The relationship between temperature change, coefficient of thermal expansion, and change in length is described by the following formula:

ΔL = α * L₀ * ΔT

Where:

• ΔL is the change in length of the material (in meters or other consistent units).
• α is the coefficient of thermal expansion of the material (a material property, typically expressed in °C⁻¹ or K⁻¹). It indicates how much a material expands or contracts for each degree Celsius (or Kelvin) change in temperature.
• L₀ is the original length of the material (in meters or other consistent units).
• ΔT is the change in temperature (in °C or K). ΔT = T_final - T_initial.

This formula demonstrates that the change in length is directly proportional to the original length, the coefficient of thermal expansion, and the change in temperature. A higher coefficient of thermal expansion means the material will expand or contract more for the same temperature change.

Thermal expansion is the tendency of matter to change in volume in response to changes in temperature. When the temperature of a substance increases, its particles gain kinetic energy and move more vigorously. This increased particle motion leads to an expansion of the substance.

Solids: In solids, particles are held in fixed positions by strong intermolecular forces. As the temperature rises, the particles vibrate with greater amplitude around their fixed positions. This increased vibration causes the average separation between the particles to increase slightly, resulting in a small expansion. The strong intermolecular forces limit the amount of expansion compared to liquids and gases.

Liquids: In liquids, particles are still relatively close together, but they have more freedom of movement than in solids. As the temperature rises, the particles gain kinetic energy and move further apart. The intermolecular forces are weaker than in solids, allowing for greater expansion. The increased movement and separation of particles lead to a more significant volume increase compared to solids.

Gases: In gases, particles are widely separated and have considerable freedom of movement. As the temperature rises, the particles move much faster and collide more frequently with each other and the walls of the container. This increased kinetic energy and frequent collisions cause the gas to expand significantly. The weak intermolecular forces allow the particles to spread out considerably.

In all three states, the expansion is described as 'at constant pressure' because the volume change occurs while the volume of the container remains constant. This means that any increase in volume is accommodated by an increase in the number of particles, and thus an increase in pressure.

The volume of water increases when heated because the water molecules gain kinetic energy and move further apart. Water molecules are held together by hydrogen bonds, which are relatively strong intermolecular forces. At lower temperatures, these hydrogen bonds restrict the movement of the molecules, resulting in a smaller volume.

As the temperature increases, the water molecules gain kinetic energy and vibrate more vigorously. This increased vibration overcomes some of the hydrogen bonds, allowing the molecules to move further apart. The increased separation of molecules leads to an expansion of the water, resulting in an increase in volume. The hydrogen bonds are still present, but their influence is reduced by the increased thermal energy. The expansion of water is somewhat unusual compared to other liquids, as it expands upon heating up to 4°C, and then contracts above that temperature.

The strength of the hydrogen bonds is crucial. While strong, they are not strong enough to prevent significant expansion when the temperature rises sufficiently. The increased kinetic energy overcomes the attractive forces, leading to a net increase in volume.