30 Geedi socodka thermodynamic-ka isothermal - dhibaatooyinka iyo xalalka
1. Jaantuska PV ee hoose wuxuu muujinayaa gaas ku habboon oo mara habka isothermal-ka . Xisaabi shaqada waxaa qabta gaaska habka AB.
Solution
Work gaasku wuxuu la mid yahay aagga ka hooseeya qalooca PV
AB = bedka saddexagalka + bedka leydi
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
Shaqada waxaa qabta gaaska habka AB = 12 x 10 5 Joules
2. Xisaabi shaqada waxaa sameeya gaas ku habboon habka ABC.
Shaqada waxaa qabta gaas ku habboon habka ABC = aagga ka hooseeya qalooca PV
AB = bedka saddexagalka + bedka leydi
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. Gaas ku habboon oo maraya hababka isothermal-ka. Waa maxay xaddiga kulaylka ayaa lagu daraa gaaska si gaaska uu u shaqeeyo 5000 Joules deegaanka.
La yaqaan:
Shaqada (W) = 5000 Joule
La Rabo: Kulaylka ayaa lagu daraa gaaska (Q)
Xalka:
Habka isothermal-ka waa habka thermodynamic kaas oo ka dhaca heerkul joogto ah.
ΔU = 3/2 n R ΔT
ΔU = isbeddelka tamarta gudaha, n = tirada burooyinka, R = joogtada gaaska guud, ΔT = Isbeddelka heerkulka.
Sida waafaqsan isla'egta kor ku xusan, haddii ΔT = 0 markaas ΔU = 0.
Isle'egta sharciga koowaad ee thermodynamics:
ΔU = Q - W
0 = Q – W
Q = W
Q = 5000 Joules.
4. Jaantuska PV ee gaaska ku habboon ee maraya habka isothermal-ka ee lagu muujiyey jaantuska hoose. Xisaabi kulaylka waxaa lagu daray gaas ku jira habka AB.
La yaqaan:
Cadaadiska 1 (P 1 ) = 5 atm = 5 x 10 5 Pa
Cadaadiska 2 (P 2 ) = 10 atm = 10 x 10 5 Pa
Mugga 1 (V1 ) = 2 m 3
Mugga 2 (V2 ) = 6 m 3
La doonayo : Kulayl ayaa lagu daraa habka AB.
Xalka:
Isothermal = heerkul joogto ah. Sida waafaqsan isla'egta hoose, haddii ΔT = 0 markaas ΔU = 0.
ΔU = 3/2 n R ΔT
ΔU = 3/2 n R (0)
ΔU = 0
Ku dabaq sharciga ugu horreeya ee thermodynamics :
ΔU = QW
0 = QW
Q=W
Shaqada waxaa lagu qabtaa gaas ku habboon = aagga ka hooseeya qalooca PV = bedka saddexagalka + bedka leydiga
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. Xisaabi shaqada lagu qabtay 1 mol oo gaas ku habboon oo ku fidaya meel fog laga bilaabo 2 L ilaa 4 L oo ah 300 K.
Xalka: \( W = nRT \ln\left(\frac{V_2}{V_1}\right) = 1 \jeer 8.314 \jeer 300 \jeer \ln(2) \qiyaastii 1724 \, \text{J} \)
6. Go'aami wareejinta kulaylka ee dhibaatada kor ku xusan.
Xalka: \( Q = W = 1724 \, \text{J} \)
7. Xisaabi isbeddelka tamarta gudaha ee habka kor ku xusan.
Xalka: \( \Delta U = 0 \, \text{J} \) (maadaama habku uu yahay isothermal)
8. Si aad u hesho cadaadis isothermal ah oo gaas ku habboon laga bilaabo 10 L ilaa 5 L oo ah 300 K, hel shaqada la qabtay.
Xalka: \( W = 8.314 \times 300 \times \ln\left(\frac{5}{10}\right) \approx -862 \, \text{J} \)
9. Xisaabi isbeddelka entropy ee ballaarinta isothermal-ka ee Dhibaatada 1aad.
Xalka: \( \Delta S = nR\ln\left(\frac{V_2}{V_1}\right) = 8.314 \times \ln(2) \qiyaastii 5.76 \, \text{J/K} \)
10. Soo hel wareejinta kulaylka ee cadaadiska isothermal-ka ee 2 mol oo gaas ku habboon laga bilaabo 4 L ilaa 2 L oo ah 200 K.
Xalka: \( Q = 2 \jeer 8.314 \jeer 200 \jeer \ln\left(\frac{2}{4}\right) \approx -1152 \, \text{J} \)
11. Xisaabi isbeddelka tamarta xorta ah ee Gibbs si aad u hesho habka isothermal-ka.
Xalka: \( \Delta G = 0 \) (Hab-socod isothermal ah oo dib loo rogi karo oo ku jira nidaam xiran, \( \Delta G = 0 \))
12. Go'aami isbeddelka entropy ee cadaadiska isothermal-ka ee 3 mol oo gaas ku habboon laga bilaabo 6 L ilaa 3 L at 400 K.
Xalka: \( \Delta S = 3 \jeer 8.314 \jeer \ln\left(\frac{3}{6}\right) \approx -17.29 \, \text{J/K} \)
13. Soo hel shaqada uu qabtay gaaska ku habboon ee ku fidaya meel fog laga bilaabo 3 L ilaa 6 L oo ah 250 K oo ah 2 mol.
Xalka: \( W = 2 \jeer 8.314 \jeer 250 \jeer \ln(2) \qiyaastii 2874 \, \qoraalka{J} \)
14. Go'aami wareejinta kulaylka ee habka kor ku xusan.
Xalka: \( Q = W = 2874 \, \text{J} \)
15. Xisaabi isbeddelka tamarta gudaha ee ballaarinta isothermal-ka ee kor ku xusan.
Xalka: \( \Delta U = 0 \, \text{J} \)
16. Xisaabi isbeddelka entropy ee ballaarinta isothermal-ka ee 4 mol oo gaas ku habboon laga bilaabo 5 L ilaa 10 L 500 K.
Xalka: \( \Delta S = 4 \jeer 8.314 \jeer \ln(2) \qiyaastii 23.03 \, \text{J/K} \)
17. Go'aami wareejinta kulaylka ee cadaadiska isothermal-ka ee 1 mol oo gaas ku habboon laga bilaabo 8 L ilaa 4 L oo ah 300 K.
Xalka: \( Q = 8.314 \jeer 300 \jeer \ln\left(\frac{4}{8}\right) \approx -862 \, \text{J} \)
18. Soo hel shaqada ay qabatay 3 mol oo gaas ku habboon oo ku fidaya meel fog laga bilaabo 3 L ilaa 9 L oo ah 350 K.
Xalka: \( W = 3 \jeer 8.314 \jeer 350 \jeer \ln(3) \qiyaastii 5362 \, \qoraalka{J} \)
19. Xisaabi isbeddelka entropy ee habka kor ku xusan.
Xalka: \( \Delta S = 3 \jeer 8.314 \jeer \ln(3) \qiyaastii 14.88 \, \text{J/K} \)
20. Go'aami wareejinta kulaylka ee ballaarinta kulaylka ee 2 mol oo gaas ku habboon laga bilaabo 2 L ilaa 8 L oo ah 200 K.
Xalka: \( Q = 2 \jeer 8.314 \jeer 200 \jeer \ln(4) \qiyaastii 2304 \, \qoraalka{J} \)
21. Xisaabi isbeddelka tamarta gudaha ee cadaadiska isothermal-ka ee 4 mol oo gaas ku habboon laga bilaabo 10 L ilaa 5 L 500 K.
Xalka: \( \Delta U = 0 \, \text{J} \)
22. Go'aami isbeddelka entropy ee ballaarinta isothermal-ka ee 5 mol oo gaas ku habboon laga bilaabo 5 L ilaa 15 L 300 K.
Xalka: \( \Delta S = 5 \jeer 8.314 \jeer \ln(3) \qiyaastii 24.81 \, \text{J/K} \)
23. Soo hel shaqada lagu sameeyay 2 mol oo ah cadaadis gaas oo ku habboon meel fog laga bilaabo 6 L ilaa 2 L heerkul ah 400 K.
Xalka: \( W = 2 \jeer 8.314 \jeer 400 \jeer \ln\left(\frac{2}{6}\right) \approx -2874 \, \text{J} \)
24. Xisaabi isbeddelka entropy ee cadaadiska isothermal-ka ee 3 mol oo gaas ku habboon laga bilaabo 9 L ilaa 3 L 250 K.
Xalka: \( \Delta S = 3 \jeer 8.314 \jeer \ln\left(\frac{3}{9}\right) \approx -14.88 \, \text{J/K} \)
25. Go'aami wareejinta kulaylka ee ballaarinta kulaylka ee 1 mol oo gaas ku habboon laga bilaabo 4 L ilaa 12 L oo ah 350 K.
Xalka: \( Q = 8.314 \jeer 350 \jeer \ln(3) \qiyaastii 1791 \, \qoraalka{J} \)
26. Soo hel shaqada ay qabatay 4 mol oo gaas ku habboon oo ku fidaya meel fog laga bilaabo 4 L ilaa 8 L oo ah 500 K.
Xalka: \( W = 4 \jeer 8.314 \jeer 500 \jeer \ln(2) \qiyaastii 5749 \, \qoraalka{J} \)
27. Go'aami isbeddelka entropy ee cadaadiska isothermal-ka ee 2 mol oo gaas ku habboon laga bilaabo 10 L ilaa 5 L 200 K.
Xalka: \( \Delta S = 2 \jeer 8.314 \jeer \ln\left(\frac{5}{10}\right) \approx -5.76 \, \text{J/K} \)
24. Soo hel shaqada lagu sameeyay 3 mol oo ah cadaadis gaas oo ku habboon meel fog laga bilaabo 9 L ilaa 3 L heerkul ah 450 K.
Xalka: \( W = 3 \jeer 8.314 \jeer 450 \jeer \ln\left(\frac{3}{9}\right) \approx -4310 \, \text{J} \)
25. Xisaabi isbeddelka tamarta gudaha ee ballaarinta kulaylka ee 5 mol oo gaas ku habboon laga bilaabo 5 L ilaa 10 L oo ah 400 K.
Xalka: \( \Delta U = 0 \, \text{J} \)
26. Go'aami isbeddelka entropy ee ballaarinta isothermal-ka ee 4 mol oo gaas ku habboon laga bilaabo 6 L ilaa 18 L 300 K.
Xalka: \( \Delta S = 4 \jeer 8.314 \jeer \ln(3) \qiyaastii 19.85 \, \text{J/K} \)
Dhibaatooyinkani waxay daboolayaan dhinacyo kala duwan oo ka mid ah hababka isothermal-ka, oo ay ku jiraan shaqada la qabtay, wareejinta kulaylka, isbeddellada tamarta gudaha, iyo isbeddellada entropy.
