Phases and Phase Changes
Answers to Even-numbered Conceptual Questions
Carbon is monatomic, whereas oxygen is diatomic.
Therefore, one mole of oxygen has
twice as many atoms as one mole of carbon.
The bubble wrap is more effective on a warm day because the air pressure within the
bubbles will be greater, leading to more effective cushioning.
At low temperature, the
bubbles are almost flat.
If the temperature of the air in a house is increased, and the amount of air in the house
remains constant, it follows from the ideal-gas law that the pressure will increase as well.
If the pressure and volume are changed in such a way that their product remains the
same, it follows from the ideal-gas law that the temperature of the gas will remain the
If the temperature of the gas is the same, the average kinetic energy of its
molecules will not change.
Both types of molecules have the same average kinetic energy, because they experience
the same temperature.
Since the oxygen molecules are more massive, however, it follows
that their rms speed is less than the rms speed of the nitrogen.
In general, heavier
molecules move more slowly for a given temperature.
The ratio of oxygen to nitrogen decreases with increasing altitude.
The reason is that
oxygen molecules move more slowly than nitrogen molecules, on average, and are
therefore unable to rise as high above the ground as nitrogen molecules.
Airplanes can have a difficult time taking off from high-altitude airports because the air is
thin, and provides less lift than air at sea level.
When the air is cool, however, its density
is greater than when it is warm.
Therefore, taking off in the morning or evening will
provide the airplane with more lift – which can be very important at high altitude.
If the absolute temperature of an ideal gas is doubled, the average kinetic energy of its
molecules doubles as well.
Recall that kinetic energy depends on speed squared, however.
It follows, then, that the average speed of the molecules increases by a factor less than 2;
in fact, the speed increases by a factor of the square root of 2.
The change in length is inversely proportional to the cross sectional area, as we see in
The solid rod has the greater effective cross-sectional area – since the
hollow part of the other rod doesn’t resist compression.
Therefore, the hollow rod has the
greater change in length.
The temperature at which water boils on a mountain top is less than its boiling
temperature at sea level – due to the low atmospheric pressure on the mountain.
Therefore, if the stove is barely able to boil water on the mountain, it will not be able to
boil it at sea level, where the required temperature is greater.