9702 · 15.3
Kinetic theory of gases flashcards
Revision flashcards for Cambridge 9702 Kinetic theory of gases (syllabus 15.3). Flip, recall, then mark a real past-paper question.
Card
What key assumption does the kinetic theory of gases make about intermolecular forces?
It assumes there are no intermolecular forces between ideal gas molecules, except during instantaneous collisions.
Card
State the kinetic theory equation for gas pressure ($P$).
$P = \frac{1}{3}\frac{Nm\overline{c^2}}{V}$
Card
How is the average translational kinetic energy ($E_k$) of a gas molecule related to absolute temperature ($T$)?
It is directly proportional to the absolute temperature: $E_k = \frac{3}{2}kT$
Card
What does $\overline{c^2}$ represent in the kinetic theory equations?
$\overline{c^2}$ is the mean square speed of the gas molecules.
Card
Name a phenomenon that provides evidence for the constant, random motion of molecules.
Brownian motion.
Card
What is the change in momentum for a gas molecule of mass $m$ and speed $u$ that undergoes a perfectly elastic collision perpendicular to a container wall?
$2mu$
Card
Why must temperature be in Kelvin for kinetic theory calculations?
Kelvin is the absolute temperature scale, where 0 K represents zero average molecular kinetic energy.
Card
How is the Boltzmann constant ($k$) related to the molar gas constant ($R$) and Avogadro constant ($N_A$)?
$k = R/N_A$
Card
What assumption is made about the volume of the gas molecules themselves?
The total volume occupied by the molecules is negligible compared to the total volume of the gas container.
Card
What is the total translational kinetic energy for $N$ molecules in an ideal gas?
$N \times \frac{3}{2}kT$
Card
What are the five main assumptions of the kinetic theory for an ideal gas?
1. Molecules are in random motion. 2. No intermolecular forces. 3. Volume of molecules is negligible. 4. Collisions are perfectly elastic. 5. Collision time is negligible.
Card
What is the relationship between root-mean-square speed ($c_{rms}$) and mean square speed ($\overline{c^2}$)?
$c_{rms} = \sqrt{\overline{c^2}}$
Card
What is the total internal energy of an ideal monatomic gas with N molecules at temperature T?
The internal energy is the sum of the kinetic energies of all molecules: $U = N \times E_k = N \times \frac{3}{2}kT$. For an ideal gas, potential energy is zero.
Card
What does 'perfectly elastic collision' mean in the context of kinetic theory?
It means that both momentum and kinetic energy are conserved during the collision.