Thermal expansion

What Is Thermal Expansion? One day you're trying to open a pickle jar, but the lid is super tight and you just can't do it. Y...

What Is Thermal Expansion?

One day you're trying to open a pickle jar, but the lid is super tight and you just can't do it. You try using a rubber grip, but that doesn't work. You try hitting the jar lid on the counter to break the seal, but nothing happens. Finally, you try your grandma's favorite trick: you run the metal jar lid under hot water to heat it up. The jar opens easily. But why? The answer is thermal expansion.
Thermal expansion occurs when an object expands and becomes larger due to a change in the object's temperature. To understand how this happens, we need to think about what temperature actually is. Temperature is the average kinetic (or movement) energy of the molecules in a substance. A higher temperature means that the molecules are moving faster on average. If you heat up a material, the molecules move faster, and as a result, they take up more space - they tend to move into areas that were previously empty. This causes the size of the object to increase.
So when you heat up the jar lid, the same thing happens - the jar lid expands. So does the glass, but metals expand more than glass. The gaps between the metal jar lid and the glass threads increase, so it becomes easier to open.
Thermal Expansion is minimum in case of solids but maximum in case of gases.

General volumetric thermal expansion coefficient

In the general case of a gas, liquid, or solid, the volumetric coefficient of thermal expansion is given by

${\displaystyle \alpha _{V}={\frac {1}{V}}\,\left({\frac {\partial V}{\partial T}}\right)_{p}}$

The subscript p indicates that the pressure is held constant during the expansion, and the subscript V stresses that it is the volumetric (not linear) expansion that enters this general definition. In the case of a gas, the fact that the pressure is held constant is important, because the volume of a gas will vary appreciably with pressure as well as temperature. For a gas of low density this can be seen from the ideal gas law.

Linear expansion

 

Linear expansion means change in one dimension (length).  To a first approximation, the change in length measurements of an object due to thermal expansion is related to temperature change by a "linear expansion coefficient". It is the fractional change in length per degree of temperature change. Assuming negligible effect of pressure, we may write:

${\displaystyle \alpha _{L}={\frac {1}{L}}\,{\frac {dL}{dT}}}$

where ${\displaystyle L}$ is a particular length measurement and ${\displaystyle dL/dT}$ is the rate of change of that linear dimension per unit change in temperature.
The change in the linear dimension can be estimated to be:

${\displaystyle {\frac {\Delta L}{L}}=\alpha _{L}\Delta T}$

Area expansion

The area thermal expansion coefficient relates the change in a material's area dimensions to a change in temperature. It is the fractional change in area per degree of temperature change. Ignoring pressure, we may write:

${\displaystyle \alpha _{A}={\frac {1}{A}}\,{\frac {dA}{dT}}}$

where ${\displaystyle A}$ is some area of interest on the object, and ${\displaystyle dA/dT}$ is the rate of change of that area per unit change in temperature.
The change in the area can be estimated as:

${\displaystyle {\frac {\Delta A}{A}}=\alpha _{A}\Delta T}$

Volume expansion

For a solid, we can ignore the effects of pressure on the material, and the volumetric thermal
expansion coefficient can be written:

${\displaystyle \alpha _{V}={\frac {1}{V}}\,{\frac {dV}{dT}}}$

where ${\displaystyle V}$ is the volume of the material, and ${\displaystyle dV/dT}$ is the rate of change of that volume with temperature.
If we already know the expansion coefficient, then we can calculate the change in volume

${\displaystyle {\frac {\Delta V}{V}}=\alpha _{V}\Delta T}$

where ${\displaystyle \Delta V/V}$ is the fractional change in volume (e.g., 0.002) and ${\displaystyle \Delta T}$ is the change in temperature (50 °C).
The above example assumes that the expansion coefficient did not change as the temperature changed and the increase in volume is small compared to the original volume. This is not always true, but for small changes in temperature, it is a good approximation. If the volumetric expansion coefficient does change appreciably with temperature, or the increase in volume is significant, then the above equation will have to be integrated:

${\displaystyle \ln \left({\frac {V+\Delta V}{V}}\right)=\int _{T_{i}}^{T_{f}}\alpha _{V}(T)\,dT}$

${\displaystyle {\frac {\Delta V}{V}}=\exp \left(\int _{T_{i}}^{T_{f}}\alpha _{V}(T)\,dT\right)-1}$

where ${\displaystyle \alpha _{V}(T)}$ is the volumetric expansion coefficient as a function of temperature T, and ${\displaystyle T_{i}}$,${\displaystyle T_{f}}$ are the initial and final temperatures respectively.

Contraction effects (negative thermal expansion)

A number of materials contract on heating within certain temperature ranges; this is usually called negative thermal expansion, rather than "thermal contraction". For example, the coefficient of thermal expansion of water drops to zero as it is cooled to 3.983 °C and then becomes negative below this temperature; this means that water has a maximum density at this temperature, and this leads to bodies of water maintaining this temperature at their lower depths during extended periods of sub-zero weather. Also, fairly pure silicon has a negative coefficient of thermal expansion for temperatures between about 18 and 120 kelvins.
More about α, β, and γ : the co-efficient α, β, and γ for a solid are related to each other as follows

α = β/2 = γ/3 => α : β : γ 1:2:3

hence for the same temperature

Percentage change in area = 2 ˣ percentage change in length

Percentage change in volume = 3 ˣ percentage change in length

Application of Thermal Expansion in Solids:

THE BIMETALLIC STRIP IN THERMOSTATS.

In a thermostat, the central component is a bimetallic strip, consisting of thin strips of two different metals placed back to back. One of these metals is of a kind that possesses a high coefficient of linear expansion, while the other metal has a low coefficient. A temperature increase will cause the side with a higher coefficient to expand more than the side that is less responsive to temperature changes. As a result, the bimetallic strip will bend to one side.
When the strip bends far enough, it will close an electrical circuit, and, thus, direct the air conditioner to go into action. By adjusting the thermostat, one varies the distance that the bimetallic strip must be bent in order to close the circuit. Once the air in the room reaches the desired temperature, the high-coefficient metal will begin to contract, and the bimetallic strip will straighten. This will cause an opening of the electrical circuit, disengaging the air conditioner.
In cold weather, when the temperature-control system is geared toward heating rather than cooling, the bimetallic strip acts in much the same way—only this time, the high-coefficient metal contracts with cold, engaging the heater. Another type of thermostat uses the expansion of a vapor rather than a solid. In this case, heating of the vapor causes it to expand, pushing on a set of brass bellows and closing the circuit, thus, engaging the air conditioner.

JAR LIDS AND POWER LINES.

An everyday example of thermal expansion can be seen in the kitchen. Almost everyone has had the experience of trying unsuccessfully to budge a tight metal lid on a glass container, and after running hot water over the lid, finding that it gives way and opens at last. The reason for this is that the high-temperature water causes the metal lid to expand. On the other hand, glass—as noted earlier—has a low coefficient of expansion. Otherwise, it would expand with the lid, which would defeat the purpose of running hot water over it. If glass jars had a high coefficient of expansion, they would deform when exposed to relatively low levels of heat.
Another example of thermal expansion in a solid is the sagging of electrical power lines on a hot day. This happens because heat causes them to expand, and, thus, there is a greater length of power line extending from pole to pole than under lower temperature conditions. It is highly unlikely, of course, that the heat of summer could be so great as to pose a danger of power lines breaking; on the other hand, heat can create a serious threat with regard to larger structures.

EXPANSION JOINTS.

Most large bridges include expansion joints, which look rather like two metal combs facing one another, their teeth interlocking. When heat causes the bridge to expand during the sunlight hours of a hot day, the two sides of the expansion joint move toward one another; then, as the bridge cools down after dark, they begin gradually to retract. Thus the bridge has a built-in safety zone; otherwise, it would have no room for expansion or contraction in response to temperature changes. As for the use of the comb shape, this staggers the gap between the two sides of the expansion joint, thus minimizing the bump motorists experience as they drive over it.
Expansion joints of a different design can also be found in highways, and on "highways" of rail. Thermal expansion is a particularly serious problem where railroad tracks are concerned, since the tracks on which the trains run are made of steel. Steel, as noted earlier, expands by a factor of 12 parts in 1 million for every Celsius degree change in temperature, and while this may not seem like much, it can create a serious problem under conditions of high temperature.
Most tracks are built from pieces of steel supported by wooden ties, and laid with a gap between the ends. This gap provides a buffer for thermal expansion, but there is another matter to consider: the tracks are bolted to the wooden ties, and if the steel expands too much, it could pull out these bolts. Hence, instead of being placed in a hole the same size as the bolt, the bolts are fitted in slots, so that there is room for the track to slide in place slowly when the temperature rises.
Such an arrangement works agreeably for trains that run at ordinary speeds: their wheels merely make a noise as they pass over the gaps, which are rarely wider than 0.5 in (0.013 m). A high-speed train, however, cannot travel over irregular track; therefore, tracks for high-speed trains are laid under conditions of relatively high tension. Hydraulic equipment is used to pull sections of the track taut; then, once the track is secured in place along the cross ties, the tension is distributed down the length of the track.