Question

(b) at a school science exhibition, a student designed a model of a hydroelectric power station shown in fig. 2.1 (not to scale). (i) describe the main energy changes which take place when the tap is opened. (ii) the 20 w lamp operates normally when the tap is opened and water flows out at 3 kgs⁻¹. calculate the 1. potential energy lost by the water per unit time, 2. efficiency of the model. (c) explain why a hydroelectric power station would be preferable to a thermal power station.

Explanation:

Step1: Identify energy - change in (i)

When the tap is opened, water in the reservoir has gravitational potential energy. As it flows down, this potential energy is converted into kinetic energy. The flowing water then turns the turbine of the generator, converting kinetic energy into electrical energy which lights up the lamp.

Step2: Calculate potential - energy loss per unit time in (ii)1

The formula for gravitational potential energy is $E_p = mgh$. The rate of mass flow of water is $\frac{dm}{dt}=3\ kg/s$, height $h = 1.5\ m$, and $g = 9.8\ m/s^2$. The potential - energy loss per unit time $\frac{dE_p}{dt}=\frac{dm}{dt}gh$.
Substitute the values: $\frac{dE_p}{dt}=3\times9.8\times1.5 = 44.1\ J/s = 44.1\ W$.

Step3: Calculate efficiency in (ii)2

The power output is the power of the lamp, $P_{out}=20\ W$, and the power input is the rate of potential - energy loss of water, $P_{in}=44.1\ W$.
The efficiency $\eta=\frac{P_{out}}{P_{in}}\times100\%$.
Substitute the values: $\eta=\frac{20}{44.1}\times100\%\approx45.4\%$.

Step4: Answer (c)

Hydroelectric power stations are more environmentally friendly as they do not produce greenhouse - gas emissions during operation. They also use a renewable energy source (water), while thermal power stations often use non - renewable fossil fuels.

Answer:

(i) Gravitational potential energy of water in the reservoir is converted into kinetic energy as it flows down, and then kinetic energy is converted into electrical energy by the generator to light up the lamp.
(ii)1. $44.1\ W$

1. Approximately $45.4\%$

(c) Hydroelectric power stations are more environmentally friendly as they do not emit greenhouse gases during operation and use a renewable energy source, while thermal power stations often rely on non - renewable fossil fuels.