Why are RMS values considered DC equivalent?
Average power is what gives rise to a sustained heating effect: -



Power is the instantaneous multiplication of v and i.

If we translate i into v/R then power is \$\dfrac{v^2}{R}\$

And, average power is the mean of \$\dfrac{v^2}{R}\$

If we then say that R = 1 ohm (just for convenience) we can say: -

Average power = mean(\${v^2}\$)

Then it follows that if we take the square root we get RMS voltage