How long will an iphone 4 battery last if it is left on all day?

I'm getting an ipod touch 5th generation for Christmas and was wondering if its possible to use my iphones internet on that for a full day without the battery dying.

It really depends if you do a lot on the itouch/iphone. If you are somewhere with no outlet, you might want to try a website called dinodirect or amazon to find battery chargers that are solar and plug into the bottom of the device. If it has the new lightning connector, I don't think they made those chargers for that yet. Hope this helps!

If your brightness is all the way down it's possible if you aren't watching videos or playing games, but if you are no.

You should be okay. Just pull down the brightness a bit.