Classical Mechanics Level 3

Suppose a block of constant cross section area $$A$$ and length $$L$$ has its ends maintained at temperature $$0^{\circ}C$$ and $$100^{\circ}C$$. And the thermal conductivity of block varies as $$K = K_0(1 + \alpha x)$$ where $$x$$ is distance from the end which is at $$100^{\circ}C$$ and $$\alpha$$ is a positive constant

Then the temperature in the middle of rod at steady state will be (options in $$^{\circ}C$$

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