the energy that can extracted from a storage battery is always less than the energy that goes into it while it is being charged. why?

Perpetual motion is impossible. If you could get more energy out of a battery than you put in, you could run a perpetual motion device.

The reason the energy extracted from a storage battery is always less than the energy that goes into it while it is being charged is due to several factors:

1. Efficiency: No energy conversion process is 100% efficient. When a battery is being charged, there are losses in the form of heat, resistance, and chemical reactions that reduce the overall efficiency. These losses result in a smaller amount of energy being stored in the battery compared to the energy supplied during charging.

2. Chemical Processes: Batteries operate based on chemical reactions. During the charging process, a chemical reaction occurs to store energy in the battery. However, these chemical reactions are not perfect and can result in energy losses. Some energy is consumed in overcoming activation barriers, generating heat, or producing unwanted side reactions. These losses further contribute to the reduced energy available for extraction.

3. Internal Resistance: Batteries possess internal resistance, which opposes the flow of electrical current. When electricity flows through the battery, a portion of the energy gets dissipated as heat due to the resistance within the battery itself. This internal resistance contributes to the overall loss in energy.

4. Voltage Conversion: Batteries typically operate at a specific voltage, and the energy extracted from the battery needs to be converted to a different voltage or type for various applications. However, voltage conversion processes also introduce efficiency losses, resulting in further reduction of available energy.

To calculate the amount of energy extracted from a storage battery, you would need to consider these factors and account for the efficiency of the battery, the specific chemical reactions involved, the internal resistance, and any voltage conversion losses. It is important to note that different types of batteries, such as lithium-ion, lead-acid, or nickel-metal hydride, can have varying efficiencies and characteristics, hence yielding different energy extraction percentages.