \text{J} \)
7. Verenga shanduko yesimba remukati memuviri wemunhu ari pamusoro apa.
Mhinduro: \( \Delta U = 0 \, \text{J} \) (sezvo maitiro acho ari e-isothermal)
8. Kuti uwane kudzvanywa kwegasi rakakodzera kubva pa10 L kusvika pa5 L pa300 K, tsvaga basa raitwa.
Mhinduro: \( W = 8.314 \times 300 \times \ln\left(\frac{5}{10}\right) \approx -862 \, \text{J} \)
9. Verenga shanduko ye entropy yekuwedzera kwe isothermal muDambudziko 1.
Mhinduro: \( \Delta S = nR\ln\left(\frac{V_2}{V_1}\right) = 8.314 \times \ln(2) \approx 5.76 \, \text{J/K} \)
10. Tsvaga nzira yekufambisa kupisa kuti uwane kudzvanywa kwe2 mol yegesi yakakodzera kubva pa4 L kusvika pa2 L pa200 K.
Mhinduro: \( Q = 2 \nguva 8.314 \nguva 200 \nguva \ln\left(\frac{2}{4}\right) \approx -1152 \, \text{J} \)
11. Verenga shanduko musimba risingabhadharwe reGibbs pakuita kwe isothermal.
Mhinduro: \( \Delta G = 0 \) (Kune maitiro e-isothermal anodzoreka muhurongwa hwakavharwa, \( \Delta G = 0 \))
12. Tsvaga shanduko ye entropy yekudzvanywa kwe isothermal kwe 3 mol yegasi rakakodzera kubva pa 6 L kusvika pa 3 L pa 400 K.
Mhinduro: \( \Delta S = 3 \times 8.314 \times \ln\left(\frac{3}{6}\right) \approx -17.29 \, \text{J/K} \)
13. Tsvaga basa rakaitwa negasi rinokwanisa kuwedzera kubva pa3 L kusvika pa6 L pa250 K ye2 mol.
Mhinduro: \( W = 2 \times 8.314 \times 250 \times \ln(2) \approx 2874 \, \text{J} \)
14. Sarudza kuti kupisa kuchafambiswa sei pakuita zviri pamusoro apa.
Mhinduro: \( Q = W = 2874 \, \text{J} \)
15. Verenga shanduko yesimba remukati memuviri nekuda kwekuwedzera kwemafuta ari pamusoro apa.
Mhinduro: \( \Delta U = 0 \, \text{J} \)
16. Verenga shanduko ye entropy yekuwedzera kwe isothermal kwe 4 mol yegasi rakakodzera kubva pa 5 L kusvika 10 L pa 500 K.
Mhinduro: \( \Delta S = 4 \times 8.314 \times \ln(2) \approx 23.03 \, \text{J/K} \)
17. Sarudza kuti kupisa kunofambiswa sei kuti pave nekudzvanywa kwe 1 mol yegesi yakanaka kubva pa 8 L kusvika 4 L pa 300 K.
Mhinduro: \( Q = 8.314 \times 300 \times \ln\left(\frac{4}{8}\right) \approx -862 \, \text{J} \)
18. Tsvaga basa rakaitwa ne3 mol yegasi rakanaka richiwedzera kubva pa3 L kusvika pa9 L pa350 K.
Mhinduro: \( W = 3 \times 8.314 \times 350 \times \ln(3) \approx 5362 \, \text{J} \)
19. Verenga shanduko ye entropy yemaitiro ari pamusoro apa.
Mhinduro: \( \Delta S = 3 \times 8.314 \times \ln(3) \approx 14.88 \, \text{J/K} \)
20. Sarudza kuti kupisa kunofambiswa sei kuti pave nekuwedzera kwe2 mol yegesi yakakodzera kubva pa2 L kusvika 8 L pa200 K.
Mhinduro: \( Q = 2 \times 8.314 \times 200 \times \ln(4) \approx 2304 \, \text{J} \)
21. Verenga shanduko yesimba remukati memhepo kuti pave nekudzvanywa kwe4 mol yegasi rakakodzera kubva pa10 L kusvika pa5 L pa500 K.
Mhinduro: \( \Delta U = 0 \, \text{J} \)
22. Tsvaga shanduko ye entropy yekuwedzera kwe isothermal kwe 5 mol yegasi rakakodzera kubva pa 5 L kusvika 15 L pa 300 K.
Mhinduro: \( \Delta S = 5 \times 8.314 \times \ln(3) \approx 24.81 \, \text{J/K} \)
23. Tsvaga basa rakaitwa ne2 mol yemhepo yakakodzera yekudzvanya gasi inodziya kubva pa6 L kusvika pa2 L pa400 K.
Mhinduro: \( W = 2 \kawa 8.314 \kawa 400 \kawa \ln\left(\frac{2}{6}\right) \approx -2874 \, \text{J} \)
24. Verenga shanduko ye entropy ye 3 mol ye isothermal compression ye gasi rakakodzera kubva pa 9 L kusvika pa 3 L pa 250 K.
Mhinduro: \( \Delta S = 3 \times 8.314 \times \ln\left(\frac{3}{9}\right) \approx -14.88 \, \text{J/K} \)
25. Sarudza kuti kupisa kunofambiswa sei kuti pave nekuwedzera kwe1 mol yegesi yakakodzera kubva pa4 L kusvika 12 L pa350 K.
Mhinduro: \( Q = 8.314 \times 350 \times \ln(3) \approx 1791 \, \text{J} \)
26. Tsvaga basa rakaitwa ne4 mol yegasi rakanaka richiwedzera kubva pa4 L kusvika pa8 L pa500 K.
Mhinduro: \( W = 4 \times 8.314 \times 500 \times \ln(2) \approx 5749 \, \text{J} \)
27. Tsvaga shanduko ye entropy yekudzvanywa kwe isothermal kwe 2 mol yegasi rakakodzera kubva pa 10 L kusvika 5 L pa 200 K.
Mhinduro: \( \Delta S = 2 \times 8.314 \times \ln\left(\frac{5}{10}\right) \approx -5.76 \, \text{J/K} \)
24. Tsvaga basa rakaitwa ne3 mol yemhepo yakakodzera yekudzvanya gasi inodziya kubva pa9 L kusvika pa3 L pa450 K.
Mhinduro: \( W = 3 \kawa 8.314 \kawa 450 \kawa \ln\left(\frac{3}{9}\right) \approx -4310 \, \text{J} \)
25. Verenga shanduko yesimba remukati memhepo kuti pave nekuwedzera kwe5 mol yegasi rakakodzera kubva pa5 L kusvika pa10 L pa400 K.
Mhinduro: \( \Delta U = 0 \, \text{J} \)
26. Tsvaga shanduko ye entropy yekuwedzera kwe isothermal kwe 4 mol yegasi rakakodzera kubva pa 6 L kusvika 18 L pa 300 K.
Mhinduro: \( \Delta S = 4 \times 8.314 \times \ln(3) \approx 19.85 \, \text{J/K} \)
Matambudziko aya anosanganisira zvinhu zvakasiyana-siyana zvemaitiro e-isothermal, kusanganisira basa rinoitwa, kutamiswa kwekupisa, shanduko musimba remukati, uye shanduko dze entropy.
