Thermal expansion (surface area)

In summary, thermal expansion is the phenomenon where matter changes in shape, area, and volume in response to a change in temperature. This is due to an increase in the vibration of particles, causing the substance to expand. This expansion also affects surface area, but not necessarily in proportion to the temperature change. The coefficient of thermal expansion is a measure of this change and varies for different materials. In everyday life, thermal expansion is used in construction, design, and in devices such as thermometers. However, it can also lead to structural damage and affect measurements. In terms of climate change, thermal expansion of seawater contributes to rising sea levels, which can have serious consequences for coastal communities.
  • #1
jisbon
476
30
Homework Statement
Consider an empty and closed box made of isotropic material. The surface
area of the box is ##52 cm^2## at 25 °C. The linear coefficient of thermal expansion
of the material is ##24*10^{-6}##K. If the temperature of the box is raised to 125 °C,
calculate
(i) its surface area and
(ii) the percentage increase of the volume using the percentage increase of
the surface area.
Relevant Equations
-
Hi all,

For area expansion, I know the equation goes like:

1580267456696.png

Hence, my answer to part i is
##\begin{aligned}A=A_{0}\left( 1+2\alpha \Delta T\right) \\ = 52\left( 1+2*24\times 10^{-6}\right) \left( 100\right) \\ =52.2496cm^{2}\end{aligned} ##

Now I am unsure how to proceed with part 2 in this case, any pointers?

Thanks
 
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  • #2
You shall find the relation between
[tex](V-V_0)/V_0[/tex] and [tex](A-A_0)/A_0[/tex] with the further formula [tex]V=V_0(1+3\alpha\triangle T)[/tex]
 

FAQ: Thermal expansion (surface area)

1. What is thermal expansion?

Thermal expansion is the phenomenon where a material's volume increases as its temperature increases. This is caused by the increase in the kinetic energy of the particles that make up the material, causing them to vibrate and take up more space.

2. How does thermal expansion affect surface area?

As a material's volume increases due to thermal expansion, its surface area also increases. This is because the material's particles are moving further apart from each other, causing the material to expand in all directions.

3. What factors affect the amount of thermal expansion in a material?

The amount of thermal expansion in a material is dependent on its coefficient of thermal expansion, which is a measure of how much the material's volume changes per degree of temperature change. It is also affected by the material's initial temperature, the temperature change, and the material's dimensions.

4. Can thermal expansion be a problem in everyday life?

Yes, thermal expansion can cause problems in everyday life. For example, it can cause cracks in pavement or buildings as the material expands and contracts with temperature changes. It can also affect the accuracy of measuring devices, as their dimensions may change with temperature.

5. How is thermal expansion used in engineering and construction?

Thermal expansion is an important factor to consider in engineering and construction. It is taken into account when designing structures and choosing materials, as it can affect the stability and durability of the structure. It is also used to create tight seals in machines and devices, as different materials expand and contract at different rates, creating a secure fit.

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