(II) Energy may be stored by pumping water to a high reservoir when demand is low and then releasing it to drive turbines (Fig. 20–15) during peak demand. Suppose water is pumped to a lake 105 m above the turbines at a rate of 1.00 x 10⁵ kg/s for 10.0 h at night.

(a) How much energy (kWh) is needed to do this each night?

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Verified step by step guidance

1. Identify the relevant physical quantities: the height the water is pumped (h = 105 m), the mass flow rate of the water (\( \dot{m} = 1.00 \times 10^5 \, \text{kg/s} \)), and the duration of the pumping (t = 10.0 h).
2. Convert the time of pumping from hours to seconds to maintain consistency in units (1 hour = 3600 seconds).
3. Calculate the total mass of water pumped during the time interval using the mass flow rate and the total time in seconds (Total mass, M = \( \dot{m} \times t \)).
4. Use the formula for gravitational potential energy (PE = mgh) to calculate the energy required to lift the total mass of water to the height of 105 m, where g is the acceleration due to gravity (approximately 9.81 m/s²).
5. Convert the energy from joules to kilowatt-hours (1 kWh = 3.6 x 10^6 J) to find the total energy in kWh needed each night.