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GAS PROPERTIES
24
PROBLEMS
2. I
t State the assumptions that form the basis of kinetic theory.
2.2 Consider a 1-cm-diameter pipe 10 meters long. (a) Sketch the selfdiffusion constant of air in this pipe over the pressure range 0.01 Pa to
lo5 Pa. (b) Knowing that the diffusion fiont moves as d2 oc Dt,
estimate the time required for air to diffuse to the end of the 1O-meterlong pipe over the pressure range given in (a).
2.3 The diffbsion constant for gas (1) in gas (2), 0 1 2 describes how gas a
gas of one molecular weight diffuses in the background of a second
gas. For the case where the d i f h i n g gas (1) is light (ml << MZ), and is
present in a small concentration (nl << n2), derive a simplified
relationship for (2.30). This happens during helium leak checking.
2.4
t Room temperature N2 molecules are directed toward a surface 100-
cm distant. To what pressure must a chamber be evacuated in order
that the molecules reach the surface, on average, without first
colliding with another N2 molecule?
2.5 j- What is the advantage of low-pressure chemical vapor deposition
over atmospheric pressure chemical vapor deposition?
2.6 Explain why the viscosity of a gas should increase with increasing
particle mass and temperature. (The viscosity of a liquid decreases
with increasing temperature.)
2.7 j- The air surrounding it cools an object that is heated by a constantpower source. What would happen to its temperature, if the
surrounding air were replaced (a) by helium and (b) by argon?
2.8 What is the heat flow by thermal conduction between two 0.1 m2
sheets of copper with a temperature difference of 100°C and which
are separated by 0.1 cm of C02 at pressures of (a) lo5 Pa, (b) lo3 Pa,
and (c) 100 Pa.
2.9 A 0.5-cm-diameter tube interconnects two chambers. The left-hand
chamber is heated to a temperature of 250°C, while the right-hand
chamber remains at room temperature. Over what pressure range is
the pressure in the two chambers the same? Over what pressure range
does the transpiration equation apply? Sketch a plot of Pha/Pmld versus
the pressure of the cold chamber. Assume diffuse scattering.
2.10111 Problem 2.9, nitrogen is replaced by helium. Sketch a plot of
Phot/Pcoldversus the pressure of the cold chamber in the transition
region. How does this compare to the curve in Problem 2.9 for
helium?