9.4. Thermal Expansion of Gases

Charles' Law describes the relationship between the volume and temperature of a gas at constant pressure. It states that the volume of a gas is directly proportional to its temperature (in Kelvin):

V∝Tat constant pressure

Mathematically:

V1T1=V2T2

Where:

• V1 and V2 are the volumes at temperatures T1 and T2, respectively.

Charles' Law explains how gas volume changes with temperature when pressure is held constant. If you heat a gas, its temperature increases. As the temperature goes up, the gas particles move more energetically and spread apart, resulting in an increase in volume. Mathematically, the relationship can be expressed as V1/T1 = V2/T2, meaning if you know the initial volume and temperature, you can calculate the new volume at a different temperature.

Imagine a balloon. When you place it in a warm room, the air inside heats up, causing the balloon to expand. If you were to measure the balloon's volume at different temperatures, you'd find that the volume increases with temperature, just like Charles' Law says.

Boyle’s Law states that at constant temperature, the pressure of a gas is inversely proportional to its volume:

P∝1Vat constant temperature.

Boyle’s Law explains that if the temperature remains unchanged, increasing the volume of a gas will decrease its pressure, and vice versa. This is because gas molecules have more space to move around when the volume increases, leading to fewer collisions against the walls of the container, which reduces pressure. The mathematical representation shows that pressure and volume are inversely related.

Think about a syringe filled with air. If you pull the plunger back, you're increasing the volume inside the syringe. As the volume increases, the air pressure decreases, making it easier to draw in more air. Conversely, if you push the plunger in, the pressure increases because the volume decreases.

The ideal gas law combines Boyle’s Law, Charles’ Law, and Avogadro’s Law to describe the behavior of gases:

PV=nRT

Where:

• P = Pressure of the gas
• V = Volume of the gas
• n = Number of moles of the gas
• R = Universal gas constant
• T = Temperature in Kelvin.

The ideal gas law is a comprehensive equation that relates pressure, volume, temperature, and the quantity of gas. It states that for a given amount of gas at a certain temperature, the product of pressure and volume is constant. Suppose you know any three variables (pressure, volume, temperature, number of moles); you can solve for the fourth. This law assumes that gases behave ideally—meaning molecules occupy no volume and have no interactions, which is mostly true at high temperatures and low pressures.

Consider a sealed balloon containing air. If you heat the balloon (increasing temperature), you might notice it expands (increased volume) because more gas molecules are moving around, which leads to increased pressure. The ideal gas law helps explain and predict these changes mathematically.

If 1 mole of an ideal gas at 300 K occupies 0.03 m³, the new volume at 350 K (assuming constant pressure) can be calculated using Charles’ Law:

V1T1=V2T2 ⇒ V2=V1T2T1=0.03×350300=0.035 m³

Hence, the volume increases to 0.035 m³.

In this example, we are applying Charles’ Law to find out how the volume of a gas changes when its temperature increases from 300 K to 350 K. We can use the proportion defined in Charles’ Law to calculate the new volume (V2). By substituting the known values into the equation V1/T1 = V2/T2, we rearrange to find V2 and see that it increases from 0.03 m³ to 0.035 m³, showing how temperature affects volume.

Think of heating a gas-stove ignited air-filled balloon. As the air inside heats up with increased temperature, the balloon expands, and we can observe the increase in volume similar to the calculation in this example. It’s a practical demonstration of Charles’ Law in action.

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