4.1.1 Energy changes in a system, and the ways energy is stored

Key content

Energy is never used up. It is stored in different ways and transferred from one store to another. When you describe what happens in a situation, you describe which stores gain energy and which lose it.

Energy stores and systems

A system is an object or group of objects that you choose to study. Energy can be stored in a system in these stores:

kinetic – anything moving
gravitational potential – anything raised up in a gravitational field
elastic potential – anything stretched, squashed or bent
thermal (internal) – the hotter something is, the more energy is in its thermal store
chemical – fuels, food and batteries
magnetic, electrostatic and nuclear

Energy is transferred between stores by mechanical work (a force moving an object), electrical work (charges moving through a circuit), heating, and by radiation (such as light and sound).

Describing the changes in some common situations:

An object projected upwards: the kinetic store decreases and the gravitational potential store increases as it rises.
A moving object hitting an obstacle: the kinetic store decreases; the thermal stores of the object and obstacle increase, and some energy is transferred by sound.
An object accelerated by a constant force: work done by the force increases the object's kinetic store.
A vehicle slowing down: the kinetic store decreases; work done by friction in the brakes increases the thermal store of the brakes and surroundings.
Bringing water to the boil in an electric kettle: electrical work increases the thermal store of the water (and a little of the kettle and the air).

A closed system is one where no energy enters or leaves, so the total energy in it stays the same. In a closed system, energy can only move between stores inside it.

Changes in energy

You can calculate how much energy is in some stores.

The kinetic energy of a moving object depends on its mass and speed:

E_k = \tfrac{1}{2} m v^2

Doubling the speed makes the kinetic energy four times bigger, because speed is squared.

The elastic potential energy stored in a stretched spring (as long as it has not gone past its limit of proportionality) is:

E_e = \tfrac{1}{2} k e^2

where $k$ is the spring constant in N/m and $e$ is the extension in metres.

The energy gained in the gravitational potential store when an object is raised through a height $h$ is:

E_p = m g h

On Earth, the gravitational field strength $g$ is about 9.8 N/kg. In any calculation, the value of $g$ is given to you.

You can use these equations to show how the energy in a system is redistributed when it changes. For example, if a 0.50 kg ball is dropped from 5.0 m and air resistance is ignored, the decrease in its gravitational potential store equals the increase in its kinetic store: $mgh = 0.50 \times 9.8 \times 5.0 = 24.5$ J, so $\tfrac{1}{2} \times 0.50 \times v^2 = 24.5$ and $v \approx 9.9$ m/s.

Energy changes in systems

When a system is heated, the energy in its thermal store increases and its temperature usually rises. The increase depends on the mass, the material and the temperature rise:

\Delta E = m c \Delta \theta

The specific heat capacity $c$ is the energy needed to raise the temperature of 1 kg of a substance by 1 °C. Water has a high specific heat capacity (about 4200 J/kg °C), so it takes a lot of energy to heat it up.

You find the specific heat capacity of a material in Required practical 1.

Power

Power is the rate at which energy is transferred, or the rate at which work is done.

P = \frac{E}{t} \qquad P = \frac{W}{t}

The unit of power is the watt (W). An energy transfer of 1 joule per second is a power of 1 watt.

Two motors lifting the same load to the same height do the same work. The more powerful motor does it in less time.

Equations

Must recall

kinetic energy = 0.5 × mass × speed²

E_k = \tfrac{1}{2} m v^2

Symbol	Meaning	Unit
Eₖ	kinetic energy	J
m	mass	kg
v	speed	m/s

Given on equation sheet

elastic potential energy = 0.5 × spring constant × extension²

E_e = \tfrac{1}{2} k e^2

Symbol	Meaning	Unit
Eₑ	elastic potential energy	J
k	spring constant	N/m
e	extension	m

Must recall

gravitational potential energy = mass × gravitational field strength × height

E_p = m g h

Symbol	Meaning	Unit
Eₚ	gravitational potential energy	J
m	mass	kg
g	gravitational field strength	N/kg
h	height	m

Given on equation sheet

change in thermal energy = mass × specific heat capacity × temperature change

\Delta E = m c \Delta \theta

Symbol	Meaning	Unit
ΔE	change in thermal energy	J
m	mass	kg
c	specific heat capacity	J/kg°C
Δθ	temperature change	°C

Must recall

power = energy transferred ÷ time

P = \frac{E}{t}

Symbol	Meaning	Unit
P	power	W
E	energy transferred	J
t	time	s

Must recall

power = work done ÷ time

P = \frac{W}{t}

Symbol	Meaning	Unit
P	power	W
W	work done	J
t	time	s

Worked examples

Worked example

A 1200 kg car travels at 15 m/s. Calculate its kinetic energy.

$E_k = \tfrac{1}{2} m v^2 = 0.5 \times 1200 \times 15^2 = 0.5 \times 1200 \times 225 = 135\,000$ J

The car has 135 000 J (135 kJ) in its kinetic store.

Worked example

A 2.0 kg block of aluminium is heated from 20 °C to 45 °C. Aluminium has a specific heat capacity of 900 J/kg °C. How much energy was transferred to its thermal store?

$\Delta\theta = 45 - 20 = 25$ °C

$\Delta E = m c \Delta\theta = 2.0 \times 900 \times 25 = 45\,000$ J

Worked example

A kettle transfers 180 000 J of energy in 90 s. What is its power?

$P = \dfrac{E}{t} = \dfrac{180\,000}{90} = 2000$ W (2 kW)

Common misconceptions

Common misconception

"Energy gets used up." It doesn't – it is transferred to other stores. Often it ends up in the thermal store of the surroundings, where it is spread out and less useful.

Common misconception

"Doubling the speed doubles the kinetic energy." Speed is squared, so doubling the speed makes the kinetic energy four times bigger.

Common misconception

"Heat and temperature are the same thing." Temperature tells you how hot something is. The energy in the thermal store also depends on the mass and the material.