Thermal Expansion of Gasses

Thermal expansion is a phenomenon that all states of matter (solids, liquids & gases) undergo when subjected to increased temperature. It refers to an object’s tendency to expand or contract in length, density, area or volume as a result of heat. On getting heat energy, the potential energy stored inside atoms gets converted into kinetic energy. Thus, the kinetic energy of a substance increases when it is heated. There are three types of thermal expansion:

1. Linear Expansion
2. Area Expansion
3. Volume Expansion

Thermal Expansion of Gases

The thermal expansion of gases is a change in their volume in response to a change in temperature. Heating a gas increases the kinetic energy of the particles, causing the gas to expand. The thermal expansion of gases is larger than that for solids and liquids. The particles in a gas are farther apart than those in a liquid or solid. This means that they have more room to move around when they are heated. The distance between each particle increases as the kinetic energy increases.

Properties of Gases

The distribution of molecules in gases differs greatly from the distribution of molecules in liquids and solids. Therefore, the behaviour of gas molecules is determined by certain properties and laws that the gas molecules obey.

The five properties of gases are

1. Temperature (T)
2. Volume (V)
3. Pressure (P)
4. Quantity (n)
5. Density (d)

The Equation for Thermal Expansion of Gases

The volume expansion coefficient of a gas is the fractional change in volume per unit change in temperature at constant pressure. At ordinary temperatures, gases expand more than solid and liquid. The coefficient of gas expansion is dependent on temperature. For an ideal gas, the coefficient of volume expansion at constant pressure can be found from the ideal gas equation:

PV = μRT

At constant pressure

PΔV = μR ΔT

ΔV/V = ΔT/T

i.e. αv = 1/T for ideal gas

At 0 °C, αv = 3.7 × 10-3 K–1, which is much larger than that for solids and liquids.

Where V is the volume, n is the number of moles of gas, R is the gas constant, αv is the coefficient of expansion and T is the absolute temperature.

Understanding the Gas Laws

We have already studied that the behaviour of gases is affected by certain properties like temperature, pressure, volume and the amount of gas present. How their change is governed by a set of equations known as the Gas Laws. The gas laws deal with how gases behave with respect to pressure, volume, temperature and amount. Let’s take a look at these Gas Laws.

1. Boyle’s Law

As per Boyle’s law, a change in the volume occupied by a gas (at constant quantity and temperature) will result in a change in the pressure exerted by it. In other words, the product of the initial pressure and the initial volume of a gas is equal to the product of its final pressure and final volume (at constant temperature and number of moles).

Boyle’s Law Equation: P₁V₁ = P₁V₂

Where

• P1 – initial pressure exerted by the gas
• V1 – the initial volume occupied by the gas
• P2 – final pressure exerted by the gas
• V2 – the final volume occupied by the gas

Boyle’s law equation is useful in determining the rise in pressure exerted by a gas on the walls of a container whose volume is reduced. It should be noted that its quantity and absolute temperature remain constant.

2. Charles’s Law

Charles’s law says that at a constant pressure of the gas, any change in the volume of the gas is directly proportional to the temperature of the gas (Kelvin scale). In other words, if you increase the temperature of a gas by 1 kelvin, its volume will increase by a definite amount. This is also known as the law of volumes.

Charles’s Law Equation: V₂/V₁=T₂/T₁ or V₁T₂ = V₂T₁

Where,

• V1 – Volume of 1st gas
• V2 – Volume of 2nd gas
• T1 – Temperature of 1st gas
• T2 – Temperature of 2nd gas

It can be inferred from Charle’s law equation that the absolute temperature of a gas is directly proportional to its volume.

3. Ideal Gas Law

In the Ideal Gas Law, the pressure, volume and temperature are directly proportional to each other. The relationship between the variables is given as PV = NRT. Here, P is the pressure of the gas, V is the volume of gas, T is the temperature and N is the number of moles of gas. R is a constant value that depends on the units used and this constant value is also known as the universal gas constant.

Formula: PV = nRT

Where

• P-pressure
• V-volume
• n-moles
• R-universal gas constant (0.0821 L atm/mol K)
• T-temperature in Kelvin.

Thermal Expansion of Gases Examples

• Thermal expansion of nitrogen gas in car tires occurs due to the rise in temperature caused by friction. Being an inert gas, the thermal expansion of nitrogen gas is negligible compared to other gases. This is the reason they are widely used in tires.
• Expansion of a partially filled balloon to its full size when immersed in warm water.
• Air bubbles trapped inside cake batter expand when baked.

Conclusion

Thermal expansion is a concept that most people witness or experience, whether they realise it or not. After reading this article, you may have a better understanding of how air and other gases change in volume when exposed to a range of temperatures.