How is energy consumed when charging a battery?
Since I supplied the same amount of electrical energy during the first
  and second one-hours, is a significant part of energy wasted during
  the second one-hour?


Your assumptions are wrong. Take a Lithium Ion battery for instance: -



Picture source.

In stage 1 capacity rises linearly with time because the current is constant. When stage 2 occurs (the terminal voltage reaches a set-point) capacity rises more slowly and tails off just as the charging current tails off.

In other words in stage 1 there is roughly a constant wattage pumped into the battery but during stage 2 that wattage gradually reduces as current falls.