Is my battery dead?

Have you been using Chrome? Chrome is a resource hog.

 

The battery doesn't just drain (unless it has quite a major internal fault), look at your Activity Monitor, CPU tab, to see what using the highest CPU cycles and therefore causing the battery usage. Or click on the battery icon in the menubar, it will, after a short pause, tell you which apps are using significant battery.

 

Apple actually gives a figure of 8 hours, not 7, for your 2014 15-inch rMBPro.
Also, notice that 8 hours is not guaranteed, nor does it say you always get 8 hours.
In fact, the specs do not say just "8 hours", but does say "up to 8 hours

Battery life is very dependent on your usage.
Lots of info here: http://www.apple.com/batteries/