Can you save power by closing programs?

I was reading a blog the other day, minding my own business, when I came across this question in the comments section:

What about the green argument? Holding information in RAM requires power to keep it there, or else the computer forgets it. RAM that has nothing in it has no power cost to the system, therefore you are being more power-wise by keeping system memory clear?

Well, that’s half true. I wrote a quick reply, but thought it was an interesting enough question to go a bit more in-depth here. I guess another title for this post could be: How does memory work?

Thankfully, writing about the latter would require a lot more typing than I’m willing to do, so I’ll just discuss the original topic in a long-winded way.
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