To store the energy produced in 1.5 hour by a 160 MW (160 10^6 W) electric-power plant, how many cubic meters of water will have to be pumped from the lower to the upper reservoir? Assume the upper reservoir is 500 m above the lower and we can neglect the small change in depths within each. Water has a mass of 1000 kg for every 1.0 m^3. Express your answer using two significant figures.
To find the amount of water that needs to be pumped from the lower to the upper reservoir, we need to calculate the potential energy stored in the electrical power produced.
The formula for potential energy is given by:
Potential Energy = Mass * Gravitational Acceleration * Height
In this case, the mass of water is equal to its volume multiplied by its density. The density of water is 1000 kg/m^3.
Let's start by calculating the potential energy of the electrical power produced:
Given:
Power plant capacity = 160 MW = 160 * 10^6 W
Time = 1.5 hours = 1.5 * 60 * 60 seconds
Energy produced = Power * Time
Energy produced = 160 * 10^6 W * 1.5 * 60 * 60 s
Next, we need to calculate the height difference between the upper and lower reservoirs:
Height difference = 500 m
Now, we can calculate the mass of water required to store this energy:
Potential energy = Mass * Gravitational acceleration * Height difference
Mass = Potential energy / (Gravitational acceleration * Height difference)
Mass = Energy produced / (Gravitational acceleration * Height difference)
Mass = (160 * 10^6 W * 1.5 * 60 * 60 s) / (9.8 m/s^2 * 500 m)
Now, let's calculate the volume of water required:
Volume = Mass / Density
Volume = Mass / (1000 kg/m^3)
Finally, we can plug in the values to calculate the volume of water in cubic meters:
Volume = [(160 * 10^6 W * 1.5 * 60 * 60 s) / (9.8 m/s^2 * 500 m)] / (1000 kg/m^3)
Simplifying and rounding to two significant figures:
Volume = 466 m^3
Therefore, approximately 466 cubic meters of water will have to be pumped from the lower to the upper reservoir to store the energy produced in 1.5 hours by the 160 MW electric power plant.