Thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature.
Thermal expansion is the tendency of matter (i.e., solid, liquid, or gas) to change its shape, size, and volume due to a change in temperature. In general, when matter is heated, its molecules gain kinetic energy and move faster, leading to an increase in volume.
There are three main types of thermal expansion:
A Train Track Expands Due to High Temperature: When the temperature rises, the metal tracks used in trains tend to expand, which can cause the tracks to buckle or warp, which can lead to accidents. To counteract this, gaps are left between the tracks to allow for expansion.
Expansion of Metal Pipes: When hot water is passed through metal pipes, they tend to expand. This can lead to damage to the pipes if not properly installed with expansion joints.
Expansion of Buildings: As the temperature rises, buildings made of materials such as concrete, brick, and steel tend to expand. This can cause cracks to form in walls and floors.
Expansion of Car Tires: During hot summer days, car tires tend to expand, increasing the pressure inside the tire. This can cause the tire to burst if not properly inflated.
Expansion of aluminium foil: When heated, aluminium foil expands, making it useful in cooking and baking as it can be moulded to fit different shapes and sizes of containers.
Expansion of water: Water also expands when heated, which is why water heaters have expansion tanks to accommodate the increased volume of water. This can prevent damage to the pipes and other components of the system.
Expansion of Bridges and Highways: Concrete and steel bridges and highways also expand when exposed to high temperatures, causing them to bulge and warp. Engineers have to account for thermal expansion and contraction when designing these structures.
Expansion of solids is the phenomenon where the size, shape, and volume of a solid material change due to the influence of various factors such as heat, pressure, and stress.
The Expansion in length of Solid object on heating is called linear expansion. It is one dimensional expansion as it occurs only along the length of the object.
Suppose a rod of some material with original length L,temperature T, is heated through a certain temperature T`, then its length increases and becomes L`.
Therefore
T` = New temperature
L` = New length
Lo = Original Length
To = Initial temperature
Change in Temperature = ΔT = T` – To——(1)
Change in Length = ΔL = L`- Lo——(2)
It has been experimentally proved that change in length is directly proportional to the original length and change in temperature.Therefore
ΔL = α L ΔT
Where ΔL is the change in length of the object, α is the coefficient of linear expansion, L is the original length of the object, and ΔT is the change in temperature.
To find the derivative of this equation, we need to use the product rule and the chain rule:
d(ΔL)/dt = d/dt (αLΔT)
= α(dL/dt)ΔT + αL(dΔT/dt)
= αvΔT + αL(dΔT/dt)
Where v is the velocity of the object.
This equation shows how the change in length of an object is related to its velocity and the rate of change of temperature. It can be used to calculate the expansion of materials due to temperature changes, which is important in many engineering and construction applications.
Volumetric expansion is the change in volume of a material due to a change in temperature. When an object is heated, its particles gain kinetic energy and move faster, causing the material to expand. Similarly, when an object is cooled, its particles lose kinetic energy and move slower, causing the material to contract.
The amount of volumetric expansion or contraction can be calculated using the coefficient of volume expansion (β), which is a property of the material. The formula for calculating volumetric expansion is:
ΔV = V₀βΔT
Where:
ΔV = Change in Volume
V₀ = Initial Volume
β = Coefficient of Volume Expansion
ΔT = Change in Temperature
The coefficient of volume expansion varies for different materials and can be found in tables of material properties. It is typically measured in units of (1/K), where K represents degrees Kelvin, the unit for temperature.
If the initial volume of a sample of water is 1 litre (1000 cm³) and the temperature is raised by 10 degrees Celsius, the change in volume can be calculated as:
ΔV = (1000 cm³)(0.00021 (1/K))(10 K) = 2.1 cm³
Therefore, the new volume of the water would be 1002.1 cm³.
As linear expansion occurs in one dimension ,whereas volume expansion occurs in three dimensions. Hence ,the coefficient of volume expansion “β” is three times greater than the coefficient of linear expansion “ α”.
Therefore:
β=3α
Application and Consequences of Thermal Expansion:
Thermal expansion of solids is useful in some situations of daily life and in some situations it creates problems;
Applications:
Thermal expansion refers to the tendency of materials to expand or contract in response to changes in temperature. This phenomenon has a wide range of applications in various fields. Here are some examples:
Bridges and Buildings: Thermal expansion and contraction are important factors to consider in the design and construction of bridges and buildings. Materials such as concrete, steel, and wood can expand or contract significantly with changes in temperature, which can cause stress on the structure. Engineers must take into account the expected temperature ranges in the location of the structure and design accordingly to prevent structural damage.
Plumbing Systems: Pipes made of metals such as copper or steel can expand or contract with changes in temperature. This can cause stress on the pipes and fittings, leading to leaks or bursts. To prevent this, plumbers use expansion joints, which allow the pipes to expand and contract without causing damage.
Thermal Expansion Valves: These are components used in refrigeration and air conditioning systems to regulate the flow of refrigerant. They use the thermal expansion of a temperature-sensitive liquid or gas to control the flow of refrigerant through the system.
Railways: Railway tracks are made of steel, which can expand and contract with temperature changes. This can cause the tracks to buckle or warp, which can be dangerous for trains. To prevent this, railway engineers leave gaps between the sections of the tracks to allow for expansion and contraction.
Cooking: Thermal expansion is also used in cooking. For example, when bread is baked, the dough expands as it heats up, creating air pockets that make the bread rise. Similarly, when water is heated, it expands, which can cause it to boil and create steam.
These are just a few examples of the many ways in which thermal expansion is used in various applications.
Real and Apparent Expansion of Liquids
The real expansion of a liquid refers to the actual increase in volume that occurs when the temperature of the liquid increases. When the temperature of a liquid increases, the average kinetic energy of the molecules within the liquid increases, causing the molecules to move farther apart and occupy more space. This results in an increase in the volume of the liquid.
The apparent expansion of a liquid, on the other hand, refers to the expansion that is observed when the liquid is viewed from the outside. This expansion is affected not only by the real expansion of the liquid, but also by the expansion or contraction of the container that holds the liquid. For example, if a liquid is contained in a glass flask, and the flask expands or contracts due to a change in temperature, the apparent expansion of the liquid will be affected by the change in the volume of the flask.