Expansion of Substances (Thermal Expansion) - Expansion of Gases

Gases expand significantly when heated due to the high energy and free movement of their particles. Unlike solids and liquids, gases have no fixed shape or volume. When heated in a closed container, the gas's pressure increases because its volume cannot change. However, if the gas is in a container with a movable piston, its volume increases while the pressure remains constant. The expansion of gases is usually measured under constant pressure using the constant pressure expansion coefficient (β), which relates the change in volume to temperature.

1. Gas in a Closed Bottle

When a gas in a closed container is heated, its volume cannot change due to the fixed walls, but the energy of the particles increases.

• The gas particles collide more forcefully with the walls, causing the pressure to increase while the volume remains constant.
• Using the formula density=`"mass" / "volume"`
• The mass and volume of the gas remain constant in a closed system. Therefore, the density stays unchanged, even though the pressure increases.

2. Gas in an Open Container

When gas in an open container is heated, its particles gain energy and move faster. Since the container is open, the gas can escape into the surroundings.

• The gas expands freely and its volume increases as it spreads out. The gas may diffuse completely into the surrounding atmosphere.
• Using the formula density=`"mass" / "volume"`
• As the gas escapes, both the mass of gas in the container decreases and the volume it occupies increases. This leads to a significant decrease in the density of the gas within the container.

3. Gas in a Bottle with a Movable Piston

In this case, the gas is allowed to expand freely as the piston can move.

• When the gas is heated, its particles gain energy, causing the gas to push the piston outward and increase its volume.
• The volume of the gas increases while the pressure remains constant. This type of expansion is called constant pressure expansion, which is commonly used to study gas expansion.

Effect of heat on a gas

Constant Pressure Expansion Coefficient,

The expansion of a gas is typically measured by keeping the pressure constant and allowing the gas to expand freely.

The relationship between the initial and final volumes of the gas is given by: V₂=V₁(1+βΔT)

Where:

• V_1​: initial volume of the gas.
• V₂​: final volume of the gas.
• ΔT: change in temperature (T₂−T₁​).
• β: constant pressure expansion coefficient of the gas.

$\beta$ represents how much the volume of the gas changes per unit temperature increase at constant pressure. Gases expand much more than liquids or solids when heated, due to the weaker interactions between their particles.