Kinetic Particle Model of Matter Worked ExamplesIGCSE Physics 0625

(a) Y has particles touching in a regular, repeating pattern: solid. X has particles close together (mostly touching) but in an irregular arrangement: liquid. Z has particles far apart: gas.

(b) Separation: the particles in a gas are far apart — the distance between them is much larger than the size of a particle.

Arrangement: they are arranged randomly (irregularly), with no pattern.

Motion: they move rapidly in random directions, travelling in straight lines between collisions with each other and with the walls.

A liquid flows and takes the shape of the bottom of its container, so it has no fixed shape.

Its particles are close together, so a liquid has a fixed volume and is not easily compressed — there is almost no space between the particles.

So the answer is B. A describes a gas, C describes a solid, and D does not describe any state.

(a) Add $273$ to a Celsius temperature to get kelvin.

(b) The particles move faster on average: the average kinetic energy of the particles increases as the temperature rises.

(c) Absolute zero ($0\text{ K}$, or $-273\,^{\circ}\text{C}$) is the lowest possible temperature, at which the particles have the least possible kinetic energy.

The container is rigid, so the volume is constant and the particles do not move further apart on average. Heating increases the average speed of the particles.

Faster particles collide with the walls more frequently, and each collision exerts a greater force. So the force per unit area — the pressure — increases. The answer is B.

A is a misconception: the particles themselves do not get bigger. C is wrong because the volume is fixed. D is wrong because the mass is fixed, so the number of particles cannot change.

(a) When a particle hits the wall and bounces back, its direction of motion changes, so its momentum changes. A change of momentum needs a force: the wall exerts a force on the particle, and the particle exerts an equal and opposite force on the wall.

Very many particles hit the wall every second, so their forces add up to a steady total force on the wall. Pressure is this force per unit area of the wall.

(b) At constant temperature the particles keep the same average speed, so each collision gives the same force on average. In a smaller volume the particles are closer together and have less distance to travel between walls, so they hit each unit area of the walls more frequently.

More collisions per second on each unit area means a greater force per unit area, so the pressure increases.

(a) The smoke particle moves in a random, jerky (zig-zag) way — short straight movements in constantly changing directions.

(b) The smoke particle is hit by air molecules, which are much smaller and lighter but are moving very fast in random directions.

At any instant the number of collisions on different sides of the smoke particle is unequal, so there is a resultant force on it in a random direction. This force keeps changing, so the smoke particle's direction keeps changing.

(c) Air molecules are far too small to be seen with a light microscope; only the much larger smoke particles are visible. The random motion of the visible smoke particles is evidence for the invisible, fast-moving air molecules.

Air (gas): the molecules are very far apart compared with their size, so most of the volume is empty space. The forces between the molecules are very weak (almost zero except during collisions).

So the molecules can easily be pushed closer together — the air is easily compressed and the plunger moves a long way.

Water (liquid): the molecules are already very close together, almost touching.

Pushing them any closer causes very strong repulsive forces between them, so the water can hardly be compressed and the plunger barely moves.

For a fixed mass of gas at constant temperature, $pV$ is constant. Multiply pressure by volume for each reading.

Reading 3 is the odd one out. The correct volume would be:

So the answer is B. Checking only whether the volume decreases as the pressure increases is not enough — every reading does that.

(a) A fixed mass of gas at constant temperature obeys $pV = \text{constant}$. List the quantities first.

Write the equation and rearrange for $V_2$.

Substitute.

(b) At constant temperature the particles have the same average speed. In a larger volume they are further apart and have further to travel between collisions with the walls, so they hit each unit area of the walls less frequently.

Fewer collisions per second on each unit area give a smaller force per unit area, so the pressure is lower.

Boyle's law says $pV = \text{constant}$. So a graph of $pV$ against $p$ is a horizontal straight line: whatever the pressure, $pV$ has the same value. That is A.

B shows $p$ and $V$ in a linear relationship with a straight line; for $pV = \text{constant}$, the graph of $p$ against $V$ is a curve (halving $V$ doubles $p$), so B is wrong.

C shows $pV$ increasing with $p$, which is not constant. D is wrong because $p = \frac{\text{constant}}{V}$, so $p$ against $\frac{1}{V}$ is a straight line through the origin, not a curve.

(a) Go across from $240\text{ kPa}$ to the curve and down. The reading is halfway between $10$ and $15\text{ cm}^3$.

(b) Take two points that are far apart on the curve and multiply.

The products are equal, so $pV$ is constant: doubling the volume halves the pressure.

(c) Use the constant.

(d) Compressing the air quickly warms it slightly. Boyle's law only applies at constant temperature, so she waits for the air to return to room temperature before reading the pressure.

(a) The trapped air is at the same pressure as the water at its surface inside the bell: atmospheric pressure plus the pressure due to $12\text{ m}$ of water.

Add atmospheric pressure.

(b) The mass of air and its temperature are fixed, so $p_1V_1 = p_2V_2$.

Evaluate. The pressure has roughly doubled, so the volume has roughly halved.