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A.3.14—Fuel energy density

Syllabus
First assessment 2025
Objective
—
Level
SL

Compare Fuel Energy Density

Energy per volume

For the current IB Physics definition, fuel energy density uu is the transferable energy per unit volume:

u=EVu=\frac{E}{V}

Its SI unit is J m−3\mathrm{J\,m^{-3}}. This lets fuels be compared when storage volume is the constraint.

Connect it to a fuel flow

If fuel flows at volume rate V˙\dot V, its input power is Pin=uV˙P_{in}=u\dot V. Apply efficiency only after finding the input energy or power.

Worked example from local Question Bank row 36970

An engine produces 20 kW20\,\mathrm{kW} useful power at 50%50\% efficiency while consuming 1.0×10−5 m3 s−11.0\times10^{-5}\,\mathrm{m^3\,s^{-1}} of fuel.

Pin=20 kW0.50=40 kWP_{in}=\frac{20\,\mathrm{kW}}{0.50}=40\,\mathrm{kW}
u=PinV˙=4.0×1041.0×10−5=4.0×109 J m−3=4.0 GJ m−3u=\frac{P_{in}}{\dot V}=\frac{4.0\times10^4}{1.0\times10^{-5}}=4.0\times10^9\,\mathrm{J\,m^{-3}}=4.0\,\mathrm{GJ\,m^{-3}}

Common trap

Specific energy is energy per unit mass, measured in J kg−1\mathrm{J\,kg^{-1}}. Some sources use the words loosely, so let the stated definition and units determine whether to divide by volume or mass.

A.3.14 Exam Analysis

[ 2 ]

At the end of the 30-day period, rockets are fired to bring the ISS back to its initial height. The energy density of liquid hydrogen rocket fuel is 8.5×103MJm−38.5 \times 10^{3} \mathrm{MJ} \mathrm{m}^{-3}.

Estimate the volume of fuel needed.

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.