The SI unit of the coefficient of areal expansion is?

1 Answer
Feb 28, 2018

Inverse Kelvin

Explanation:

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

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.