[etep]

I think it is linear for frequency and non-linear for voltage, i.e. P~fCV^2. But in many current CPUS, the feature that adjusts frequency also adjusts voltage. That's why I stipulated that, for my comments to be true, such shenanigans as dynamic frequency (and voltage) scaling must be "turned off." I think the OP was asking, what happens to CPU energy if you load the web page with and without the optimized compilation. The OP was interested in core sleep states, but I think that dynamic frequency scaling is a confounding factor. It would be interesting to see the measurements w/ and w/out that feature perhaps.

[tspiteri]

To increase the frequency, you also have to increase the voltage so that the transistors charge faster, otherwise they won't be able to switch in the shorter time.