Why is the coefficient of volume expansion zero for water at $4\,^{\circ}C$?

(N/A) The coefficient of volume expansion $\gamma$ is defined as $\gamma = \frac{1}{V} \left( \frac{dV}{dT} \right)$. At $4\,^{\circ}C$,water reaches its maximum density,which implies that its volume $V$ is at a minimum. Since the volume is at a minimum at this temperature,the rate of change of volume with respect to temperature $\left( \frac{dV}{dT} \right)$ is equal to $0$. Therefore,the coefficient of volume expansion for water at $4\,^{\circ}C$ is $0$.