One method of meeting the extra electric power demand at...

One method of meeting the extra electric power demand at peak periods is to pump some water from a large body of water (such as a lake) to a reservoir at a higher eleva. tion at times of low demand and to generate electricity at times of high demand by letting this water run down and rotate $a$ turbine (i.e., convert the electric energy to potential energy and then back to electric energy). For an energy storage capacity of $5 \times 10^{6} \mathrm{kWh}$, determine the minimum amount of water that needs to be stored at an average elevation (relative to the ground level) of $75 \mathrm{~m}$. Answer: $2.45 \times 10^{10} \mathrm{~kg}$

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Key Concepts

Pumped Hydro Energy Storage

This is a method of storing energy by utilizing water that is pumped from a lower elevation to a higher one during periods of low energy demand. The stored potential energy in the elevated water can later be converted back to electrical energy during high demand by releasing the water to drive turbines.

Gravitational Potential Energy

This concept refers to the energy held by an object because of its position in a gravitational field. In energy storage systems, the potential energy is determined by the mass of the water, the height to which it is raised, and the gravitational acceleration, and it represents the energy available for later conversion back to electricity.

Energy Conversion Efficiency

This involves the process of converting electrical energy into potential energy (by pumping water uphill) and then back into electrical energy (by turbine generation). Understanding this conversion is crucial, as practical systems must account for losses and inefficiencies in the process.

Unit Conversion in Energy Calculations

Calculating energy storage often requires converting between different energy units, such as kilowatt-hours and joules. This conversion ensures that the energy values are consistent and comparable when applying formulas like those for gravitational potential energy.

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