13.4 Kinetic theory: atomic and molecular explanation of pressure  (Page 5/6)

What is the average kinetic energy of a nitrogen molecule (N ₂ ) if its rms speed is 560 m/s? At what temperature is this rms speed achieved?

What will be the ratio of kinetic energies and rms speeds of a nitrogen molecule and a helium atom at the same temperature?

How is momentum related to the pressure exerted by a gas? Explain on the atomic and molecular level, considering the behavior of atoms and molecules.

Some incandescent light bulbs are filled with argon gas. What is $v_{\text{rms}}$ for argon atoms near the filament, assuming their temperature is 2500 K?

Average atomic and molecular speeds $(v_{\text{rms}})$ are large, even at low temperatures. What is $v_{\text{rms}}$ for helium atoms at 5.00 K, just one degree above helium’s liquefaction temperature?

(a) What is the average kinetic energy in joules of hydrogen atoms on the $\text{5500}\text{º}\text{C}$ surface of the Sun? (b) What is the average kinetic energy of helium atoms in a region of the solar corona where the temperature is $6\text{.}\text{00}\times {\text{10}}^5\text{K}$ ?

The escape velocity of any object from Earth is 11.2 km/s. (a) Express this speed in m/s and km/h. (b) At what temperature would oxygen molecules (molecular mass is equal to 32.0 g/mol) have an average velocity $v_{\text{rms}}$ equal to Earth’s escape velocity of 11.1 km/s?

The escape velocity from the Moon is much smaller than from Earth and is only 2.38 km/s. At what temperature would hydrogen molecules (molecular mass is equal to 2.016 g/mol) have an average velocity $v_{\text{rms}}$ equal to the Moon’s escape velocity?

Nuclear fusion, the energy source of the Sun, hydrogen bombs, and fusion reactors, occurs much more readily when the average kinetic energy of the atoms is high—that is, at high temperatures. Suppose you want the atoms in your fusion experiment to have average kinetic energies of $6\text{.}\text{40}\times {\text{10}}^{–\text{14}}\text{J}$ . What temperature is needed?

Suppose that the average velocity $(v_{\text{rms}})$ of carbon dioxide molecules (molecular mass is equal to 44.0 g/mol) in a flame is found to be $1\text{.}\text{05}\times {\text{10}}^5\text{m/s}$ . What temperature does this represent?

Hydrogen molecules (molecular mass is equal to 2.016 g/mol) have an average velocity $v_{\text{rms}}$ equal to 193 m/s. What is the temperature?

Much of the gas near the Sun is atomic hydrogen. Its temperature would have to be $1\text{.}5\times {\text{10}}^7\text{K}$ for the average velocity $v_{\text{rms}}$ to equal the escape velocity from the Sun. What is that velocity?

There are two important isotopes of uranium— ${}^{\text{235}}\text{U}$ and ${}^{\text{238}}\text{U}$ ; these isotopes are nearly identical chemically but have different atomic masses. Only ${}^{\text{235}}\text{U}$ is very useful in nuclear reactors. One of the techniques for separating them (gas diffusion) is based on the different average velocities $v_{\text{rms}}$ of uranium hexafluoride gas, ${\text{UF}}_6$ . (a) The molecular masses for ${}^{\text{235}}\text{U}$ ${\text{UF}}_6$ and ${}^{\text{238}}\text{U}$ ${\text{UF}}_6$ are 349.0 g/mol and 352.0 g/mol, respectively. What is the ratio of their average velocities? (b) At what temperature would their average velocities differ by 1.00 m/s? (c) Do your answers in this problem imply that this technique may be difficult?