Right there. You said it really does matter how you cool it.

What I said:

It does. It really does. All the stuff you're discounting is the difference between "real world performance" and "ideal performance" and even "ideal performance" doesn't get anywhere without conduction and convection at a bare minimum.

What you said:

The amount of energy it takes to raise or lower a gram of water by 1C doesn't change depending on how you do it.

What I said:

No. But the SPEED does. The EFFICIENCY does. And your entire line of questioning is about "how long."

So what you're saying is that I agreed with you when I quoted you to say you were incorrect.

Just so we're clear:

Your standpoint is that the amount of energy is the same, therefore nothing else needs to be calculated.

My standpoint is that the speed of energy transfer is what we're focused on, therefore we have to calculate a whole bunch of ugly shit.

Worse, you're no longer arguing fact, you're attempting to depose me - you're trying to argue my statements hold no value because you think you've tricked me into contradicting myself. This isn't court, this is physics, and no matter how much you wish to dance around the issue, I have a lot more training in it than you do - which means, I suspect, that you can't even follow my arguments closely enough to understand them. Further, it doesn't matter how much smarter you think you are or how incorrect you presume me to be, the fact remains: I spent several thousands of dollars being tested on this stuff in an ABET-certified 4-year institution (one of the top ten in the country at the time, in fact) and I feel like I'm beating a dead horse: This isn't a Physics 101 problem. Which only makes the following that much more insulting:

It's clear to me that you're not going to wrap your head around this problem or how it's solved. I was hoping to get the light bulb to come on for you.

So. You and your high school physics can be as self-assured as you wish about this particular problem. I said before and I'll say again: it's a lot more complex than you think. I'll add this, though: I no longer have any interest in helping to illuminate the problem to you. I've been purposefully ignoring your condescending tone in the face of an exceptional amount of patience, but I can't do it any more.

Good luck with this and your future endeavors.