**A** and **B** are fixed on the left wall in the above diagram. The lengths and the linear expansion coefficients of **A** and **B** are $3L$, $\alpha$ and $L$,$2\alpha$, respectively. A third metal stick **C** with length $3L$ is fixed on the right joint bar on which the right end of **B** is also fixed. Suppose that there is a temperature change $\Delta T$ which is the same for all of **A**, **B** and **C**, and the distance between the wall and **C** remains constant, which is $L_0$ as shown in the diagram. What is the linear expansion coefficients of the metal **C**?