Pressure & Volume

Relationship Between Pressure and Volume

Pressure and volume of a gas are inversely proportional when the temperature is kept constant. This means that if the volume decreases, the pressure increases, and vice versa.

This relationship is described by Boyle's Law, which states:

$$P \propto \frac{1}{V}$$

or more precisely,

$$P \times V = \text{constant}$$

where:

• P is the pressure of the gas (in pascals, Pa)
• V is the volume of the gas (in cubic metres, m8 or cubic centimetres, cm8)

This means if you halve the volume of a gas, its pressure doubles (assuming temperature stays the same).

For example, if a gas at a pressure of 100 kPa occupies a volume of 2.0 m8, reducing the volume to 1.0 m8 will increase the pressure to 200 kPa.

The effect of changing volume on pressure is important in many real-life situations, such as inflating tyres or syringes.

Remember, Boyle's Law only applies if the temperature and the amount of gas remain constant.

For instance, if a gas has a volume of 4.0 litres at a pressure of 50 kPa, and the volume is reduced to 2.0 litres, the new pressure is:

$$P_1 V_1 = P_2 V_2$$

$$50 \times 4.0 = P_2 \times 2.0$$

$$P_2 = \frac{50 \times 4.0}{2.0} = 100 \text{ kPa}$$

Particle Model Explanation

According to the particle model, gases are made up of tiny particles (atoms or molecules) that move randomly in all directions.

These particles collide with each other and with the walls of their container.

Each collision with the container walls exerts a small force on the wall. The pressure of the gas is the total force from all these collisions per unit area of the container walls.

If the volume of the container is reduced, the particles have less space to move around.

This causes the particles to collide with the walls more frequently, increasing the total force per unit area, and thus increasing the pressure.

So, reducing volume increases collision frequency, which increases pressure.

This explains why pressure and volume are inversely related: smaller volume means particles hit the walls more often, raising pressure.

Practical Applications

This relationship between pressure and volume is seen in everyday objects and biological processes:

• Syringes: When you pull the plunger back, the volume inside the syringe increases, so the pressure decreases. This causes air or liquid to be drawn in.
• Balloons: Squeezing a balloon reduces its volume, increasing the pressure inside, which makes the balloon feel harder.
• Breathing: Breathing works by changing the volume of the chest cavity. When you breathe in, the chest volume increases, pressure inside the lungs decreases, and air flows in. When you breathe out, volume decreases, pressure increases, and air flows out.
• Pressure changes in containers: If a sealed containers volume is reduced (e.g., squeezing a plastic bottle), the pressure inside increases, which can cause the container to deform or burst if the pressure gets too high.

Understanding pressure and volume changes helps in designing medical devices, sports equipment, and understanding natural processes like breathing.

Example: When you breathe in, the diaphragm moves down, increasing the chest volume. This lowers the pressure inside the lungs below atmospheric pressure, causing air to flow in.