Discussion
In the heat equation \( \partial u/\partial t = \alpha\,\partial^{2}u/\partial x^{2} \), the constant \( \alpha \) has dimensions of
Answer: C
For the two sides to agree dimensionally, \( \alpha \) must carry the dimensions of the left side divided by those of \( u/x^{2} \), that is
\[ \left[\alpha\right] \;=\; \frac{\Theta/T}{\Theta/L^{2}} \;=\; \frac{L^{2}}{T}, \]
units of square metres per second. This is why a diffusion length grows as the square root of time rather than in proportion to it
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