How To Calculate Energy Density

What makes gasoline and other fuels so powerful? The potential of chemical mixtures such as fuels that power cars come from the reactions these materials are able to cause.

You can measure this energy density using straightforward formulas and equations that govern these chemical and physical properties when the fuels are put to use. The energy density equation gives a way of measuring this powerful energy with respect to the fuel itself.

The formula for ​energy density​ is

\(E_d=\frac{E}{V}\)

for energy density ​_E_d​, energy ​E​ and volume ​V​. You can also measure the ​specific energy​ ​E_s​ as ​E/M_​ for mass instead of volume. The specific energy is more closely correlated with the energy available that fuels use when powering cars than energy density is. Reference tables show that gasoline, kerosene and diesel fuels have much higher energy densities than coal, methanol and wood.

Regardless, chemists, physicists and engineers use both energy density and specific energy when designing automobiles and testing materials for physical properties. You can determine how much energy a fuel will give off based on the combustion of this densely packed energy. This is measured through energy content.

The amount of energy per unit mass or volume that a fuel gives off when it combusts is the energy content of fuel. While more densely packed fuels have higher values of energy content in terms of volume, lower-density fuels generally produce more energy content per unit mass.

The energy content has to be measured for a given volume of gas t a specific temperature and pressure. In the United States, engineers and scientists report the energy content in international British thermal units (BtuIT) while, in Canada and Mexico, energy content is reported in joules (J).

You can also use ​calories​ to report energy content. More standard methods of calculating energy content in science and engineering use the amount of heat produced when you burn a single gram of that material in joules per gram (J/g).

Using this unit of joules per gram, you can calculate how much heat is given off by increasing the temperature of a specific substance when you know the specific heat capacity ​_C_p​ of that material. The ​C_p_​ of water is 4.18 J/g°C. You use the equation for heat ​H​ as

\(H=\Delta T\times m\times C_p\)

in which ​∆T​ is a change in temperature, and m is the mass of the substance in grams.

If you experimentally measure the initial and final temperatures of a chemical material, you can determine the heat given off by the reaction. If you were to heat a flask of fuel as a container and record the change in temperature in the space directly outside the container, you can measure the heat given off using this equation.

When measuring temperatures, a temperature probe can continuously measure temperature over time. This will give you a broad range of temperatures for which you can use the heat equation. You should also look for places in the graph that show a ​linear relationship​ between temperature over time, as this would show that temperature is being given off at a constant rate. This likely indicates the linear relationship between temperature and heat that the heat equation uses.

Then, if you measure how much the mass of the fuel has changed, you can determine how energy was stored in that amount of mass for the fuel. Alternatively, you could measure how much of a volume difference this is for the appropriate energy density units.

This method, known as the ​bomb calorimeter​ method, gives you an experimental method of using the energy density formula to calculate this density. More refined methods can take into account heat lost to the walls of the container itself or the conduction of heat through the container's material.

You can also express energy content as a variation of the higher heating value (​HHV​). This is the amount of heat released at room temperature (25 °C) by a mass or volume of fuel after it combusts, and the products have returned to room temperature. This method accounts for the latent heat, the enthalpy heat that emerges when solidification and solid-state phase transformations occur during the cooling of a material.

Through this method, the energy content is given by the higher heating value at base volume conditions (​_HHV_b​). At standard or base conditions, the energy flow rate ​q_Hb​ is equal to the product of the volumetric flow rate ​q_vb_​ and the higher heating value at base volume conditions in the equation

\(q_{Hb}=q_{vb}\times HHV_b\)

Through experimental methods, scientists and engineers have studied the ​_HHV_b_​ for various fuels to determine how it can be determined as function of other variables pertinent to fuel efficiency. Standard conditions are defined as 10 °C (273.15 K or 32 oF) and 105 pascals (1 bar).

These empirical results have shown that ​_HHV_b​ depends on pressure and temperature at base conditions as well as the composition of the fuel or gas. In contrast, the lower heating value ​LHV_​ is the same measurement, but at the point at which the water in the final combustion products remains as vapor or steam.

Other research has shown that you can calculate ​HHV​ from the composition of the fuel itself. This should give you

\(HHV = .35X_C + 1.18X_H + 0.10X_S – 0.02X_N – 0.10X_O – 0.02X_{ash}\)

with each ​X​ as the fractional mass for carbon (C), hydrogen (H), sulfur (S), nitrogen (N), oxygen (O) and the remaining ash content. Nitrogen and oxygen have an adverse effect on the ​HHV​ as they don't contribute to the release of heat as other elements and molecules do.

Biodiesel fuels offer an environmentally-friendly method of producing fuel as an alternative to other, more harmful fuels. They're created from natural oils, soybean extracts and algae. This renewable fuel source results in less pollution to the environment, and they are usually mixed with petroleum fuels (gasoline and diesel fuels). This makes them ideal candidates for studying how much energy a fuel uses using quantities like energy density and energy content.

Unfortunately from an energy content perspective, biodiesel fuels have a large amount of oxygen, so they produce lower energy values with respect to their mass (in units of MJ/kg). Biodiesel fuels have about a 10 percent lower mass energy content. B100, for example, has an energy content of 119,550 Btu/gal.

Another way of measuring how much energy a fuel uses is the energy balance, which, for biodiesel is 4.56. This means biodiesel fuels produce 4.56 units of energy for every unit of fossil energy they use. Other fuels pack more energy, such as B20, a blend of diesel with biomass fuel. This fuel has about 99 percent of the energy of one gallon of diesel or 109 percent of the energy of one gallon of gasoline.

Alternative methods exist for determining the efficiency of heat given off by biomass in general. Scientists and engineers that study biomass use the bomb calorimeter method to measure the heat released from combustion that is transferred to either air or water surrounding the container. From this, you can determine the ​HHV​ for the biomass.