Here are the formulas concerning thermal expansion in physics: 1. Linear Thermal Expansion This describes the change in length of a material due to a change in temperature. The change in length $\Delta L$ is given by: $$\Delta L = L_0 \alpha \Delta T$$ The final length $L$ is given by: $$L = L_0 (1 + \alpha \Delta T)$$ Where: • $\Delta L$ is the change in length • $L_0$ is the original length • $\alpha$ is the coefficient of linear thermal expansion • $\Delta T$ is the change in temperature 2. Area Thermal Expansion This describes the change in the surface area of a material due to a change in temperature. The change in area $\Delta A$ is given by: $$\Delta A = A_0 \beta \Delta T$$ The final area $A$ is given by: $$A = A_0 (1 + \beta \Delta T)$$ Where: • $\Delta A$ is the change in area • $A_0$ is the original area • $\beta$ is the coefficient of area thermal expansion ($\beta \approx 2\alpha$) • $\Delta T$ is the change in temperature 3. Volume Thermal Expansion This describes the change in the volume of a material (solid, liquid, or gas) due to a change in temperature. The change in volume $\Delta V$ is given by: $$\Delta V = V_0 \gamma \Delta T$$ The final volume $V$ is given by: $$V = V_0 (1 + \gamma \Delta T)$$ Where: • $\Delta V$ is the change in volume • $V_0$ is the original volume • $\gamma$ is the coefficient of volume thermal expansion ($\gamma \approx 3\alpha$ for isotropic solids) • $\Delta T$ is the change in temperature