# 7.2 Thermal expansion of solids and liquids

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• Define and describe thermal expansion.
• Calculate the linear expansion of an object given its initial length, change in temperature, and coefficient of linear expansion.
• Calculate the volume expansion of an object given its initial volume, change in temperature, and coefficient of volume expansion.
• Calculate thermal stress on an object given its original volume, temperature change, volume change, and bulk modulus.

The expansion of alcohol in a thermometer is one of many commonly encountered examples of thermal expansion    , the change in size or volume of a given mass with temperature. Hot air rises because its volume increases, which causes the hot air’s density to be smaller than the density of surrounding air, causing a buoyant (upward) force on the hot air. The same happens in all liquids and gases, driving natural heat transfer upwards in homes, oceans, and weather systems. Solids also undergo thermal expansion. Railroad tracks and bridges, for example, have expansion joints to allow them to freely expand and contract with temperature changes.

What are the basic properties of thermal expansion? First, thermal expansion is clearly related to temperature change. The greater the temperature change, the more a bimetallic strip will bend. Second, it depends on the material. In a thermometer, for example, the expansion of alcohol is much greater than the expansion of the glass containing it.

What is the underlying cause of thermal expansion? As is discussed in Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature , an increase in temperature implies an increase in the kinetic energy of the individual atoms. In a solid, unlike in a gas, the atoms or molecules are closely packed together, but their kinetic energy (in the form of small, rapid vibrations) pushes neighboring atoms or molecules apart from each other. This neighbor-to-neighbor pushing results in a slightly greater distance, on average, between neighbors, and adds up to a larger size for the whole body. For most substances under ordinary conditions, there is no preferred direction, and an increase in temperature will increase the solid’s size by a certain fraction in each dimension.

## Linear thermal expansion—thermal expansion in one dimension

The change in length $\text{Δ}L$ is proportional to length $L$ . The dependence of thermal expansion on temperature, substance, and length is summarized in the equation

$\text{Δ}L=\mathrm{\alpha L}\text{Δ}T,$

where $\text{Δ}L$ is the change in length $L$ , $\text{Δ}T$ is the change in temperature, and $\alpha$ is the coefficient of linear expansion    , which varies slightly with temperature.

[link] lists representative values of the coefficient of linear expansion, which may have units of $1/\text{º}\text{C}$ or 1/K. Because the size of a kelvin and a degree Celsius are the same, both $\alpha$ and $\text{Δ}T$ can be expressed in units of kelvins or degrees Celsius. The equation $\text{Δ}L=\mathrm{\alpha L}\text{Δ}T$ is accurate for small changes in temperature and can be used for large changes in temperature if an average value of $\alpha$ is used.

what is the stm
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Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
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LITNING
scanning tunneling microscope
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The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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what king of growth are you checking .?
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research.net
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sciencedirect big data base
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Introduction about quantum dots in nanotechnology
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what is fullerene does it is used to make bukky balls
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fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
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