Question 1

A molecule in a box collides elastically with a wall. Which statement best describes the change in its velocity components after the collision?

Accepted Answer

The x-component of velocity reverses direction, while the y-component remains unchanged.

Question 2

In the kinetic theory derivation, what is the change in momentum ($$\Delta p) of a $$molecule with mass $$m$$ and velocity component $$v_x$$ after it collides with a wall perpendicular to the x-axis?

Accepted Answer

$$\Delta p = -2mv_x ($$for the molecule), but the wall receives $$+2mv_x$$

Question 3

Given a cubical box of length $$l$$, what is the time required for a molecule with velocity component $$v_x to $$travel from one wall to the opposite wall?

Accepted Answer

$$t = \frac{l}{v_x}$$

Question 4

How is the pressure $$p$$ exerted by an ideal gas related to the density $$\rho$$ and the average squared speed $$v^2 of $$its molecules?

Accepted Answer

$$p = \frac{1}{3} \rho v^2$

Question 5

If the average squared speed of molecules in a gas is $$v^2$$, what is the average value of the squared x-component $$v_x^2$?

Accepted Answer

$$v_x^2$ = \frac{1}{3} v^2$

Question 6

A hydrogen molecule ($$\mathrm{H}_2) at$$ $$0.0\ ^\circ\mathrm{C}$$ has a molar mass $$M_{H_2$} = 0.002\ \mathrm{kg/mol}. $$What is the root-mean-square speed ($$v_{rms}) of $$the molecules? Use $$R = 8.314\ \mathrm{J/(mol\cdot K)}$$ and $$T = 273.15\ \mathrm{K}.$$

Accepted Answer

$$v_{rms} = \sqrt{\frac{3RT}{M}} = 1846\ \mathrm{m/s}$$

Question 7

Which equation connects the root-mean-square speed $$v_{rms} of $$gas molecules to the pressure $$p$$ and density $$\rho$$?

Accepted Answer

$$v_{rms} = \sqrt{\frac{3p}{\rho}}$$

Question 8

What is the physical significance of the equation $$p = \frac{1}{3} \rho v^2$ in kinetic theory?

Accepted Answer

It relates the macroscopic observable pressure to the molecular speed and density.

Question 9

According to kinetic theory, what happens to the average kinetic energy per molecule as the temperature increases?

Accepted Answer

It increases.

Question 10

Which statement best describes the mean free path $$\lambda of a $$gas molecule?

Accepted Answer

It decreases as the radius of the molecule increases.

Question 11

A gas at room temperature and atmospheric pressure has a mean free path $$\lambda \approx 10$$^{-7}$$\ \mathrm{m}. If $$the molecular diameter is $$0.3\ \mathrm{nm}$$, how does $$\lambda$$ compare to the molecular diameter?

Accepted Answer

$$\lambda is $$about 300 times the molecular diameter.

Question 12

Which law states that the pressure in a fluid is transmitted equally in all directions?

Accepted Answer

Pascal's Law

Question 13

If a molecule collides with a wall and its speed $$v$$ does not change, what happens to its kinetic energy?

Accepted Answer

It remains unchanged.

Question 14

Which parameter is used to describe the average time between collisions of gas molecules?

Accepted Answer

Mean free time

Question 15

A gas molecule travels a mean free path $$\lambda$$ between collisions. If the number density of molecules increases, what happens to $$\lambda$$?

Accepted Answer

$$\lambda$$ decreases.

Question 16

Which equation expresses the root-mean-square speed $$v_{rms} in $$terms of the gas constant $$R$$, temperature $$T$$, and molar mass $$M$$?

Accepted Answer

$$v_{rms} = \sqrt{\frac{3RT}{M}}$$

Question 17

Which physical property is directly proportional to the absolute temperature in kinetic theory?

Accepted Answer

Translational kinetic energy

Question 18

In the kinetic theory, what is the relationship between the average values of $$v_x^2$, v$$_$$y^2$$, and $$v_z^2$ for a large number of randomly moving molecules?

Accepted Answer

They are all equal and each is $$\frac{1}{3} of$$ $$v^2.$$

Question 19

Which of the following best describes the connection between the gas constant $$R$$, Boltzmann constant $$k$$, and Avogadro's number $$N_A$$?

Accepted Answer

$$R = k N_A$$

Kinetic Theory of Gases: Pressure, Molecular Speeds, and Collisions

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