Question

The SI unit of the coefficient of areal expansion is?

Answer 1

Inverse Kelvin

Explanation:

We know the definition of the areal expansion coefficient:
`alpha = 1/A (dA)/(dT)`

Doing unit analysis (in any system with L being a length, `Theta` being a temperature),
`[alpha] = 1/([A]) cdot ([A])/([T]) = L^2/(L^2 cdot Theta) = Theta^-1`

Since the SI unit for temperature is Kelvin, the unit for the areal expansion coefficient is `K^-1`.

If we were also really tricky, we could notice that the expansion coefficient can be written as
`alpha = (d(ln(A)))/(dT)`
which obviously has units of `1/K` since `ln(A)` is unitless.