The formula to calculate the final volume after thermal expansion is:
\[ V_f = V_i \cdot (1 + \beta \cdot \Delta T) \]
Where:
Volume increase due to thermal expansion is the change in volume of a material when it is heated or cooled. The amount of expansion or contraction is determined by the material’s expansion coefficient and the degree of temperature change. This concept is critical in engineering and construction, as it affects the design of structures, containers, and systems that must accommodate changes in volume due to temperature fluctuations.
Let's say the initial volume (Vi) is 100 liters, the expansion coefficient (β) is 0.0005 (1/°C), and the temperature change (ΔT) is 50°C. Using the formula:
\[ V_f = 100 \cdot (1 + 0.0005 \cdot 50) = 100 \cdot (1 + 0.025) = 100 \cdot 1.025 = 102.5 \text{ liters} \]
So, the final volume (Vf) is 102.5 liters.