A 40 W electric lamp shines for 10 hours. How much water must pass through a hydroelectric

A 40 W electric lamp shines for 10 hours. How much water must pass through a hydroelectric power plant (HPP) dam in order for the lamp to work? The height of the dam is 20 m, the efficiency of the hydroelectric power station is 90%.

Given:

W = 40 watts – the power of the electric lamp;

t = 40 hours = 144000 seconds – the operating time of the electric lamp;

h = 20 meters – the height of the hydroelectric dam;

n = 90% = 0.9 is the efficiency of the HPP;

g = 10 N / kg – acceleration of gravity.

It is required to determine, m (kilogram) – how much water must pass through the hydroelectric dam.

Let’s find the energy consumed by the light bulb during this time:

A = W * t = 40 * 144000 = 5760000 Joules.

Then, according to the law of conservation of energy:

Q = A, where Q is the potential energy of water at the height of the dam;

m * h * g * n = A;

m = A / (g * h * n) = 5760000 / (10 * 20 * 0.9) = 576000 / (20 * 0.9) =

= 28800 / 0.9 = 32000 kilograms.

Answer: 32,000 kilograms of water must pass through the dam.