When pumped storage power plants operate at night, due to excess electricity, water is pumped

When pumped storage power plants operate at night, due to excess electricity, water is pumped into a reservoir on a hill by pumps, and in the daytime water flows down from the reservoir and the pumps act as hydraulic turbines. At what height should be pumped 2.5 * 10 ^ 6 tons of water so that its supply is sufficient for production , 5 * 10 ^ 12 J energy energy losses neglected

Initial data: m (mass of water injected on the hill) = 2.5 * 10 ^ 6 tons (2.5 * 10 ^ 9 kg); Q (required energy production) = 2.5 * 10 ^ 12 J.

Reference values: g (acceleration due to gravity) ≈ 10 m / s2.

The height to which it will be necessary to raise water with pumps is determined from the formula: Q = ΔEp = m * g * h, whence h = Q / (m * g).

Calculation: h = 2.5 * 10 ^ 12 / (2.5 * 10 ^ 9 * 10) = 100 m.

Answer: The pumps will need to pump water to a height of 100 meters.