Law of Energy Conservation: Renewable Energy - Physics (Grade 10)

Energy Does Not Vanish, It Changes Path

The law of energy conservation states that energy cannot be created or destroyed. Energy can move from one object to another, or change from one form to another.

In the International System of Units (SI), every form of energy can still be expressed in joules with symbol $\text{J}$ .

\text{total energy before a process}=\text{total energy after a process}

That sentence sounds simple, but it is often misread. If the electrical energy from a device is smaller than the energy supplied to it, the remaining energy has not disappeared. It usually becomes heat, sound, vibration, unused light, or internal energy in the device components.

OpenStax College Physics 2e discusses energy conservation on the Conservation of Energy page, which can be opened through openstax.org.

Choose the System First

A system is the part we choose to analyze. Everything outside the system is called the surroundings. The law of energy conservation is clearest when the system is chosen explicitly.

mermaid

The diagram is not decorative. It reminds us that a system can have more than one energy output.

Chosen system	Energy entering the system	Energy leaving the system
Falling water	gravitational potential energy	kinetic energy of water
Turbine and generator	rotational kinetic energy	electrical energy, heat, sound
Solar panel	radiant energy from sunlight	electrical energy, heat, reflected light

If the system is too narrow, some energy appears to leave. If the system is expanded to include the surroundings, total energy stays the same.

When Friction Is Ignored

In many introductory problems, friction and air resistance are ignored so the main idea is easier to see. For motion involving only kinetic energy and gravitational potential energy, mechanical energy is written as:

\begin{aligned} E_m &= E_k+E_p \\ &= \frac{1}{2}mv^2+mgh \end{aligned}

If there is no friction, no air resistance, and no external work, mechanical energy remains constant.

\frac{1}{2}mv_i^2+mgh_i=\frac{1}{2}mv_f^2+mgh_f

The subscript $i$ means initial state, while the subscript $f$ means final state.

Suppose water with mass $1 \text{ kg}$ falls from a height of $12 \text{ m}$ . If we use $g=10 \text{ m/s}^2$ and treat the water as initially at rest, its initial gravitational potential energy is:

\begin{aligned} E_p &= mgh \\ &= (1 \text{ kg})(10 \text{ m/s}^2)(12 \text{ m}) \\ &= 120 \text{ J} \end{aligned}

If no energy is dissipated, that $120 \text{ J}$ changes into kinetic energy of water. In real devices, part of the energy still moves to the surroundings as heat, sound, and vibration.

Useful Energy Is Not Total Energy

In renewable-energy technology, the desired output is usually useful energy, such as electrical energy. Energy conservation still applies, but the energy input does not all become electricity.

E_{\text{input}}=E_{\text{useful}}+E_{\text{dissipated}}

Example: flowing water carries $120 \text{ J}$ of energy toward a small turbine. The generator produces $90 \text{ J}$ of electrical energy. The dissipated energy is:

\begin{aligned} E_{\text{dissipated}} &= E_{\text{input}}-E_{\text{useful}} \\ &= 120 \text{ J}-90 \text{ J} \\ &= 30 \text{ J} \end{aligned}

So the $30 \text{ J}$ has not vanished. It has moved to the surroundings, for example as heat in the shaft, sound from rotation, or vibration in the structure.

The U.S. Department of Energy explains that hydropower plants use a height difference in water to move turbines and generators. The mechanism can be opened through energy.gov.

Testing Energy Claims with Conservation

The law of energy conservation can be used like an audit tool. If there is an energy claim, add up all the paths.

Claim	Check with energy conservation
A panel receives $500 \text{ J}$ of radiation and produces $500 \text{ J}$ of electricity	not realistic for a real panel; from energy conservation alone, the claim is possible only if no energy is reflected or becomes heat
A turbine receives $120 \text{ J}$ and produces $90 \text{ J}$ of electricity	reasonable if $30 \text{ J}$ is dissipated
A machine produces $150 \text{ J}$ of electricity from $120 \text{ J}$ of input without another source	not consistent with energy conservation

The U.S. Department of Energy explains that not all light reaching a photovoltaic cell becomes electricity; some can be reflected or converted to heat. The solar-panel efficiency factors can be opened through energy.gov.

This law helps us read words like saving, efficient, and clean more carefully. An efficient device is not a device that creates new energy. An efficient device makes the useful part of the energy larger and the dissipated part smaller.

Why This Matters for Renewable Energy

Renewable energy sources still obey the law of energy conservation. Sunlight, wind, water, geothermal heat, and biomass provide energy input. Technology helps transform that input into the energy we need.

\text{energy source} \rightarrow \text{conversion device} \rightarrow \text{useful energy}+\text{dissipated energy}

Because energy is not created from nothing, renewable-energy discussion always returns to three questions:

Where does the input energy come from?
Where does the energy that does not become useful output go?
How much of the energy actually becomes useful output?

If you can answer those three questions, you are not just memorizing the law of energy conservation. You are using it to read energy technology critically.