Page 89 - Essentials of physical chemistry

The Kinetic Molecular Theory of Gases 51

outcome of KMTG is a revelation about the actual size of atoms and molecules. Some may question
why we needed such an intellectual investment in the derivation of laminar viscosity, but the
application to polymer molecular weights is a valuable spin-off and some occasional chemical
4
engineers in the class should find the r dependence of flow rate important. However, that foundation
in the theory of laminar viscosity yielded a window into the whole Boltzmann KMTG and that alone
justifies the time spent in the derivation of Poiseuille’s law.

PROBLEMS

3.1 Compute hvi, v rms , and the most probable speed a for Ar gas at 258C and 1 atm pressure in mph.
3.2 Given the viscosity of N 2 is 17.9 mPa s at 278C and 1 atm pressure, calculate d, l, Z 1 ,and Z 11
for this gas.
3.3 Given the viscosity of He is 20.0 mPa s at 278C and 1 atm pressure, calculate d, l, Z 1 , and Z 11
for this gas.
ð
1
3.4 Evaluate x e 2x dx.
0
ð
1
5
3.5 Evaluate x e 3x dx.
0
ð
1 2
6
3.6 Evaluate x e 4x dx.
0
ð
1 2
5
3.7 Evaluate x e 9x dx.
0
ð
1
5 9x 2
3.8 Evaluate x e dx.
1
2p p
ð ð
3.9 Evaluate df sin (u)du.
0 0
ð a ð 2p ð p
2
3.10 Evaluate r dr df sin (u) du.
0 0 0
ð
þ1 2
4
3.11 Evaluate e 9x x dx (note limits of integration).
1
ð
þ1 2
5
3.12 Evaluate e 9x x dx (note limits of integration).
0
ð
þ1 2
3
3.13 Evaluate e 4x x dx (note limits of integration).
1
ð
þ1 2
6
3.14 Evaluate e 4x x dx (note limits of integration).
1
ð
þ1
x dx.
3.15 Evaluate e 4x 6
0
REFERENCES
1. Hilsenrath, J., Tables of Thermal Properties of Gases, table 1-B. U.S. Natl. Bur. Stand. Circ. 564. U.S.
Government Printing Office, Washington, DC (1955).
2. Shoemaker, D. P., C. W. Garland, and J. W. Nibler, Experiments in Physical Chemistry., 6th Edn.,
McGraw-Hill Co., New York, 1996, p. 129.
3. Pease, R., Kinetic theory of gases. Part II, J. Chem. Ed., 16, 366 (1939).