2.5. (a) p = (v1 + v2 + v3 ) RT/V = 2.0 atm; (b) M =
v2M2
v31113)/(vi ± v2
v3) = 36.7 g/mol.
2.6. T
olli 012 — 1)/i (112 — 1)
0.42 kK.
2.7. n—
In
In (1+ AIT/17) •
2.8. p =
2.9. t = (V/C) In 11 = 1.0 min.
2.10. AT = (mg Po AS) l/R ---- 0.9 K.
2.11. (a) Tmax = 3(PoIR)17 Pd 3a; (b) Tmax=Po/ePR.
2.12. Pmin = 2/117aTo.
2.13. dT/dh = —MgIR = —33 mK/m.
2.14. dT/dh = —Mg (n — 1)/nR.
2.15. 0.5 and 2 atm.
2.16. (a) h = RT IMg = 8.0 km; (b) h 1RTIMg = 0.08 km.
2.17. m = (1 — e -MghIRT) poSIg.
OP
00
2.18. he = .c hp dh I p dh = RTI Mg.
2.19. (a) p = Po (1 — ah.)n , h < 11a; (b) p = p 01 (1 + ah)n. Here
n = MglaRT o.
2.20. p
p0elt1(02r2/2RT
2.21. pid =pRTIM =80 atm; p = pRTI(M — pb) — ap2/M2=
= 80 atm.
2.22. (a) T = a (V — b) (1 + 1))/RV (QV
b) = 133 K; (b)
p = RTI(V — b) — alV2 = 9.9 atm.
2.23. a = V2 (T1p2 — T 2pi)I(T 2 — T1) = 185 atm•12/mo12, b
= V — R (T 2 — T1)I(p2 — pi) = 0.042 1/mol.
2.24. x = VZ (V — b)-2/1R7T3 — 2a (V — b)2].
2.25. T > a/bR.
2.26. U = pVl•y — 1) = 10 ML
2.27. AT = 1/2/Vv2 (' — 1)/R.
2.28. T = T1T2
+ P2 V2)/(PiViT2
p2V2T1); P
(PiVi
P2V2)/(Vi + V2).
2.29. AU = —poVATIT0 (7 — 1) = —0.25 kJ, Q'
—AU.
2.30. Q = A?/(? — 1) = 7 J.
2.31. A = RAT = 0.60 kJ, AU = Q — RAT = 1.00 kJ,
.17 = Ql(Q — RAT) = 1.6.
2.32. Q = vRT 0 (1 — 1/n) = 2.5 kJ.
2.33.
vai
(v1-1) ___ .33.
vl (72 —1) ± V2 (71 -1)
2.34. cy = 0.42 J/(g•K), cp = 0.65 J/(g•K).
2.35. A
RT (n — 1. — ln n).
2.36. A' = PoVo In [(n + 1) 2/44
2.37. y = 1 + (n — 1)1(Q1vRT, — ln n) = 1.4.
2.38. See Fig. 13 where V is an isochore, p is an isobaric line, T
is an isothermal line, and S is an adiabatic line.
2.39. (a) T = T
- niv = 0.56 kK; (b) A' = RT
ivy
— 1)/(y — 1) = 5.6 kJ
v2M2
v31113)/(vi ± v2
v3) = 36.7 g/mol.
2.6. T
olli 012 — 1)/i (112 — 1)
0.42 kK.
2.7. n—
In
In (1+ AIT/17) •
2.8. p =
2.9. t = (V/C) In 11 = 1.0 min.
2.10. AT = (mg Po AS) l/R ---- 0.9 K.
2.11. (a) Tmax = 3(PoIR)17 Pd 3a; (b) Tmax=Po/ePR.
2.12. Pmin = 2/117aTo.
2.13. dT/dh = —MgIR = —33 mK/m.
2.14. dT/dh = —Mg (n — 1)/nR.
2.15. 0.5 and 2 atm.
2.16. (a) h = RT IMg = 8.0 km; (b) h 1RTIMg = 0.08 km.
2.17. m = (1 — e -MghIRT) poSIg.
OP
00
2.18. he = .c hp dh I p dh = RTI Mg.
2.19. (a) p = Po (1 — ah.)n , h < 11a; (b) p = p 01 (1 + ah)n. Here
n = MglaRT o.
2.20. p
p0elt1(02r2/2RT
2.21. pid =pRTIM =80 atm; p = pRTI(M — pb) — ap2/M2=
= 80 atm.
2.22. (a) T = a (V — b) (1 + 1))/RV (QV
b) = 133 K; (b)
p = RTI(V — b) — alV2 = 9.9 atm.
2.23. a = V2 (T1p2 — T 2pi)I(T 2 — T1) = 185 atm•12/mo12, b
= V — R (T 2 — T1)I(p2 — pi) = 0.042 1/mol.
2.24. x = VZ (V — b)-2/1R7T3 — 2a (V — b)2].
2.25. T > a/bR.
2.26. U = pVl•y — 1) = 10 ML
2.27. AT = 1/2/Vv2 (' — 1)/R.
2.28. T = T1T2
+ P2 V2)/(PiViT2
p2V2T1); P
(PiVi
P2V2)/(Vi + V2).
2.29. AU = —poVATIT0 (7 — 1) = —0.25 kJ, Q'
—AU.
2.30. Q = A?/(? — 1) = 7 J.
2.31. A = RAT = 0.60 kJ, AU = Q — RAT = 1.00 kJ,
.17 = Ql(Q — RAT) = 1.6.
2.32. Q = vRT 0 (1 — 1/n) = 2.5 kJ.
2.33.
vai
(v1-1) ___ .33.
vl (72 —1) ± V2 (71 -1)
2.34. cy = 0.42 J/(g•K), cp = 0.65 J/(g•K).
2.35. A
RT (n — 1. — ln n).
2.36. A' = PoVo In [(n + 1) 2/44
2.37. y = 1 + (n — 1)1(Q1vRT, — ln n) = 1.4.
2.38. See Fig. 13 where V is an isochore, p is an isobaric line, T
is an isothermal line, and S is an adiabatic line.
2.39. (a) T = T
- niv = 0.56 kK; (b) A' = RT
ivy
— 1)/(y — 1) = 5.6 kJ