CHEM 331
Physical Chemistry
Fall 2014
Problem Set 6
(Heat Capacity & Thermochemistry, part 1)
1.
Suppose a gas has the following behavior:
= 0
P (V – b) = RT
Calculate the following two quantities:
Cp - Cv
2.
In this problem we will step outside our usual constraint that we only consider P-V work
done by/on a system.
Consider a stretched rubber band.
The restoring force provided by the band F is a function of temperature and the length of
the band; F = F(T, l). (Think about why this might be so.) In this case,
W = F dl
i)
Justify the sign convention used.
ii)
We can certainly write U = U(T, l). Given this, show that:
CF =
Recall, we define any general Heat Capacity Cx as:
Cx =
(Hint: Go back and examine how the relationship giving CP - CV was derived.)
3.
For Air,  = CP/CV = 1.40. Based on this datum, how would you model an Average Air
Molecule? Note:  is a common designation for Cp/Cv for gases. Measurements of ,
along with Equation of State information, are needed to fully describe the behavior of a
gas.
4.
Compare the Specific Heat of Ice with that calculated from the Law of Dulong-Petit.
Explain any difference.
5.
Calculate the Final Temperature of the system if 20g of Ice at -5oC is added to 100g of
Water at 21oC in a Dewar flask. The following data may prove to be useful:
Ho = 6009 J/mol for H2O(s)
H2O(l)
Cp,H2O(s) = 37.7 J/K mol
Cp,H2O(l) = 75.3 J/K mol
6.
The temperature dependence of Heat Capacity data is frequently reported as:
= a + b T + c T2
Use the following data for Carbon Dioxide to determine a, b, and c for this gas.
T [K]
298.15
400
600
800
1000
1200
1400
1600
1800
2000
7.
Cpo [Joule/K mol]
37.154
42.358
47.109
49.915
52.158
54.179
56.096
57.957
59.786
61.594
From the following data at 25oC:
Ho
Rxn
Fe2O3(s) + 3 C(gr)
2 Fe(s) + 3 CO(g)
492.6
FeO(s) + C(gr)
Fe(s) + CO(g)
155.8
C(gr) + O2(g)
CO2(g)
- 393.51
CO(g) + ½ O2(g)
CO2(g)
-282.98
Compute the Standard Heats of Formation of FeO(s) and Fe2O3(s).
[Ans. -266.3 kJ/mol, -824.2 kJ/mol]