What is the mass of water in kilograms in a hydroelectric power station?

Answer 1

The mass of water will vary. The mass of water entering the system will depend on the temperature of the water as mass is measured in terms of a standard volume. As the temperature rises and falls, the enery change of the molecules will increase or decrease the number of molecules that are needed to fill the standard volume. As water travels through the system the temperature will rise due to the frictional forces of the containment vessels and the conversion that occurs as energy is converted between potential and kinetic energies and the work being done by the exchange of energy.

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That does not really answer the question: what is the mass of water used? Mass of a given volume of water does depend on its temperature hence density, but the differences with seasonal temperature range in the power-station's location are negligible.

The water will gain some heat as explained, but by then it's done its work in the turbines and is on its way back to the river below the power-station. (This was the principle of the experiments by which the pioneering scientist Henri Joule discovered the relationship between energy forms, and the fundamental Systeme Internationale unit of energy is named after him - the Joule (J). )

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One cubic metre of cold, fresh water in a reservoir weighs one tonne, for all practical purposes. The actual mass per hour of water used by each turbine depends entirely on the size of the turbine and the operating conditions - full-flow or throttled back.