Physics P2 - Kinetic Theory Model

What is Brownian motion?

It is the random motion of larger particles in a fluid caused by collisions with surrounding particles.

How does a simple molecular model explain Boyle’s law?

If you increase the volume of a fixed mass of gas, its molecules will move further apart so collisions will be less frequent therefore pressure decreases.

How does a simple molecular model explain Charles’s law?

When a temperature of a gas is increased, its molecules gain kinetic energy therefore move quicker therefore molecules move further apart and volume increases.

How does a simple molecular model explain Pressure law?

When gas temperature is increased, its molecules gain Ek meaning they will move more quickly, as volume is constant the frequency of particles-container collisions increases and they collide at a higher speed, therefore increased pressure.

What is the kinetic theory model?

It relates several features of a fixed mass of gas, and uses assumptions to derive the equation.

What is the assumption made about intermolecular forces?

No intermolecular forces act on molecules.

What assumption is made about duration of collisions?

Negligable in comparison to time between collisions.

What assumptions are made about motion?

• Random

• Elastic collisions

• Follow Newton’s laws

• Move in straight lines

What is the equation for kinetic model theory?

pV = 1/3 * Nmc²

What is mean square speed?

The mean of all the square speeds of the gas molecules.

What is an ideal gas?

A gas that follows all gas laws perfectly.

How much potential energy does an ideal gas have?

Zero.

What is the first step in deriving pV = 1/3Nmc²?

Find the force due to a single particle.

How do you find the force due to a single particle?

• Average force = rate of change of momentum

• Change in momentum = mu—mu = 2mu

• Time between collisions = distance / speed = 2L3/u

• Average force = change in p / time = 2mu * (u/2L3) = mu²/L3

What is the second step of deriving pV = 1/3Nmc²?

Considering all particles acting on one wall

What is the third step of deriving pV = 1/3Nmc²?

Considering all directions.

What is the fourth and final step of deriving pV = 1/3Nmc²?

Considering pressure.

How do you consider all particles when deriving pV = 1/3Nmc²?

• Calculate total average force = m/L3 * (u1²+u2²+…)

• Calculate mean square speed which is sum of square speeds / number of particles

• Average force = mNu²/L3

How do you consider all directions when deriving pV = 1/3Nmc²?

• Use pythagoras to calculate resultant c²

• As u² = v² = w², c² = 3u²

• Therefore u² = c²/3

• Average force on Y = mNc²/3L3

How do you consider pressure when deriving pV = 1/3Nmc²?

• Pressure = force/area

• Area of Y = L1L2

• Pressure = 1/3 * Nmc²/L1L2L3

• Pressure = 1/3 * Nmc²/V

• pV = 1/3 Nmc²

What is the equation for density involving ideal gases?

Density = number of molecules * mass / volume

What equation links kinetic energy and molecules?

Ek = N * 3kT/2