power output of unsteady dc

Since power dissipation is proportional to the aquare of voltage of current, this is the reason why any calcuation on power should be baed on the mean-square value of the voltage or current.

I don't know what you mean by a "unsteady" square-dc. Even in the case of a steady square signal (i.e. signal with a certain constant voltage during half of the period and zero voltage for the other half), you need to use the rms value to calculate the power output..