Law of Energy Conservation

Energy Is Transferred or Converted

The law of energy conservation states that energy cannot be created or destroyed. Energy can be transferred from one object or system to another and converted from one form to another.

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

For the system and its surroundings taken together, the total energy before the process equals the total energy after it.

If a device supplies less electrical energy than it receives, the difference is transferred to the surroundings or stored as internal energy in the device. It may appear as heating, sound, vibration, or unwanted radiation.

Energy conservation applies to each transfer and transformation in a system.

Choose the System First

A system is the part we choose to analyze. Everything outside the system is called the surroundings. State the system boundary before applying energy conservation, because that boundary determines which energy transfers cross into or out of the calculation.

System Boundary Decides the Energy Count

The diagram tracks every output. A system can deliver useful energy while also transferring energy to the surroundings as heat, sound, or vibration.

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 expanded to include the device and its nearby surroundings, transfers that previously left the device remain inside the larger system. The total energy inside that larger system stays constant only when no energy crosses its outer boundary.

When Friction Is Ignored

Many introductory problems ignore friction and air resistance so that only kinetic energy and gravitational potential energy remain in the model. Mechanical energy is then 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 crosses into the surroundings, that $120 \text{ J}$ changes into the kinetic energy of the water. In a real device, some energy moves to the surroundings as heat, sound, and vibration.

Useful Energy Depends on the Device Purpose

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.

\begin{aligned} E_{\text{input}} &=E_{\text{useful}} +E_{\text{surroundings}} \\ &\quad{}+\Delta E_{\text{stored}} \end{aligned}

In the following example, the stored energy of the device does not change, so $\Delta E_{\text{stored}}=0$ . Flowing water carries $120 \text{ J}$ of energy toward a small turbine. The generator produces $90 \text{ J}$ of electrical energy. The energy transferred to the surroundings is:

\begin{aligned} E_{\text{surroundings}} &= 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 may appear as an increase in the shaft's internal energy, sound carried away through the air, or vibration in the structure.

Hydropower plants use a difference in water height to drive turbines and generators.

Testing Energy Claims with Conservation

The law of energy conservation can test an energy claim by accounting for every transfer and transformation.

Claim	Check with energy conservation
A panel receives $500 \text{ J}$ of radiation and produces $500 \text{ J}$ of electricity	This claim is not realistic for a real panel. Under the law of energy conservation, it would be possible only if no energy were reflected or converted to heat.
A turbine receives $120 \text{ J}$ and produces $90 \text{ J}$ of electricity	This claim is reasonable if the remaining $30 \text{ J}$ moves to the surroundings.
A machine produces $150 \text{ J}$ of electricity from $120 \text{ J}$ of input without another source	This claim violates the law of energy conservation.

A photovoltaic cell does not convert all incident light into electricity. Some light is reflected, and some becomes heat.

An efficient device converts a larger share of its input into useful energy and transfers a smaller share to the surroundings. Calling a device clean requires additional evidence about emissions, materials, land or water use, and waste.

Energy Conservation Applies to 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.

Follow the energy from its source into the conversion device. Part becomes useful output, while part is transferred to the surroundings.

To check energy conservation in a renewable-energy technology, answer three questions:

Where does the input energy come from?
Where is energy transferred when it does not become useful output?
What fraction of the input energy becomes useful output?

These answers identify the energy input, every transfer out of the system, and the useful fraction of the output.