Particle Model and Pressure

This section explains particle model and pressure covering, gas under pressure, increasing and decreasing the temperature of gas, Gay-Lussac’s Law and when the volume of gas is altered: Boyle’s Law. 

Gas Under Pressure

In a gas, particles are in constant, random motion, and they collide with the walls of their container. These collisions create a force, which, when spread over the area of the container's walls, results in pressure. The pressure of a gas is directly related to the frequency and force of these collisions.

• Pressure (P) is the force exerted per unit area of the container’s walls.
• Unit of pressure is the pascal (Pa), where 1 Pa = 1 newton per square metre (N/m²).

As gas particles collide with the walls, they exert a force. If the number of collisions increases (such as when you increase the temperature or amount of gas), the pressure increases. Conversely, if the volume of the gas increases or the temperature decreases, the pressure decreases.

Increasing and Decreasing the Temperature of Gas

The temperature of a gas is a measure of the average kinetic energy of the gas particles. When you increase the temperature, the particles move faster, collide more often, and with greater force, which increases the pressure (if the volume is kept constant). Conversely, when the temperature decreases, the particles move slower, collide less often, and with less force, resulting in a decrease in pressure.

Key Points:

• Increasing the temperature: As the temperature rises, the particles gain more kinetic energy, leading to more frequent and more forceful collisions with the walls of the container. This increases the pressure.
• Decreasing the temperature: As the temperature drops, the particles lose kinetic energy, leading to fewer and less forceful collisions. This decreases the pressure.

This relationship between temperature and pressure (at constant volume) is explained by Gay-Lussac’s Law, which states that the pressure of a gas is directly proportional to its absolute temperature (measured in kelvins).

Gay-Lussac’s Law:

$$P_1 / T_1 = P_2 / T_2$$​

Where:

• P₁ and P₂ are the initial and final pressures,
• T₁ and T₂ are the initial and final temperatures in kelvins.

When the Volume of Gas is Altered: Boyle’s Law

Boyle’s Law describes the relationship between the pressure and volume of a gas when the temperature is kept constant. According to Boyle’s Law, if the volume of a gas decreases, the pressure increases, and if the volume increases, the pressure decreases, provided the temperature remains unchanged.

The equation for Boyle’s Law is:

$$P₁ \times V₁ = P₂ \times V₂$$ 

Where:

• P₁ and P₂ are the initial and final pressures,
• V₁ and V₂ are the initial and final volumes.

This shows that the pressure and volume of a gas are inversely proportional. When the volume is halved, the pressure will double, and vice versa.

Example:

Suppose a gas in a piston has an initial volume of 4 m³ and a pressure of 100 Pa. If the volume is reduced to 2 m³, we can calculate the new pressure.

Using Boyle’s Law:

$$P₁ \times V₁ = P₂ \times V₂$$ 

Substitute the known values:

$$100 \, \text{Pa} \times 4 \, \text{m}^3 = P₂ \times 2 \, \text{m}^3$$ 

Now solve for P₂:

$$P₂ = \frac{100 \, \text{Pa} \times 4 \, \text{m}^3}{2 \, \text{m}^3}$$

$$P_2​=200Pa$$

So, when the volume of the gas is halved from 4 m³ to 2 m³, the pressure doubles to 200 Pa.

Summary

• Gas Under Pressure: Gas particles collide with the walls of their container, creating pressure. The frequency and force of these collisions depend on the temperature, volume, and amount of gas.
• Increasing and Decreasing the Temperature: As the temperature of a gas increases, its pressure increases (at constant volume), and as the temperature decreases, its pressure decreases.
• Boyle’s Law: The pressure and volume of a gas are inversely proportional when the temperature is kept constant. The equation for this relationship is P₁ × V₁ = P₂ × V₂.

Understanding these key principles helps explain how gases behave under different conditions and forms the basis for many applications, from airbags in cars to the operation of engines and even weather systems.