Energy Stores and Transfers

Where Energy Is Present and How It Crosses System Boundaries

Energy is measured in joules, with the symbol $\text{J}$ . In a calculation, we track where energy is present and how it moves from one system to another. A moving object has kinetic energy, an elevated object has gravitational potential energy, and a battery or biomass contains chemical energy. Energy can move between systems through heating, radiation, mechanical work, or electrical work.

All of these descriptions refer to the same physical quantity. The relevant formula depends on the object or process being analyzed.

Energy in Systems and Energy Transfers

The diagram keeps two questions separate. The left branch asks where energy is present. The right branch asks how energy crosses from one system to another. Heat is energy transferred because of a temperature difference, while internal energy is energy present in the material.

Four Common Energy Calculations

Renewable-energy systems often involve motion, height, temperature differences, and moving electric charge. Each situation uses a different calculation.

Quantity being calculated	When it appears	Mathematical model	Renewable-energy example
Kinetic energy	an object moves	$E_k=\frac{1}{2}mv^2$	wind turns a turbine
Gravitational potential energy	an object is above a reference level	$E_p=mgh$	stored water is higher than a turbine
Energy transferred by heating	two systems have different temperatures	$Q=mc\Delta T$	geothermal fluid heats a power system
Energy transferred electrically	electric charge moves through a potential difference	$E=VIt$	a generator sends energy into the grid

Biomass and batteries also contain chemical energy, while solar panels receive energy carried by sunlight. The four formulas in the table calculate energy from motion, height, temperature change, and electrical power.

Match the Formula to the Situation

Kinetic energy is the energy an object has because of its motion.

E_k=\frac{1}{2}mv^2

Symbol guide:

Symbol	Meaning	SI unit
$E_k$	kinetic energy	$\text{J}$
$m$	object mass	$\text{kg}$
$v$	object speed	$\text{m/s}$

If the air mass passing a turbine is $2 \text{ kg}$ and its speed is $3 \text{ m/s}$ , its kinetic energy is:

\begin{aligned} E_k &= \frac{1}{2}mv^2 \\ &= \frac{1}{2}(2 \text{ kg})(3 \text{ m/s})^2 \\ &= 9 \text{ J} \end{aligned}

The work-energy theorem relates net work to the change in kinetic energy.

Gravitational potential energy is energy related to an object's position in a gravitational field. For objects near Earth's surface, the common model is:

E_p=mgh

Symbol guide:

Symbol	Meaning	SI unit
$E_p$	gravitational potential energy	$\text{J}$
$m$	object mass	$\text{kg}$
$g$	gravitational acceleration	$\text{m/s}^2$
$h$	height relative to a reference level	$\text{m}$

The value of $g$ near Earth's surface is about $9.8 \text{ m/s}^2$ . Many basic calculations use $g=10 \text{ m/s}^2$ to make multiplication by hand simpler. Results calculated with that rounded value are approximations.

An object contains internal energy. When two systems have different temperatures, energy moves from the hotter system to the colder system. Energy transferred because of this temperature difference is called heat. If the substance does not change phase and its specific heat is treated as constant over the temperature interval, the transferred energy is:

Q=mc\Delta T

Symbol guide:

Symbol	Meaning	SI unit
$Q$	heat or transferred energy	$\text{J}$
$m$	object mass	$\text{kg}$
$c$	specific heat capacity	$\text{J/(kg K)}$
$\Delta T$	temperature change	$\text{K}$

When no phase change occurs, $Q=mc\Delta T$ relates heat transferred to mass, specific heat capacity, and temperature change.

Electrical energy can be calculated from electric power over a time interval. The model below is used when $V$ and $I$ are treated as constant during the time interval.

\begin{aligned} P &= VI \\ E &= Pt \\ E &= VIt \end{aligned}

Symbol guide:

Symbol	Meaning	SI unit
$E$	electrical energy	$\text{J}$
$P$	electric power	$\text{W}$
$V$	electric potential difference	$\text{V}$
$I$	electric current	$\text{A}$
$t$	time	$\text{s}$

Here $E$ denotes electrical energy. Upright $\text{W}$ is the unit symbol for watt, while italic $W$ often represents work.

At constant power, electrical energy equals power multiplied by time.

One Power Plant Converts Several Forms of Energy

Hydropower, for example, follows this chain:

The water first has gravitational potential energy. As it flows downward, energy becomes kinetic energy of the flowing water, then kinetic energy of the turning turbine, and finally electrical energy.

A solar panel receives radiant energy from sunlight, then changes part of that energy into electrical energy.

A complete energy chain names the initial energy, the desired output, and each conversion between them.

Distinguish Commonly Confused Ideas

Misconception	Correction
Kinetic energy is treated as depending only on mass	Kinetic energy also depends on the square of speed, written as $v^2$
Heat is treated as a substance stored inside an object	Heat is energy transferred because of a temperature difference
$\text{kWh}$ is treated as a unit of power	$\text{kWh}$ is a unit of energy because it comes from $P \times t$
All energy from a renewable source is treated as directly becoming electricity	A conversion device also transfers some energy to the surroundings, so only part of the input becomes useful electrical output

To choose the relevant formula for a renewable-energy device, identify the form of energy entering it. Moving air has kinetic energy, elevated water has gravitational potential energy, geothermal fluids carry thermal energy, biomass stores chemical energy, and sunlight carries radiant energy.

Where Energy Is Present and How It Crosses System Boundaries

All of these descriptions refer to the same physical quantity. The relevant formula depends on the object or process being analyzed.

Energy in Systems and Energy Transfers

Four Common Energy Calculations

Renewable-energy systems often involve motion, height, temperature differences, and moving electric charge. Each situation uses a different calculation.

Quantity being calculated	When it appears	Mathematical model	Renewable-energy example
Kinetic energy	an object moves	$E_k=\frac{1}{2}mv^2$	wind turns a turbine
Gravitational potential energy	an object is above a reference level	$E_p=mgh$	stored water is higher than a turbine
Energy transferred by heating	two systems have different temperatures	$Q=mc\Delta T$	geothermal fluid heats a power system
Energy transferred electrically	electric charge moves through a potential difference	$E=VIt$	a generator sends energy into the grid

Match the Formula to the Situation

Kinetic energy is the energy an object has because of its motion.

E_k=\frac{1}{2}mv^2

Symbol guide:

Symbol	Meaning	SI unit
$E_k$	kinetic energy	$\text{J}$
$m$	object mass	$\text{kg}$
$v$	object speed	$\text{m/s}$

If the air mass passing a turbine is $2 \text{ kg}$ and its speed is $3 \text{ m/s}$ , its kinetic energy is:

\begin{aligned} E_k &= \frac{1}{2}mv^2 \\ &= \frac{1}{2}(2 \text{ kg})(3 \text{ m/s})^2 \\ &= 9 \text{ J} \end{aligned}

The work-energy theorem relates net work to the change in kinetic energy.

Gravitational potential energy is energy related to an object's position in a gravitational field. For objects near Earth's surface, the common model is:

E_p=mgh

Symbol guide:

Symbol	Meaning	SI unit
$E_p$	gravitational potential energy	$\text{J}$
$m$	object mass	$\text{kg}$
$g$	gravitational acceleration	$\text{m/s}^2$
$h$	height relative to a reference level	$\text{m}$

Q=mc\Delta T

Symbol guide:

Symbol	Meaning	SI unit
$Q$	heat or transferred energy	$\text{J}$
$m$	object mass	$\text{kg}$
$c$	specific heat capacity	$\text{J/(kg K)}$
$\Delta T$	temperature change	$\text{K}$

When no phase change occurs, $Q=mc\Delta T$ relates heat transferred to mass, specific heat capacity, and temperature change.

Electrical energy can be calculated from electric power over a time interval. The model below is used when $V$ and $I$ are treated as constant during the time interval.

\begin{aligned} P &= VI \\ E &= Pt \\ E &= VIt \end{aligned}

Symbol guide:

Symbol	Meaning	SI unit
$E$	electrical energy	$\text{J}$
$P$	electric power	$\text{W}$
$V$	electric potential difference	$\text{V}$
$I$	electric current	$\text{A}$
$t$	time	$\text{s}$

Here $E$ denotes electrical energy. Upright $\text{W}$ is the unit symbol for watt, while italic $W$ often represents work.

At constant power, electrical energy equals power multiplied by time.

One Power Plant Converts Several Forms of Energy

Hydropower, for example, follows this chain:

A solar panel receives radiant energy from sunlight, then changes part of that energy into electrical energy.

A complete energy chain names the initial energy, the desired output, and each conversion between them.

Distinguish Commonly Confused Ideas

Misconception	Correction
Kinetic energy is treated as depending only on mass	Kinetic energy also depends on the square of speed, written as $v^2$
Heat is treated as a substance stored inside an object	Heat is energy transferred because of a temperature difference
$\text{kWh}$ is treated as a unit of power	$\text{kWh}$ is a unit of energy because it comes from $P \times t$
All energy from a renewable source is treated as directly becoming electricity	A conversion device also transfers some energy to the surroundings, so only part of the input becomes useful electrical output