What Is Energy Density of a Fuel and Why Does It Matter?

Energy density measures how much energy a fuel can release per unit mass, usually in joules per kilogram ($\text{J kg}^{-1}$) or megajoules per kilogram ($\text{MJ kg}^{-1}$). It matters because a higher energy density means less fuel mass is needed to provide a particular quantity of energy.

This is part of A.3 Work, energy and power and applies to both SL and HL.

Calculating energy density

For a fuel with mass $m$ that transfers energy $E$, its energy density is

$$e=\frac{E}{m}$$

Therefore, the energy transferred is $E=em$. For example, suppose a fuel has an energy density of $40\,\text{MJ kg}^{-1}$, and an engine requires $200\,\text{MJ}$ of input energy:

$$m=\frac{E}{e}=\frac{200\,\text{MJ}}{40\,\text{MJ kg}^{-1}}=5.0\,\text{kg}$$

A fuel with only $20\,\text{MJ kg}^{-1}$ would require $10\,\text{kg}$ to supply the same input energy.

A common misconception is that high energy density means high efficiency. Energy density describes the energy available per unit mass; efficiency is the fraction of input energy transferred usefully:

$$\eta=\frac{\text{useful energy output}}{\text{total energy input}}$$

Exam technique

In an IB response, state the definition, include the unit $\text{J kg}^{-1}$, and compare fuels using the same required energy. If asked to explain why energy density matters, connect it explicitly to the mass of fuel required rather than claiming that a high-energy-density fuel is automatically more efficient or environmentally preferable.