Is the flow of electricity in the Daniell cell infinite?

I was reading in my chemistry book the other day, about the Daniell cell... I actually stumbled upon here searching on how to distill water. Anyway, I wanted to know if the flow of electricity in the Daniell cell is infinite...? I was kind of curious... I actually have forgotten the thread of thought which lead me to ask that, but I'd like to know all the same. Thanks =)

P.S. I'm in ninth grade.

First of two simultaneous responses --

It cannot be infinite, because eventually the zinc supply is exhausted.

Second of two simultaneous responses --

The answer is no. The source of the electrons is a final limiting factor and the dynamics of the reaction is a speed limiting factor. Google "  'Daniell Cell'  " for several good articles including the reactions involved.

Maryam... No power source is "infinite". A battery (even the Daniell Battery) is simply a storage container for electrical power. It relies on a chemical reaction (or a mechanical transference) which is finite. Physics Rule #1; energy and matter can not be created nor destroyed, only transferred, or transmuted... There is, however, measurable "LOST" energy when this transference or transmutation takes place.
It's not truly "lost", it is simply expended in the effort to complete the change. Sort of like losing weight by riding a bicycle... Your body (the battery) is "burning" the chemical fuel it has stored, to make the muscles flex and release, blood pump, to make all those motors in you run. And you "lose" weight... but where did that weight go? Sweat, exhalation, dead cells (hair and skin) trailing behind you as you pedal...
You have to feed the battery, or it will eventually stop.
Same thing with the "Daniell Battery".
You have to put it in it to get it out.