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A.3.3—Sankey diagrams

Syllabus
First assessment 2025
Objective
—
Level
HL

Read a Sankey Diagram

Read the width as energy

A Sankey diagram shows an input energy flowing into useful output and other transfers. Arrow width is proportional to energy, so the branches must account for the whole input.

Identify useful output

Label the useful branch before calculating efficiency. Other branches may represent heating, sound or unwanted mechanical transfers.

Connect to efficiency

The useful fraction of the input is

η=EusefulEinput=PusefulPinput\eta=\frac{E_{useful}}{E_{input}}=\frac{P_{useful}}{P_{input}}

Common trap

Do not compare branch widths without checking whether the diagram uses the same scale and whether the requested quantity is energy or power.

A.3.3 Exam Analysis

Assessment in practice

1–3 marks
How it is assessed

The evidence asks for an efficiency statement from a lamp diagram and for thermal power loss in a nuclear power-station Sankey diagram.

Command terms

Identify / Calculate

What earns marks

Read input, useful output and loss branches from the Sankey diagram. Use branch widths or labelled values to calculate efficiency or a missing power, and keep energy and power dimensions consistent.

Watch for

Reading a loss branch as useful output or applying an energy ratio to power values without checking the time basis.

Representative question

Question 1

[Maximum number: 1]

The Sankey diagram shows the energy input from fuel that is eventually converted to useful domestic energy in the form of light in a filament lamp.

What is true for this Sankey diagram?

A

The overall efficiency of the process is 10 %.

B

Generation and transmission losses account for 55 % of the energy input.

C

Useful energy accounts for half of the transmission losses.

D

The energy loss in the power station equals the energy that leaves it.

Retrieve the A.3 Work, Energy and Power Model

Account for energy

Define the system, identify energy stores and describe transfers. Work done by a force transfers energy; total energy is conserved even when mechanical energy is not.

Use the mechanical model

E_k= rac12mv^2,\quad \Delta E_{p,g}=mg\Delta h,\quad E_{p,elastic}= rac12k(\Delta x)^2

Conserve their sum only when resistive transfers are absent or included explicitly.

Use rates and ratios

P= rac{\Delta E}{\Delta t}=Fv,\qquad \eta= rac{E_{useful}}{E_{input}}= rac{P_{useful}}{P_{input}}

Fuel energy density connects available input energy to a chosen volume.

Final checks

Check the system boundary, signs of work and potential-energy changes, the reference height, extension from natural length, and whether the quantity is energy, power, efficiency or energy density.