By what percentage does the volume of a brass cube increase when its temperature is raised by 200°C?

To determine how much the volume of a brass cube increases when its temperature is raised by 200°C, we can use the formula that relates the change in volume to temperature change, which is based on the concept of thermal expansion. The volume expansion can be approximated as:

[

\Delta V = V_0 \beta \Delta T

]

where:

• (\Delta V) is the change in volume,

• (V_0) is the initial volume,

• (\beta) is the volumetric expansion coefficient of the material, and

• (\Delta T) is the change in temperature.

For brass, the volumetric expansion coefficient (\beta) is approximately (0.000018 , \text{°C}^{-1}).

Given a temperature change of (200 , \text{°C}), we can express the percentage increase in volume as:

[

\text{Percentage Increase} = \left( \frac{\Delta V}{V_0} \right) \times 100%

]

Substituting the values, we can calculate:

[

\Delta V = V_0 \cdot \beta \cdot 200