Gas Pressure and Temperature

Gas particles move rapidly and randomly in all directions. When they collide with the walls of their container, they exert a force on the wall. The total force of billions of these collisions per second creates gas pressure.

$\text{Pressure} = \frac{\text{Total force from collisions}}{\text{Area of container walls}}$

When the temperature of a gas increases (at constant volume):

1. Particles gain kinetic energy → move faster
2. They collide with the walls more frequently and with greater force
3. Therefore, the pressure increases

Relationship: $P \propto T$ (pressure is directly proportional to absolute temperature, at constant volume)

Boyle's Law: For a fixed mass of gas at constant temperature:

$\boxed{P_1 V_1 = P_2 V_2}$

Or: $PV = \text{constant}$

When volume decreases (at constant temperature):

1. Particles are in a smaller space
2. They hit the walls more frequently
3. Pressure increases

Pressure and volume are inversely proportional (at constant temperature).

Absolute zero is the lowest possible temperature: −273°C (or 0 K).

At absolute zero, particles have minimum internal energy — they (theoretically) stop moving entirely.

Converting Temperature

$T(K) = T(°C) + 273$ $T(°C) = T(K) - 273$

Important: Gas law calculations must use Kelvin, not Celsius.

For a fixed mass of gas:

$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$

Where $T$ is in Kelvin.

• Gas pressure is caused by particle collisions with container walls
• Higher temperature → faster particles → more frequent/harder collisions → higher pressure
• Boyle's Law: $P_1V_1 = P_2V_2$ (constant temperature)
• Absolute zero: −273°C = 0 K (minimum energy)
• Kelvin = Celsius + 273; always use Kelvin in gas calculations