Conceptual Questions
2.1 Molecular Model of an Ideal Gas
Two molecules can react with one molecule to produce two molecules. How many moles of hydrogen molecules are needed to react with one mole of oxygen molecules?
Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?
A constant-volume gas thermometer contains a fixed amount of gas. What property of the gas is measured to indicate its temperature?
Inflate a balloon at room temperature. Leave the inflated balloon in the refrigerator overnight. What happens to the balloon, and why?
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.
2.2 Pressure, Temperature, and RMS Speed
How is momentum related to the pressure exerted by a gas? Explain on the molecular level, considering the behavior of molecules.
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?
What is the average velocity of the air molecules in the room where you are right now?
Why do the atmospheres of Jupiter, Saturn, Uranus, and Neptune, which are much more massive and farther from the Sun than Earth is, contain large amounts of hydrogen and helium?
Statistical mechanics says that in a gas maintained at a constant temperature through thermal contact with a bigger system (a “reservoir”) at that temperature, the fluctuations in internal energy are typically a fraction of the internal energy. As a fraction of the total internal energy of a mole of gas, how big are the fluctuations in the internal energy? Are we justified in ignoring them?
Which is more dangerous, a closet where tanks of nitrogen are stored, or one where tanks of carbon dioxide are stored?
2.3 Heat Capacity and Equipartition of Energy
Experimentally it appears that many polyatomic molecules’ vibrational degrees of freedom can contribute to some extent to their energy at room temperature. Would you expect that fact to increase or decrease their heat capacity from the value R? Explain.
One might think that the internal energy of diatomic gases is given by Do diatomic gases near room temperature have more or less internal energy than that? Hint: Their internal energy includes the total energy added in raising the temperature from the boiling point (very low) to room temperature.
You mix 5 moles of at 300 K with 5 moles of He at 360 K in a perfectly insulated calorimeter. Is the final temperature higher or lower than 330 K?
2.4 Distribution of Molecular Speeds
One cylinder contains helium gas and another contains krypton gas at the same temperature. Mark each of these statements true, false, or impossible to determine from the given information. (a) The rms speeds of atoms in the two gases are the same. (b) The average kinetic energies of atoms in the two gases are the same. (c) The internal energies of 1 mole of gas in each cylinder are the same. (d) The pressures in the two cylinders are the same.
Repeat the previous question if one gas is still helium but the other is changed to fluorine, .
An ideal gas is at a temperature of 300 K. To double the average speed of its molecules, what does the temperature need to be changed to?