Question

A container is filled to the brim with 1.5 L of mercury at 20°C. As the temperature of the container and mercury is increased to 55°C, a total of 7.8 mL of mercury spill over the brim of the container. Determine the linear expansion coefficient of the material that makes up the container.

Answer 1

The linear expansion coefficient of the material is
`4.952*10^(-5)\ K^(-1)`

Step-by-step explanation:

Given that,

Volume = 1.5 l

Temperature = 20°C

Increased temperature = 55°C

Volume = 7.8 mL

We need to calculate the linear expansion coefficient of the material

Using formula of linear expansion

`\Delta V=V_(0)\beta \Delta T`

`\Delta V=V_(0)(3\alpha \Delta T)`

`\alpha =(\Delta V)/(3V_(0)\Delta T)`

Put the value into the formula

`\alpha=(7.8*10^(-3))/(3*1.5*(55-20))`

`\alpha=0.00004952`

`\alpha=4.952*10^(-5)\ K^(-1)`

Hence, The linear expansion coefficient of the material is
`4.952*10^(-5)\ K^(-1)`