What's the average amount of damage that a caster can do in three rounds with AoE's? How many hp does the average charger build have at (7th level assuming no healing items or hp boosting items).
When counting damage, are you adding multiple targets dps, or are you simply counting how much damage he can do to each target?
How well build is the caster for doing damage? If he's a cheesed out dragonwrought kobold he can do a bit more damage than a transmuter that just happens to have fireball prepared.
In said example where you hit your enemy with Solid Fog, you could then stack black tentacles on it to make their speed 2.5ft. Giving you even more turns.
But assuming that you get only three turns and none of the builds are optimized for it but the wizard still decides to throw in a bunch of fireballs when the solid fog is up:
Usually charger builds have around 14-16 con, and have roughly 5 levels with d12 hp and 2 with d10 hp. That's 4*6.5+2*5.5+7*2.5+12 = 26+11+17.5+12=56.5 hp on average.
The fireballs, cast by a 7th level wizard deal 7d6 damage each or half that on a succesful save. Meaning 24.5 damage on a failed save and 12.25 damage on a succesful one. So over three rounds that's 36.75-73.5 damage.
Therefore the charger has to fail two saving throws to go down from the three fireballs. Assuming he has no resistances or other defenses.
This is highly theoretical though. Since it raises a multitude of questions like who prepares 3 fireballs to cast after you solid fog? Who doesn't have any defenses against the most used element ever?