# Thermal expansion and coefficient of linear expansion

• hils0005
In summary, the coefficient of linear expansion for the material of the rod is 23 x 10-6 /C˚, based on the change in length of the rod and steel ruler after being placed in an oven at 270C, using the equation ΔL = LαΔT.
hils0005
at 20C a rod is exactly 20.05cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 270C, where the rod now measures 20.11cm on the same ruler. What is the coefficient of linear expansion for the material of which the rod is made?

## Homework Equations

$$\Delta$$L=L$$\alpha$$$$\Delta$$T
L(i)rod=20.05cm
L(f)rod=20.11
L(i)steel=20.05 ??
$$\Delta$$T=250C
$$\alpha$$steel=11 x 10^-6

## The Attempt at a Solution

Ls=20.05cm(11x10^-6)(250C)
L=.055cm

I don't know what to do now-

The change in length for the rod is 20.11cm-20.05cm plus
the expansion of the steel ruler at its 20.11cm mark:
∆L = La∆T = (20.11 cm)(11 x 10-6 /C˚)(270˚C-20˚C)-- u should assume it
= 0.055 cm
∆L = (20.11cm-20.05cm) + 0.055 cm = 0.115 cm
The coefficient of thermal expansion of the material the rod
a = ∆L/L∆T=23 x 10-6 /C˚

## 1. What is thermal expansion?

Thermal expansion is the tendency of materials to expand or contract in size when exposed to changes in temperature. This phenomenon occurs because when temperature increases, the particles in a material gain more energy and move further apart, causing the material to expand. Conversely, when temperature decreases, the particles lose energy and move closer together, resulting in contraction.

## 2. What is the coefficient of linear expansion?

The coefficient of linear expansion is a measure of how much a material will expand or contract in length when the temperature changes by one degree. It is denoted by the symbol alpha (α) and has units of 1/degree Celsius (or 1/Kelvin). It is different for different materials and is typically higher for materials with weaker intermolecular forces.

## 3. How is the coefficient of linear expansion calculated?

The coefficient of linear expansion can be calculated by dividing the change in length (ΔL) of a material by its original length (L) and the change in temperature (ΔT). In other words, α = (ΔL / L) / ΔT. It is important to note that the coefficient of linear expansion may vary with temperature.

## 4. What are some real-life applications of thermal expansion and the coefficient of linear expansion?

Thermal expansion and the coefficient of linear expansion have various real-life applications. Some examples include the use of bimetallic strips in thermostats, the design of expansion joints in bridges and buildings, and the use of heat sinks in electronic devices to dissipate heat. In addition, knowledge of these concepts is crucial in industries such as construction, engineering, and manufacturing.

## 5. How does thermal expansion affect everyday objects?

Thermal expansion can affect everyday objects in various ways. For example, if a glass bottle containing a liquid is heated, the liquid may expand and cause the bottle to crack. Similarly, metal train tracks may buckle in extreme heat due to thermal expansion, causing disruptions in train schedules. In addition, thermal expansion can also affect the accuracy of measurements, as changes in temperature can lead to changes in the size of rulers and measuring tapes.

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