While studying circuits I am having a question that when we say a battery is dead.Do we mean that the voltage difference between the ends has become zero?If no,then what actually happens?
You can make the simplest form of an electrochemical cell (battery) in your kitchen. Stick a zink thing (i.e. anythin galvanized) and a cobber piece into a lemon or into a cup of Coca Cola, and you'll have a voltage (half a volt or so) across them. The citric acid or phosphoric acid will start to "eat" or "etch" the metals away.
During the etching process (redox reactions), atoms are removed from the metal bulks, leaving behind their electrons (we call them ions now) so the metal gets a net charge. The net charge on either metal will be different due to different reaction rates, so charge will flow from one to the other if there is a path. This is what is meant by a voltage. Those charges may then, when arriving at the other metal, recombine with their counterpart-atoms (ions), or to other substances, such as hydrogen ions in the acids (then hydrogen gas will be produced and will bubble up).
In this simplified description of the battery electrochemical process, which factors limit the lifetime?
Surely, the amount of metal bulks do. No more metal means no more charge accumulation. In fact, for high-power cells such as aluminium-air batteries, I have with the naked eye seen pinholes forming in the thin aluminum sheet during fast discharging-cycles in the laboratory as the aggressive reactions ate through the material.
Also, the acid (called an electrolyte; it can also be for example a salt solution or other substances) may be "used up", so to speak, so that there for instance are no more available hydrogen ions for recombination with the electrons or no more phosphate ions (from the phosphoric acid) to etch away metal (they may bond with the metal atom and reach a neutral, unreactive state, maybe as a precipitate falling to the bottom).
Most commonly when we loosely say a battery is dead, it means the potential across the battery is too low to drive current/electrons hard enough to do what we want. It's pretty rare to completely drain a battery to zero, because it'll have been more or less useless before then. No matter how drained a battery is though, it can't reach absolute zero (every last piece of electron for every last hole).