Question

If the volume of a block of metal changes by 0.09percent when it is heated through 100degree Celsius then the coefficient of linear expansion is

Answer 1

Answer:

Given:

Volume of a block of metal changes by 0.09 %

$\rm \implies \dfrac{\Delta V}{V} = 0.09\%$

Temperature = 100°C

$\rm \implies \Delta T = 100^0C$

To Find:

Coefficient of linear expansion ($\alpha$)

Solution:

We know that,

Coefficient of volume expansion ($\gamma$)

$\green{\boxed{\rm \gamma = \dfrac{1}{V} \times \dfrac{\Delta V}{\Delta T}\;\;/^0C }}$

Rearranging the formula,

$\implies \rm \gamma = \dfrac{\Delta V}{V} \times \dfrac{1}{\Delta T}$

Given that,

$\rm \implies \dfrac{\Delta V}{V} = 0.09\%$

$\rm \implies \Delta T = 100^0C$

Hence,

Substituting the above values in the given formula,

We get,

$\implies \rm \gamma = \dfrac{0.09}{100} \times \dfrac{1}{100}$

On Further simplification,

We get,

$\implies \rm \gamma = 9 \times 10^-6\;\;/^0C$

We have found out the Coefficient of volume expansion ($\gamma$)

We are asked to find Coefficient of linear expansion ($\alpha$)

We know that

$\boxed{\rm \alpha = \dfrac{\gamma}{3} }$

Hence,

$\implies \rm \alpha = \dfrac{9 \times 10^-6}{3}$

$\rm \implies \alpha = 3 \times 10^-6 \;\;/^0C$

Coefficient of linear expansion ($\alpha$) = 3 x 10⁻⁶

For further information:

https://brainly.in/question/17314762