# A bar made from an unknown material expands by 10 mm when the temperature rises by 30^oC. If the...

## Question:

A bar made from an unknown material expands by 10 mm when the temperature rises by 30{eq}^o {/eq}C. If the bar is originally 2 m in length, calculate the coefficient of thermal coefficient

## Thermal Expansion

Whenever a solid is heated then its length gets increased. We take the coefficient of thermal expansion of solid as {eq}\alpha {/eq}

The increase in the length of the solid is calculated using the equation

$$\Delta L = L_o \alpha \Delta T $$

- where {eq}L_o {/eq} is the original length.

- {eq}\alpha {/eq} is the coefficient of thermal expansion

- {eq}\Delta T {/eq} is the change in temperature

## Answer and Explanation:

Given:

- The initial length of the rod is {eq}L_o = 10 \ mm. {/eq} .

- The change in temperature is {eq}\Delta T =30^o C {/eq}.

- The increase in length of the rod is {eq}\Delta L =2 \ mm {/eq}

Let the coefficient of linear expansion of the material of the rod be {eq}\alpha. {/eq}

From the expression of the increase in the length of the wire we have

{eq}\begin{align*} \Delta L& = L_o \alpha \Delta T \\ 2 & = 10 \times \alpha \times (30) \\ \alpha & = 0.007 \ C ^{-1} \Rightarrow (Answer) \end{align*} {/eq}

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from UExcel Physics: Study Guide & Test Prep

Chapter 11 / Lesson 8