ENGR 145, Chemistry of Materials

1
Lecture 25 Practice Problems

• Reading assignment these slides
• Learning objectives
• Master typical problems in
• Thermodynamics of materials
• One- and two-component phase equilibria

2
Estimating Heat Capacities of Solids

• Above Debye temperature (?D), heat capacity at
  constant volume, CV ? 3R 25 J mol1 K1
• HW7, problems 1 2 For metals and ceramics,
  (CPCV)/CV lt 3 ? CP ? 3R also
• Elemental metals, 25 C CV ? CP ? 3R
• specific heat, cV ? cP ? 3R/AW
• Ceramics
• Higher ?D ? 3R limit reached 1000 C
• 25 C CP ? 0.75(3R)
• Multiply 3R by ofatoms per formula unit
• MgO CP ? 0.75(6R)
• SiO2 CP ? 0.75(9R)

Callister Fig. 20.2
3
Estimating Heat Capacities of Solids

• Examples
• Cu vs.0.386 _at_ 25 C
• W vs. 0.142
• MgO vs. 0.940
• SiO2 vs. 0.740
• At room T, 3R estimate is correct to a few
  for metals may overestimate by 25-67 for
  ceramics

4
Enthalpy vs. Temperature

• Which of these graphs best depicts the variation
  of enthalpy with temperature for a one-component
  system with melting temperature Tm?

a.
b.
c.
d.

• Justify your answer.
• Hsolid must be lt Hliquid
• Slopes ( CP or CV) must be gt 0
• Csolid should be lt Cliquid

5
OGN Ch. 5 Cumulative Exercise
?Bi,liq gt ?Bi,solid (!)
Expansion of Bi offsets shrinkage of other metals
in alloy
It will melt (!)
At normal Tboil, Pvap  1 atm
6
OGN Example Problem 7.3

• Why Styrofoam?
• Keeps heat in
• Low thermal mass

qwater -qFe
1 eqn, 1 unknown
7
OGN Example Problem 7.3 Problem 8.21
For a single phase undergoing a ?T,

• Compute
• Compute
• Check net ?S for this spontaneous process gt 0?
• Yes 1.25 J K1 small, but positive as in all
  cases of spontaneous heat transfer
• See also OGN Example 8.6

8
OGN Figure 7.11 Thermite
9
OGN Problem 7.38 (HW7, 7) Thermite

• 2Al(s) Fe2O3(s) 2Fe(s) Al2O3(s)
• To compute ?H, combine the ?Hf for these phases
  (Appendix D)
• Estimate ?S298 for this reaction 0
• Note large qP to surrngs ? ?Ssys?Ssurr gtgt 0 ?
  spontaneous
• Estimate ?G298 for this reaction ?G ?H T?S
  ? ?H
• How good is this estimate? Compute ?S298
• Assume ?H and ?S are indep. of T _at_1000 K, T?S
  39 kJ (small)
• See also OGN problems 8.35, 8.39, 8.40

10
OGN Problem 9.101 Metal-Oxygen Eqm

• Calculate pO2 at equilibrium at 25 C for the
  reaction
• NiO(s) Ni(s) 0.5O2(g)

unmeasurably low!

• But at 1000 C ( 1273 K), ?G 120 kJ and pO2
  1.5?10-10 low, but achievable