Cooling the wort

I'm a beginner home brewer and this is one of my first questions. I've noticed a couple of ways to cool the wort after the boiling process. One is to put the boiling pot in ice water to bring the temp down and the other uses a copper tubing coil to remove heat. Would it also work to pour the hot wort into your fermenting pail, then add enough cold water to reach the 5 or 6 gallon capacity of the pail, thus cooling off the wort? It may not be cool enough to pitch the yeast but it won't be long after that, that it will be around 70 degrees Fahrenheit. Is this one of those things where there are many ways to do a process and the end result is the same?

As you mentioned, there are many different ways of accomplishing the same thing. If you're doing partial boils and topping off with cold water that will be a good start, but even so you'll probably not get it down to pitching temps doing that alone.

Water retains heat very well so if you don't get it cold enough from the start and expect it to drop further by just sitting around in a room with ambient temps of 70 you're in for a long wait.

Since you're just getting started your best bet will be using a combination of an ice bath and topping off with cool/cold water. If you're only boiling a couple gallons this can get your wort down to ~70 without too much trouble. When you start boiling larger amounts of water it will usually be easier and more cost effective in the long run to use a wort chiller of some sort.

You can cool by adding cold water, you just need to make sure the water is clean. Also you have to take into account relative temperatures and volumes. If you are doing a 2.5 gallon boil, and adding 2.5 gallons of water, then the boiling wort (212) will only be brought down to about 12l0 by near freezing cold water. Before I had an immersion chiller and did full boils, I would try to bring the wort down to 100-120 using an ice bath and then add water. The first 50 degrees or so come off easy, after that it gets much harder

I place 4 gals of PUR filtered tap water in my freezer for 4-5 hours prior to brewing.

I use it as top off water and my wort is usually down in the 60s within minutes...

I just top off my wort with ice. Works nicely, and you can crash your wort down to 70 in no time. I dumped 20 pounds of ice in on my batch tonight (too much btw had to strain some out so I could get the wort all blended together in a timely fashion). Sure beats the hell out of sitting it in a ice bath and waiting though. I guess if you aren't comfortable with bagged ice you could boil some water and make your own ahead of time. No problems with bag ice for me so far though.

Ice will cool your wort much more than the same amount of cold water, so even if you're boiling close to your final volume, if you can get it down to 100 or so in a cold water bath, it doesn't take that much ice to finish the job. Just make sure it's clean ice: freeze clean water in a sanitized container, or check bagged ice to make sure there are no tears.