Mekhoa e 30 ea thermodynamic ea Isothermal - mathata le litharollo
1. Setšoantšo sa PV se ka tlase se bontša khase e loketseng e fetang ts'ebetsong ea isothermal . Bala mosebetsi o etsoang ke khase ts'ebetsong ea AB.
tharollo
Sebetsa e entsoeng ke khase e lekana le sebaka se ka tlas'a mothapo oa PV
AB = sebaka sa khutlotharo + sebaka sa khutlonnetsepa
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 10 5 Joule
Mosebetsi o etsoa ke khase ts'ebetsong AB = 12 x 10 5 Joules
2. Bala mosebetsi o etsoang ke khase e ntle ka ho fetisisa ts'ebetsong ea ABC.
Mosebetsi o etsoa ke khase e ntle ka ho fetisisa ts'ebetsong ABC = sebaka se ka tlas'a mothapo oa PV
AB = sebaka sa khutlotharo + sebaka sa khutlonnetsepa
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 10 5 Joule
W = 1.5 x 10 7 Joule
3. Khase e loketseng e fetang lits'ebetsong tsa isothermal. Ke bokae ba mocheso bo eketsoang khaseng e le hore khase e sebetse ka li-Joules tse 5000 tikolohong.
Tse tsejoang:
Mosebetsi (W) = 5000 Joule
Ho batloa: Mocheso o eketsoa khaseng (Q)
Tharollo:
Ts'ebetso ea isothermal ke ts'ebetso ea thermodynamic e etsahalang mochesong o sa fetoheng.
ΔU = 3/2 n R ΔT
ΔU = phetoho ea matla a ka hare, n = palo ea li-mole, R = khase e sa fetoheng ea bokahohle, ΔT = Phetoho ea mocheso.
Ho ya ka equation e ka hodimo, haeba ΔT = 0, ΔU = 0.
Tekanyo ea molao oa pele oa thermodynamics:
ΔU = Q – W
0 = Q – W
Q = W
Q = 5000 Joule.
4. Setšoantšo sa PV bakeng sa khase e loketseng e fetang ts'ebetsong ea isothermal e bontšitsoeng setšoantšong se ka tlase. Bala mocheso o eketsoa ke khase ts'ebetsong ea AB.
Tse tsejoang:
Khatello 1 (P 1 ) = 5 atm = 5 x 10 5 Pa
Khatello 2 (P 2 ) = 10 atm = 10 x 10 5 Pa
Moqolo oa 1 (V 1 ) = 2 m 3
Moqolo oa 2 (V 2 ) = 6 m 3
Ho batloa : Mocheso o eketsoa ts'ebetsong AB.
Tharollo:
Isothermal = mocheso o sa fetoheng. Ho ya ka equation e ka tlase, haeba ΔT = 0, joale ΔU = 0.
ΔU = 3/2 n R ΔT
ΔU = 3/2 n R (0)
ΔU = 0
Sebelisa molao oa pele oa thermodynamics :
ΔU = QW
0 = QW
Q=W
Mosebetsi o etsoa ka khase e loketseng = sebaka se ka tlas'a mothapo oa PV = sebaka sa khutlotharo + sebaka sa khutlotharo
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. Bala mosebetsi o entsoeng ho 1 mol ea khase e ntle e ntseng e atoloha ka isothermally ho tloha ho 2 L ho isa ho 4 L ho 300 K.
Tharollo: \( W = nRT \ln\left(\frac{V_2}{V_1}\right) = 1 \times 8.314 \times 300 \times \ln(2) \approx 1724 \, \text{J} \)
6. Fumana phetiso ea mocheso bakeng sa bothata bo boletsoeng ka holimo.
Tharollo: \( Q = W = 1724 \, \text{J} \)
7. Bala phetoho ea matla a ka hare bakeng sa ts'ebetso e boletsoeng ka holimo.
Tharollo: \( \Delta U = 0 \, \text{J} \) (kaha ts'ebetso ena ha e lekane le mocheso)
8. Bakeng sa kgatello ya isothermal ya kgase e loketseng ho tloha ho 10 L ho isa ho 5 L ho 300 K, fumana mosebetsi o phethilweng.
Tharollo: \( W = 8.314 \times 300 \times \ln\left(\frac{5}{10}\right) \approx -862 \, \text{J} \)
9. Bala phetoho ea entropy bakeng sa katoloso ea isothermal ho Bothata ba 1.
Tharollo: \( \Delta S = nR\ln\left(\frac{V_2}{V_1}\right) = 8.314 \times \ln(2) \approx 5.76 \, \text{J/K} \)
10. Fumana phetiso ea mocheso bakeng sa khatello ea isothermal ea 2 mol ea khase e loketseng ho tloha ho 4 L ho isa ho 2 L ho 200 K.
Tharollo: \( Q = 2 \ka makhetlo a 8.314 \ka makhetlo a 200 \ka makhetlo \ln\left(\frac{2}{4}\right) \ka -1152 \, \text{J} \)
11. Bala phetoho ea matla a mahala a Gibbs bakeng sa ts'ebetso ea isothermal.
Tharollo: \( \Delta G = 0 \) (Bakeng sa ts'ebetso ea isothermal e ka fetoloang tsamaisong e koetsoeng, \( \Delta G = 0 \))
12. Fumana phetoho ea entropy bakeng sa khatello ea isothermal ea 3 mol ea khase e loketseng ho tloha ho 6 L ho isa ho 3 L ho 400 K.
Tharollo: \( \Delta S = 3 \times 8.314 \times \ln\left(\frac{3}{6}\right) \approx -17.29 \, \text{J/K} \)
13. Fumana mosebetsi o entsoeng ke khase e ntle e atolohang ka isothermally ho tloha ho 3 L ho isa ho 6 L ho 250 K bakeng sa 2 mol.
Tharollo: \( W = 2 \ka makhetlo a 8.314 \ka makhetlo a 250 \ka makhetlo \ln(2) \ka hoo e ka bang 2874 \, \mongolo{J} \)
14. Fumana phetiso ea mocheso bakeng sa ts'ebetso e boletsoeng ka holimo.
Tharollo: \( Q = W = 2874 \, \text{J} \)
15. Bala phetoho ea matla a ka hare bakeng sa katoloso ea isothermal e kaholimo.
Tharollo: \( \Delta U = 0 \, \text{J} \)
16. Bala phetoho ea entropy bakeng sa katoloso ea isothermal ea 4 mol ea khase e loketseng ho tloha ho 5 L ho isa ho 10 L ho 500 K.
Tharollo: \( \Delta S = 4 \times 8.314 \times \ln(2) \approx 23.03 \, \text{J/K} \)
17. Fumana phetiso ea mocheso bakeng sa khatello ea isothermal ea 1 mol ea khase e loketseng ho tloha ho 8 L ho isa ho 4 L ho 300 K.
Tharollo: \( Q = 8.314 \times 300 \times \ln\left(\frac{4}{8}\right) \approx -862 \, \text{J} \)
18. Fumana mosebetsi o entsoeng ka 3 mol ea khase e ntle e ntseng e atoloha ka isothermally ho tloha ho 3 L ho isa ho 9 L ho 350 K.
Tharollo: \( W = 3 \ka makhetlo a 8.314 \ka makhetlo a 350 \ka makhetlo \ln(3) \ka hoo e ka bang 5362 \, \mongolo{J} \)
19. Bala phetoho ea entropy bakeng sa ts'ebetso e boletsoeng ka holimo.
Tharollo: \( \Delta S = 3 \times 8.314 \times \ln(3) \approx 14.88 \, \text{J/K} \)
20. Fumana phetiso ea mocheso bakeng sa katoloso ea isothermal ea 2 mol ea khase e loketseng ho tloha ho 2 L ho isa ho 8 L ho 200 K.
Tharollo: \( Q = 2 \ka makhetlo a 8.314 \ka makhetlo a 200 \ka makhetlo \ln(4) \ka hoo e ka bang 2304 \, \mongolo{J} \)
21. Bala phetoho ea matla a ka hare bakeng sa khatello ea isothermal ea 4 mol ea khase e loketseng ho tloha ho 10 L ho isa ho 5 L ho 500 K.
Tharollo: \( \Delta U = 0 \, \text{J} \)
22. Fumana phetoho ea entropy bakeng sa katoloso ea isothermal ea 5 mol ea khase e loketseng ho tloha ho 5 L ho isa ho 15 L ho 300 K.
Tharollo: \( \Delta S = 5 \times 8.314 \times \ln(3) \approx 24.81 \, \text{J/K} \)
23. Fumana mosebetsi o entsoeng ka 2 mol ea khase e loketseng ea ho hatella ka mokhoa o sa fetoheng ho tloha ho 6 L ho isa ho 2 L ho 400 K.
Tharollo: \( W = 2 \ka makhetlo a 8.314 \ka makhetlo a 400 \ka makhetlo \ln\left(\frac{2}{6}\right) \ka -2874 \, \text{J} \)
24. Bala phetoho ea entropy bakeng sa khatello ea isothermal ea 3 mol ea khase e loketseng ho tloha ho 9 L ho isa ho 3 L ho 250 K.
Tharollo: \( \Delta S = 3 \times 8.314 \times \ln\left(\frac{3}{9}\right) \approx -14.88 \, \text{J/K} \)
25. Fumana phetiso ea mocheso bakeng sa katoloso ea isothermal ea 1 mol ea khase e loketseng ho tloha ho 4 L ho isa ho 12 L ho 350 K.
Tharollo: \( Q = 8.314 \times 350 \times \ln(3) \approx 1791 \, \text{J} \)
26. Fumana mosebetsi o entsoeng ka 4 mol ea khase e ntle e ntseng e atoloha ka isothermally ho tloha ho 4 L ho isa ho 8 L ho 500 K.
Tharollo: \( W = 4 \ka makhetlo a 8.314 \ka makhetlo a 500 \ka makhetlo \ln(2) \ka hoo e ka bang 5749 \, \mongolo{J} \)
27. Fumana phetoho ea entropy bakeng sa khatello ea isothermal ea 2 mol ea khase e loketseng ho tloha ho 10 L ho isa ho 5 L ho 200 K.
Tharollo: \( \Delta S = 2 \times 8.314 \times \ln\left(\frac{5}{10}\right) \approx -5.76 \, \text{J/K} \)
24. Fumana mosebetsi o entsoeng ka 3 mol ea khase e loketseng ea ho hatella ka mokhoa o sa fetoheng ho tloha ho 9 L ho isa ho 3 L ho 450 K.
Tharollo: \( W = 3 \ka makhetlo a 8.314 \ka makhetlo a 450 \ka makhetlo \ln\left(\frac{3}{9}\right) \ka -4310 \, \text{J} \)
25. Bala phetoho ea matla a ka hare bakeng sa katoloso ea isothermal ea 5 mol ea khase e loketseng ho tloha ho 5 L ho isa ho 10 L ho 400 K.
Tharollo: \( \Delta U = 0 \, \text{J} \)
26. Fumana phetoho ea entropy bakeng sa katoloso ea isothermal ea 4 mol ea khase e loketseng ho tloha ho 6 L ho isa ho 18 L ho 300 K.
Tharollo: \( \Delta S = 4 \times 8.314 \times \ln(3) \approx 19.85 \, \text{J/K} \)
Mathata ana a akaretsa likarolo tse fapaneng tsa lits'ebetso tsa isothermal, ho kenyeletsoa mosebetsi o entsoeng, phetiso ea mocheso, liphetoho matla a ka hare, le liphetoho tsa entropy.
