2.2 Pressure, Temperature, and RMS Speed

If you consider a very small object, such as a grain of pollen, in a gas, then the number of molecules striking its surface would also be relatively small. Would you expect the grain of pollen to experience any fluctuations in pressure due to statistical fluctuations in the number of gas molecules striking it in a given amount of time?

Which has a longer mean free path, liquid water or water vapor in the air?

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?

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?

Which is more dangerous, a closet where tanks of nitrogen are stored, or one where tanks of carbon dioxide are stored?

In the problems in this section, assume all gases are ideal.

A person hits a tennis ball with a mass of 0.058 kg against a wall. The average component of the ball’s velocity perpendicular to the wall is 11 m/s, and the ball hits the wall every 2.1 s on average, rebounding with the opposite perpendicular velocity component. (a) What is the average force exerted on the wall? (b) If the part of the w…

In the problems in this section, assume all gases are ideal.

Five bicyclists are riding at the following speeds: 5.4 m/s, 5.7 m/s, 5.8 m/s, 6.0 m/s, and 6.5 m/s. (a) What is their average speed? (b) What is their rms speed?

In the problems in this section, assume all gases are ideal.

Typical molecular speeds $\left(v_{\text{rms}}\right)$ are large, even at low temperatures. What is $v_{\text{rms}}$ for helium atoms at 5.00 K, less than one degree above helium’s liquefaction temperature?

In the problems in this section, assume all gases are ideal.

What is the ratio of the average translational kinetic energy of a nitrogen molecule at a temperature of 300 K to the gravitational potential energy of a nitrogen-molecule−Earth system at the ceiling of a 3-m-tall room with respect to the same system with the molecule at the floor?

In the problems in this section, assume all gases are ideal.

The product of the pressure and volume of a sample of hydrogen gas at $0.00 ° \text{C}$ is 80.0 J. (a) How many moles of hydrogen are present? (b) What is the average translational kinetic energy of the hydrogen molecules? (c) What is the value of the product of pressure and volume at $200 ° \text{C}?$

In the problems in this section, assume all gases are ideal.

If the rms speed of oxygen molecules inside a refrigerator of volume $22.0 \text{ft} .^{3}$ is 465 m/s, what is the partial pressure of the oxygen? There are 5.71 moles of oxygen in the refrigerator, and the molar mass of oxygen is 32.0 g/mol.

In the problems in this section, assume all gases are ideal.

The escape velocity from the Moon is much smaller than that from the Earth, only 2.38 km/s. At what temperature would hydrogen molecules (molar mass is equal to 2.016 g/mol) have a root-mean-square velocity $v_{\text{rms}}$ equal to the Moon’s escape velocity?

In the problems in this section, assume all gases are ideal.

Suppose that the typical speed $\left(v_{\text{rms}}\right)$ of carbon dioxide molecules (molar mass is 44.0 g/mol) in a flame is found to be 1350 m/s. What temperature does this indicate?

In the problems in this section, assume all gases are ideal.

There are two important isotopes of uranium, $^{235} \text{U}$ and $^{238} \text{U}$; these isotopes are nearly identical chemically but have different atomic masses. Only $^{235} \text{U}$ is very useful in nuclear reactors. Separating the isotopes is called uranium enrichment (and is often in the news as of this writing, because of concerns that some countries are enriching uranium…

In the problems in this section, assume all gases are ideal.

Dry air consists of approximately $78 \% \text{nitrogen} , 21 \% \text{oxygen} , \text{and} 1 \% \text{argon}$ by mole, with trace amounts of other gases. A tank of compressed dry air has a volume of 1.76 cubic feet at a gauge pressure of 2200 pounds per square inch and a temperature of 293 K. How much oxygen does it contain in moles?

In the problems in this section, assume all gases are ideal.

(a) Given that air is $21 \%$ oxygen, find the minimum atmospheric pressure that gives a relatively safe partial pressure of oxygen of 0.16 atm. (b) What is the minimum pressure that gives a partial pressure of oxygen above the quickly fatal level of 0.06 atm? (c) The air pressure at the summit of Mount Everest (8848 m) is 0.334 atm. Why have…