Thermal expansion of Solids, Liquids and gases

THERMAL EXPANSION OF SOLIDS, LIQUIDS AND GASES

Thermal expansion in solids

When a metal is heated, due to increase in temperature it will expand and when it is cooled it contracts. However, an internal force will always act so as to keep the metal to regain its original length/position.

Definition

Thermal expansion: The expansion of a metal, when subjected to heat is called thermal expansion.

Thermal stress: The force (or) the stress developed inside the metal so as to regain its original position is called thermal stress.

Explanation

Let us consider a metal rod of length 'l' at a temperature T. When the rod is heated to the temperature from T to T + θ, then the length of the rod increases, linearly from l to l+dl as shown in Fig. 3.2.

The co‒efficient of thermal expansion α = dl/lθ

If = 1, then α = dl/l

Co‒efficient of thermal expansion (a)

Thus the co‒efficient of thermal expansion can be defined as the ratio between the change in length to the original length per unit rise of temperature.

Thermal expansion in liquids ‒ Volume Expansion

We know when an ordinary alcohol‒in‒glass thermometer (or) mercury‒ in‒glass thermometer is kept in the temperature bath, the alcohol (or) mercury rises, due to thermal expansion.

In this case it should be noted that the temperature rises not because of the expansion of liquid, it is only due to the volume expansion of the liquid.

Co‒efficient of volume expansion (β)

The co‒efficient of volume expansion 'β' is defined as the ratio between the fractional change (ΔV) in volume to the original volume (V) per unit rise of temperature (ΔT)

i.e., ΔV/V α ΔΤ

(or) ΔV/V = βΔΤ

When ΔT = 1

 β = ΔV/V

Thermal Expansion of Gases

Gases expand more at ordinary temperature than solid and liquid. The gas expands when it is heated. Heating a gas will increase the kinetic energy of the particles in the gas and in turn it will expand.

Example

For example, when a balloon is inflated in a cool space, the inflation is partial, but while on heating, it comes to full size. In thermal expansion, the inflation body dimension increases due to the increase in the temperature.

Thus, the gas expansion coefficient depends upon temperature. For an ideal gas, the volume expansion coefficient can be found from the ideal gas equation at constant pressure.

i.e.,  PV= μRT

During the expansion of gases, it is important to be aware that both temperature and pressure determine the change in volume of the substance. Increasing the temperature leads to increase in the volume of the gas while the increase in the pressure leads to decrease in volume.

Note: Increasing the temperature of the gas without increasing the volume that is available to accommodate the expanding gas means that the pressure builds up inside the container and may cause it to explode.