Thermal Expansion of a Substance: Concepts & Theories

The expansion of substance when heated is known as thermal expansion. Air, water, iron etc. are substances that expand on heating.

When heated to the same temperature, gases will expand more than solids or liquids. Gases exhibit the greatest degree of thermal expansion among the three states of matter.

Solids have tightly packed particles and experience minimal expansion due to their strong intermolecular forces. Liquids have more space between particles than solids, allowing for some expansion, but it is still limited compared to gases. Gases have widely spaced particles that move freely, leading to significant expansion when heated.

Expansion of Solids

When a solid is heated, it expands in all directions i.e., its length, breadth and thickness increase. Thus, the volume of the solid too increases i.e. cubical expansion.

The increase in volume of a solid depends on:

(i) The initial volume of solid: More is the initial volume of solid, more is the increase in its volume.

(ii) The rise in temperature : More is the rise in temperature, more is the increase in its volume.

(iii) The material of the solid : A brass ball increases in volume more than an iron ball of same radius for the same rise in temperature.

Expansion of metals:

When a metal plate is heated, its length and breadth, both increase. This increases the area of the plate. i.e superficial expansion. The increase in area of a metal plate depends on:

• The initial area of the plate: Larger the initial area of plate, more is the increase in its area on heating.
• The increase in temperature: More is the rise in temperature, more will be the increase in area of plate.
• Material of the plate: A brass plate expands more than an iron plate of same dimensions for the same rise in temperature.

For example, consider linear expansion of a metal rod on heating. Factors on which an increase in the length of a rod depend when heated are:

• Original length of rod: Increase in length is directly proportional to the original length.
• Temperature of the rod: Increase in length is directly proportional to the increase in temperature.
• Nature of material of rod: Example, Cu rod expands more than Fe rod of same length and for the same rise in temperature.

Here are various scenarios:

If two iron rods one 10 m long and the other 5 m long, are heated to the same rise in temperature, the longer rod will experience a greater change in length because it has a larger original length (since both rods are made of the same material and are subjected to the same temperature change).

If two identical rods of copper are heated to different temperatures – one by 5°C and the other by 10°C, the rod heated by 10°C will experience a greater change in length and will expand more than the rod heated by 5°C since both rods are identical and made of the same material.

When two identical rods (same length) are of different material (One rod of copper and another identical rod of iron) and heated to the same rise in temperature, the copper rod will expand more than iron, since expansion depends on the nature of the material.

If only linear expansion is considered, then: The increase in length of a rod on heating does not depend whether it is hollow or solid. If we heat two rods of the same metal and of the same length, but one hollow and the other solid, to the same rise in temperature, we find that both the rods expand to the same extent.

However, if overall cubical expansion is considered, when these two identical rods (hollow and solid) are heated to the same range of temperature, the solid rod will expand more overall cubical expansion as more heat is present in solid rod.

In the ball and ring experiment, if the ball after heating is left to cool on the ring for some time, the ball again passes through the ring. This is because: on heating the ball expands and increases in size and cannot pass the ring when left on it. As the ball cools, it contracts, size becomes less than ring (original size) and passes the ring.

In harsh winter, telephone wires are likely to break. In winter temperature drops causing the metal telephone wires to contract. As the wires cool, they become taut (stretched). If the contraction is more, it can lead to excessive tension on the wires, causing them to become too tight between the poles. Thus they may break. This phenomenon is due to the thermal expansion properties of metals, which contract when temperatures decrease.

A cement floor is usually laid in small pieces with gaps in between to provide space for the material to expand and contract freely without causing stress on any one section. This ensures durability and prevents cracks. Cement expands when it heats up and contracts when it cools down. If the floor were laid as a continuous slab without gaps, changes in temperature could cause the cement to crack due to the stress from expansion.

Thermal Expansion of Liquids

The anomalous behavior of water refers to its unique property where it expands instead of contracting when cooled from 4°C to 0°C. Typically, most substances contract when cooled, but water behaves differently in this temperature range.

Also, when water is heated from 0°C to 4°C, it actually contracts rather than expands. This behavior is due to the anomalous expansion of water, where water reaches its maximum density at 4°C.

As a result, the volume of water decreases when heated within this temperature range.

After reaching 4°C, if the temperature continues to rise, water will then begin to expand as expected.

One application of thermal expansion of liquids is in thermometers.

In a mercury thermometer, the liquid expands when heated, causing it to rise in the tube. This expansion allows for accurate measurement of temperature changes.

Thermal Expansion of Gases

An empty glass bottle is fitted with a narrow tube at its mouth. The open end of the tube is kept in a beaker containing water. When the bottle is heated, bubbles of air are seen escaping into water.

Reason: When the empty glass bottle is heated, the air inside warms up and expands. This increase in temperature causes the air pressure inside the bottle to rise. As a result, some of the air is pushed out through the narrow tube, creating bubbles in the water below. The bubbles form because the escaping air is less dense than water and rises to the surface.

Density of a substance

On heating, as temperature increases:

• Solids: Slight expansion; minimal density change.
• Liquids: Increased volume leads to decreased density.
• Gases: Significant expansion results in a substantial decrease in density.

There is an Exception (refer anomalous behavior of water). Water contracts on heating from 0°C to 4°C, so the density of water increases on heating it from 0°C to 4°C. On further heating above 4°C, the density of water decreases. Thus, water has maximum density (= 1000 kg m^-3) at 4°C. Also for a given mass of water, its volume is minimum at 4°C.

When an iron washer is heated, the effects on its properties are as follows:

• Mass: The mass of the iron washer remains unchanged when heated.
• Internal Diameter: The internal diameter increases due to thermal expansion.
• External Diameter: The external diameter also increases as the washer expands
• Density: The density of the iron washer decreases because its volume increases while the mass remains constant.

Thus heating an iron washer causes it to expand in size, while its mass remains the same, leading to a decrease in density.