Batteries are non-ideal energy sources - minimizing the energy consumption of a battery-powered system is not equivalent to maximizing its battery life. We propose an alternative interpretation of a previously proposed battery model, which indicates that the deviation from ideal behavior is due to the buildup of "unavailable charge" during the discharge process. Previously, battery-aware task scheduling algorithms and power management policies have been developed, which try to reduce the unavailable charge at the end of a given workload. However, they do not account for the occurrence of rest periods (user enforced, naturally occurring, or due to finite load horizon), which are present in a variety of workloads. We first obtain an analytical bound on the recovery time of a battery as a function of the extent of recovery. Then, we shown that the effect of the rest periods is to reduce the improvement of battery-charge optimizing techniques over traditional energy-optimizing techniques. Under certain conditions, the policy that only minimizes energy consumption can actually achieve a longer battery lifetime than a battery-aware policy. A formal criterion based on the recovery time is proposed to choose between a candidate battery-aware policy and a candidate energy-aware policy. We also model the battery discharge process as a Linear Time Invariant system and obtain the frequency response of a battery. This is then used to study the effect of task granularity on the improvement achieved by battery-aware task scheduling. It was observed that the response time of typical batteries are of the order of seconds to several minutes. This, along with the charge recovery effect, was seen to cause battery-aware task scheduling methods to become ineffective for both very fine-grained (less than 10 ms) and very coarse-grained (greater than 30 min) task granularities.