Molecular kinetic theory model (A-level only) Flashcards – AQA A-level Physics (7408)

What is Brownian motion?

The irregular, random movement of small particles suspended in a fluid.

Why does a suspended particle in Brownian motion change direction unpredictably?

Fluid molecules bombard it unevenly, causing the resultant force to fluctuate.

What does visible Brownian motion provide indirect evidence for?

That matter is made of atoms and molecules in continual random motion.

How does the size of a particle undergoing Brownian motion compare with that of the molecules striking it?

The suspended particle is much larger than the molecules.

For a fixed amount of gas at constant temperature, how are pressure and volume related?

Pressure is inversely proportional to volume: $p \propto \frac{1}{V}$.

For a fixed amount of gas at constant volume, how are pressure and absolute temperature related?

Pressure is directly proportional to absolute temperature: $p \propto T$.

For a fixed amount of gas at constant pressure, how are volume and absolute temperature related?

Volume is directly proportional to absolute temperature: $V \propto T$.

What equation relates pressure, volume and absolute temperature for a fixed amount of ideal gas?

$\frac{pV}{T} = \text{constant}$

How does the molecular model explain gas pressure?

Gas molecules collide with the walls of their container.

Why does reducing a gas's volume at constant temperature increase its pressure?

Molecules collide with the container walls more frequently.

How does increasing gas temperature affect molecular kinetic energy and collisions?

Average molecular kinetic energy increases, making collisions more frequent and more forceful.

How do gas laws and molecular kinetic theory differ in their approach to gas behaviour?

Gas laws are empirical relationships established by observation and measurement; molecular kinetic theory explains them using assumptions about molecular motion.

How does the simple kinetic theory model represent the molecules of a gas?

As a large number of equal-mass point particles moving randomly, with negligible volume compared with the container.

What does the simple kinetic theory model assume about forces between gas molecules?

They exert no forces on one another except during collisions.

What does the simple kinetic theory model assume about collisions?

Collisions between molecules and with the walls are elastic.

Which laws govern molecular motion in the simple kinetic theory model?

Newton’s laws of motion.

What does isotropic molecular motion imply about the mean squared velocity components?

They are equal, so $\langle c_x^2\rangle=\langle c_y^2\rangle=\langle c_z^2\rangle=\frac{1}{3}\langle c^2\rangle$.

In an elastic wall collision, what is the magnitude of the momentum transferred by a molecule of mass $m$ with perpendicular velocity component $c_x$?

$2m|c_x|$

For a molecule with perpendicular velocity component $c_x$ in a cubic container of side $L$, what is the time between successive collisions with the same wall?

$\frac{2L}{|c_x|}$

What average force does a molecule of mass $m$ and perpendicular velocity component $c_x$ exert on a wall of a cubic container of side $L$?

$\frac{mc_x^2}{L}$

In kinetic theory, how is gas pressure expressed as a sum of the molecules’ squared velocity components perpendicular to a wall?

$p=\frac{m}{V}\sum_i c_{x,i}^2$

What is the kinetic theory equation relating gas pressure and volume to molecular number, mass and rms speed?

$pV=\frac{1}{3}Nm(c_{\mathrm{rms}})^2$

How is the root mean square molecular speed defined in terms of mean squared speed?

$c_{\mathrm{rms}}=\sqrt{\langle c^2\rangle}$

What is the mean translational kinetic energy per molecule of an ideal gas in terms of molecular mass, RMS speed and absolute temperature?

$\frac{1}{2}m(c_{\mathrm{rms}})^2=\frac{3}{2}kT=\frac{3RT}{2N_A}$

How is the Boltzmann constant $k$ related to the molar gas constant $R$ and Avogadro constant $N_A$?

$k=\frac{R}{N_A}$

How do the mean translational kinetic energies per molecule of ideal gases at the same absolute temperature compare?

They are equal, even if molecular masses and RMS speeds differ.

What is the internal energy of a monatomic ideal gas?

The total random kinetic energy of its atoms.

What is the internal energy of a monatomic ideal gas containing $N$ atoms at absolute temperature $T$?

$U=\frac{3}{2}NkT$