Energy Changes in a System

This guide covers sub-topic 4.1.1 Energy changes in a system, and the ways energy is stored before and after such changes, the first of three sub-topics in Topic 4.1 Energy, from the AQA GCSE Physics (8463) specification (first teaching September 2016). Most of this content is co-teachable with GCSE Combined Science: Trilogy.

Before studying this

This is the first topic of the specification and assumes general numeracy and rearranging simple equations.

Syllabus coverage

AQA GCSE PHYSICS (8463) — Sub-topic 4.1.1

A system is an object or group of objects. There are changes in the way energy is stored when a system changes. Students should be able to describe all the changes involved in the way energy is stored when a system changes, for common situations, for example: an object projected upwards; a moving object hitting an obstacle; an object accelerated by a constant force; a vehicle slowing down; bringing water to a boil in an electric kettle. Students should be able to calculate the changes in energy involved when a system is changed by heating, work done by forces, and work done when a current flows, and use calculations to show on a common scale how the overall energy in a system is redistributed when the system is changed.

Students should be able to calculate the amount of energy associated with a moving object, a stretched spring and an object raised above ground level. The kinetic energy of a moving object can be calculated using kinetic energy = 0.5 × mass × (speed)². The amount of elastic potential energy stored in a stretched spring can be calculated using elastic potential energy = 0.5 × spring constant × (extension)² (assuming the limit of proportionality has not been exceeded). The amount of gravitational potential energy gained by an object raised above ground level can be calculated using g.p.e. = mass × gravitational field strength × height.

Required practical activity 1: investigation to determine the specific heat capacity of one or more materials, linking the decrease of one energy store (or work done) to the increase in temperature and subsequent increase in thermal energy stored.

The amount of energy stored in or released from a system as its temperature changes can be calculated using change in thermal energy = mass × specific heat capacity × temperature change. The specific heat capacity of a substance is the amount of energy required to raise the temperature of one kilogram of the substance by one degree Celsius.

Power is defined as the rate at which energy is transferred or the rate at which work is done: power = energy transferred / time, and power = work done / time. An energy transfer of 1 joule per second is equal to a power of 1 watt.

Energy stores and calculating energy changes

A system is an object or group of objects. When a system changes, energy is stored differently before and after — for example, a ball thrown upwards transfers energy from a kinetic store to a gravitational potential store as it rises. Common situations examinable include an object projected upwards, a moving object hitting an obstacle, an object accelerated by a constant force, a vehicle slowing down, and heating water in an electric kettle. These changes can occur through heating, work done by forces, or work done when a current flows.

Kinetic energy:

kinetic energy = 0.5 × mass × (speed)²
Ek = ½mv²

Elastic potential energy (within the limit of proportionality):

elastic potential energy = 0.5 × spring constant × (extension)²
Ee = ½ke²

Gravitational potential energy:

g.p.e. = mass × gravitational field strength × height
Ep = mgh

Specific heat capacity

When a system is heated, its temperature rise depends on the mass of the substance, the material’s specific heat capacity, and the energy supplied:

change in thermal energy = mass × specific heat capacity × temperature change
∆E = mc∆θ

The specific heat capacity of a substance is the amount of energy required to raise the temperature of one kilogram of the substance by one degree Celsius. Required practical activity 1 determines the specific heat capacity of one or more materials by linking the decrease of one energy store (or work done, e.g. electrically) to the resulting rise in temperature and thermal energy stored.

Power

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

power = energy transferred / time      [P = E/t]
power = work done / time               [P = W/t]

An energy transfer of 1 joule per second equals a power of 1 watt. Comparing two electric motors that both lift the same weight through the same height, but at different speeds, illustrates the definition of power: the faster motor has the greater power output.

Worked example. A ball of mass 0.20 kg is thrown vertically upward at 8.0 m/s. Using g = 9.8 N/kg, find its kinetic energy at launch and the maximum height it reaches (ignoring air resistance).

Kinetic energy at launch: Ek = 0.5 × 0.20 × (8.0)² = 6.4 J

At maximum height, all kinetic energy has transferred to gravitational potential energy: Ep = Ek, so mgh = 6.4 J.

h = 6.4 / (0.20 × 9.8) = 3.27 m

Common mistakes

Forgetting the 0.5 (½) factor in the kinetic energy and elastic potential energy equations. Using extension incorrectly in the elastic potential energy equation — it must be squared, and the equation only applies within the limit of proportionality. Confusing power (rate of energy transfer) with energy itself — always check whether a question gives a time. Mixing up mass (kg) and weight when substituting into g.p.e. = mgh.

Quick revision checklist

• Describe energy store changes for common situations (projectiles, collisions, accelerating objects, braking vehicles, heating water).
• Use Ek = ½mv², Ee = ½ke², and Ep = mgh.
• Use ∆E = mc∆θ and define specific heat capacity.
• Describe Required practical activity 1 (specific heat capacity).
• Use P = E/t and P = W/t, and state that 1 J/s = 1 W.

Related resources

• Energy Changes in a System revision notes
• Energy Changes in a System practice questions
• Conservation and Dissipation of Energy — the next sub-topic
• AQA GCSE Physics hub

This guide is intended to support, not replace, engagement with the official AQA specification and your own teacher’s guidance. Always check the current version of the specification for authoritative detail.