A horizontal tube, open at both ends, contains a column of liquid. The length of this liquid column does not change with temperature. Let $\gamma$ is the coefficient of volume expansion of the liquid and $\alpha$ is the coefficient of linear expansion of the material of the tube. Then the correct relation is ______

Let $A_0$ and $A_t$ be the areas of cross-section of the tube at temperatures 0 and t respectively,

$l=$ length of the liquid column (constant)

$V_0$ and$V_t$ be the volumes of the liquid at temperatures 0 and t respectively,

$V_0=l{A}_0$          $V_t=l{A}_t$          

$V_t=V_0\left(1+\gamma t\right)$            $A_t=A_0\left(1+2\alpha t\right)$

$\therefore V_t=l{A}_0\left(1+2\alpha t\right)=V_0\left(1+\gamma t\right)=l{A}_0\left(1+\gamma t\right)$or $\gamma =2\alpha$.