Almost all substances (solids, liquids, and gases) expand on heating and contract on cooling. The expansion of a substance on heating is called the thermal expansion of that substance. There are three kinds of expansion: linear (increase in length), superficial (increase in area), and cubical expansion (increase in volume). Solids have a definite shape, so when a solid is heated it expands in all directions i.e. the length, area, and volume all increase on heating. Liquid and gases only show cubical expansion. On heating, liquids expand more than solids and gases expand much more than liquids. In this lesson, you are going to learn:
On heating a solid, the average kinetic energy of molecules of the solid increases. They start vibrating about their mean position with a large amplitude. The result is that their mean position change such that inter-molecular separation between the molecules increases, thus the solid expands in all directions.
Experiment: Take a metal ball and a ring.
i) Arrange the metal ball and ring as shown in the picture below (figure a). The metal ball should just slip through the ring when both are at room temperature.
ii) Now heat the metal ball on a burner (figure b)
iii) Place the ring again and try to pass the ball through the ring. You will notice that the ball gets stuck.
Reason: On heating, the ball expands and becomes bigger in diameter.
Now allow the ball to cool and again try to pass the ball through the ring, you will notice that the ball now passes through the ring. This is because on cooling, the ball contracts.
Linear Expansion
Whenever there is an increase in the length of a body due to heating then the expansion is called linear expansion. Let us consider linear expansion in a metallic rod. The increase in the length of a metallic rod on heating depends on the following three factors:
Note: Increase in length of a rod on heating does not depend on whether it is hollow or solid
Superficial expansion of solids
When a metal plate is heated, its length and breadth both increase. This increases the area of the plate. An increase in the area of the plate depends on:
Cubical expansion of solids
When solid is heated, its length, breadth, and thickness all increase, thus increase in the volume. Experimentally it is observed that the increase in the volume of a solid depends on:
| If L0 is the length of a rod at 0oC and its length at t oC is Lt, then an increase in length is given as Lt - L0 = L0 α t α is the coefficient of linear expansion which depends on the material of the rod. Its unit is per oC |
| If A0 is the area of a plate at 0oC and its area at t oC is At, then an increase in area is given as At - A0 = A0 β t β is the coefficient of superficial expansion which is different for different solids. |
| If V0 is the volume of a solid at 0oC and its area at t oC is Vt, then increase in volume is given as Vt - V0 = V0 γ t γ is the coefficient of cubical expansion which is different for different materials. |
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Relationship between α, β and γ: α : β : γ = 1 : 2 : 3 |
Coefficient of linear expansion of some solids
| Substance | Coefficient of linear expansion ( x 10-6 per oC) |
| Aluminum | 24 |
| Brass | 19 |
| Copper | 17 |
| Iron | 12 |
| Invar | 0.9 |
Thermal Expansion of solids in daily life
1. Railway tracks: The rails of railway tracks are made of steel. While laying the railway tracks on the wooden or concrete plants, a small gap is left between the successive length of rails as shown in the figure below. The reason is, in summer due to the rise in atmospheric temperature each rail tends to increase in its length, so a gap is left between the two rails, otherwise, the rail will bend sideways.
2. Electric cables and telephone wires: The electric cable in the power transmission line and telephone wires between two poles may break in winter due to contraction and may sag in summer due to expansion. Therefore, while putting up the wire between two poles care is taken that in summer they are kept slightly loose so that they may not break in winter due to contraction. And while laying them in winter, they are kept tights so that they may not sag too much in summer due to expansion.
3. Glassware used in Kitchen: Glassware used in the kitchen is generally made of pyrex glass. The reason is that the pyrex glass has a very low coefficient of cubical expansion, so the glassware on heating does not expand and cracks.
Like solids, liquids also usually expand on heating. Liquids expand much more than the solids when heated. As liquid does not have a definite shape but has a definite volume, therefore liquids have only cubical expansion.
Exception: Water contracts on heating it from 0oC to 4oC and then beyond 4oC on further heating it expands. This is called anomalous behavior of water.
Experiment: Take a jar, fill the three-fourth part with water, and close the jar. Keep it on the flame. You will notice that as the water is heated more and more, the level of water in the jar rises.
Note: When a liquid contained in the jar is heated, first the jar gets heated and so it will expand due to which the level of the liquid falls. Thereafter when the heat reaches the liquid it will expand, so the level of liquid will rise. Thus, the real expansion of liquid is more than the observed expansion.
Factors affecting the cubical expansion of a liquid
The cubical expansion of a liquid depends on the following three factors:
If V0 is the volume of liquid at 0oC and Vt the volume of liquid at t oC, then an increase in the volume of liquid is given as
Vt - Vo = V0 γ t
where γ is the coefficient of cubical expansion of the liquid.
Coefficient of cubical expansion of some liquids
| Liquid | Coefficient of cubical expansion γ ( x 10-4 per oC) |
| Mercury | 1.8 |
| Water(above 15OC) | 3.7 |
| Paraffin oil | 9.0 |
| Alcohol | 11.0 |
Application of thermal expansion of liquids in daily life
Thermal expansion of liquid is used in the working of a mercury thermometer. Mercury thermometer consists of a capillary tube with one end closed and a cylindrical bulb at the other end. The bulb is filled with mercury. Mercury is a shiny liquid, so its level can be seen easily in the capillary tube. When the bulb of the thermometer is kept in contact with a hot body, the mercury expands. The level of mercury rises in the capillary tube. The tube is graduated to read the temperature. For each degree Celsius rise in temperature, mercury expands by the same volume, so the calibration of the thermometer becomes easier.
Gases also expand when they are heated. Gases expand much more than liquids and solids. Like liquids, the gases do not have a definite shape, so they also have only cubical expansion. However, gases that are contained in a fixed volume cannot expand - and so increases in temperature result in increases in pressure.
Experiment: Take an empty bottle. Attach a rubber balloon to its neck. Initially, the balloon is deflated. Place the bottle in a water bath containing boiling water. After some time you will notice that the balloon gets inflated as shown in the below figure. This shows that on heating, the air enclosed in the bottle expands and fills the balloon so the balloon gets inflated.
Application of thermal expansion of gases in daily life
Hot air balloon: Hot-air balloons works on the principle of thermal expansion difference between a gas and a solid. Because the hot air inside the balloon bag increases in size faster than the container, it stretches the bag so that it expands and displaces the colder (heavier) air outside the bag. The difference between the density of the air inside and outside the bag, causes the balloon to rise. Cooling the air inside the bag causes the balloon to descend.
When a substance is heated, its volume increases while its mass remains the same, therefore, the density of substance (being the ratio of mass to its volume), decreases with the increase in temperature. In the case of solids, the decrease in density is not noticeable but in the case of liquids and gases, as temperature increases volume increases by an appreciable amount, and therefore decrease in density is quite noticeable.
