• id: JME-10-N02
• title: Superficial and Cubical Expansion
• tags: area-expansion, volume-expansion, beta, gamma

Area expansion: $A = A_0(1 + \beta\Delta T)$ with $\beta = 2\alpha$. Volume expansion: $V = V_0(1 + \gamma\Delta T)$ with $\gamma = 3\alpha$. The relations $\beta = 2\alpha$ and $\gamma = 3\alpha$ are derived by expanding $(1 + \alpha\Delta T)^2$ and $(1 + \alpha\Delta T)^3$ respectively, neglecting higher-order terms (valid since $\alpha\Delta T \ll 1$). For liquids, only volume expansion $\gamma$ is meaningful since liquids have no fixed shape. The ratio $\alpha : \beta : \gamma = 1 : 2 : 3$ is a frequently tested relation.