Kinetic Particle Model of Matter: Question 3

Worked solution

Part (a): Converting to kelvin

To convert a Celsius temperature to kelvin, add 273:

$T(\text{K}) = \theta(\text{°C}) + 273$

$T = 17 + 273$

$T = \boxed{290}\text{ K}$

Part (b): Explaining the pressure increase

Since the cylinder is rigid, its volume cannot change, so any change in pressure must come from what is happening to the particles themselves.

1. Heating the gas transfers energy to its particles, increasing their average kinetic energy. On average, they move faster.
2. Faster particles travel across the fixed volume more quickly, so they collide with the cylinder walls more frequently in a given time.
3. Faster particles also hit the walls harder. Each collision produces a bigger change of momentum, meaning a bigger force on the wall.

More frequent, harder collisions in the same fixed area mean a greater total force per unit area on the walls, which is exactly what pressure measures. So the pressure of the gas increases as it is heated.

Part (c): Absolute zero

Absolute zero is the lowest possible temperature, equal to $-273\text{°C}$ (which corresponds to $0\text{ K}$). At this temperature, the particles of the gas have the least kinetic energy possible. Their motion is reduced to a minimum, but this is not the same as saying they have zero kinetic energy or have stopped moving entirely.

Final answers

• (a) $290\text{ K}$
• (b) Faster particles collide with the walls more often and with greater force, increasing the pressure at constant volume.
• (c) Absolute zero $= -273\text{°C}$; particles have the least possible kinetic energy at this temperature.