UniversityPhysicsVolume2-Ch02. Old Dominion University PHYS 232N

Unit 1: Thermodynamics
Chapter 2: The Kinetic Theory of Gases
University Physics Volume II
Unit 1: Thermodynamics
Chapter 2: The Kinetic Theory of Gases
Conceptual Questions
1. Two H2 molecules can react with one O2 molecule to produce two H2O molecules. How many
moles of hydrogen molecules are needed to react with one mole of oxygen molecules?
Solution
2 moles, as that will contain twice as many molecules as the 1 mole of oxygen
2. Under what circumstances would you expect a gas to behave significantly differently than
predicted by the ideal gas law?
Solution
sufficiently high pressure and low temperature that it’s close to liquefaction
3. A constant-volume gas thermometer contains a fixed amount of gas. What property of the gas
is measured to indicate its temperature?
Solution
pressure
4. Inflate a balloon at room temperature. Leave the inflated balloon in the refrigerator overnight.
What happens to the balloon, and why?
Solution
It shrinks and feels softer. The temperature decreased at a fixed amount of gas in the same, so the
pressure and volume decreased.
5. In the last chapter, free convection was explained as the result of buoyant forces on hot fluids.
Explain the upward motion of air in flames based on the ideal gas law.
Solution
The flame contains hot gas (heated by combustion). The pressure is still atmospheric pressure, in
mechanical equilibrium with the air around it (or roughly so). The density of the hot gas is
proportional to its number density N/V (neglecting the difference in composition between the gas
in the flame and the surrounding air). At higher temperature than the surrounding air, the ideal
gas law says that N V p k T / = / B is less than that of the surrounding air. Therefore the hot air has
lower density than the surrounding air and is lifted by the buoyant force.
6. How is momentum related to the pressure exerted by a gas? Explain on the molecular level,
considering the behavior of molecules.
Solution
The pressure of a gas is caused by the change in momentum of the molecules when they collide,
as they exert a force equal to the change in momentum divided by the time between collisions.
7. If one kind of molecule has double the radius of another and eight times the mass, how do
their mean free paths under the same conditions compare? How do their mean free times
compare?
Solution
The mean free path is inversely proportional to the square of the radius, so it decreases by a
factor of 4. The mean free time is proportional to the mean free path and inversely proportional
to the rms speed, which in turn is inversely proportional to the square root of the mass. That
gives a factor of 8 in the numerator, so the mean free time decreases by a factor of 2.
8. What is the average velocity of the air molecules in the room where you are right now?
Solution
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