📂Thermal Physics

Definition of the Coefficient of Thermal Expansion

Definition¹

For a substance or object with volume $V$, let $\Delta V$ be the change in volume caused by a change in temperature $\Delta T$. Then $\beta$, defined as follows, is called the coefficient of thermal expansion. $$ \beta = {\frac{ 1 }{ V }} {\frac{ \Delta V }{ \Delta T }} $$

Explanation

Defined for continuous changes using the partial derivative, it becomes the following. $$ \beta = {\frac{ 1 }{ V }} {\frac{ \partial V }{ \partial T }} $$ In principle, $\beta$ can be regarded as a function of $T$ as well as $V$, but in many cases it is assumed to be a constant that is uniform on average throughout the whole system.