# Triple metals

Two metal sticks 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?

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