Efficiency of Fuels

What is Fuel Efficiency?
Fuel efficiency refers to the measure of the amount of energy from the fuel used to perform a function. The greater the amount of energy from the fuel required to perform a function, the lower the fuel efficiency.
Example: In today's vehicles
Today's common fossil fuel engines are not very efficient. Only about 15% of energy from fuel moves the vehicle, the rest is lost to heat and exhaust. In contrast, an efficient fuel in cars is one that is able to allow the vehicle to travel the greatest distance with the least amount of fuel.

Why is Fuel Efficiency important?
[Economic Benefit]
1. Saves money - A more efficient fuel can perform a function in smaller quantities compared to a less efficient fuel.
[Environmental Benefit]
2. Reduces climate change
3. Reduces dependency on oil / fossil fuels
4. Increases energy sustainability

What affects Fuel Efficiency?
Fuel efficiency is dependent on many parameters of a vehicle including its engine parameters, aerodynamic drag, weight and rolling resistance.

How to calculate Fuel Efficiency in vehicles?
Specifically in vehicles, fuel efficiency is given as a ratio of distance travelled per unit of fuel consumed, typically miles per gallon.
Example: Given that there are 15 gallons of gas in the tank of a car and that this car is able to drive 450 miles without refueling, we can calculate the fuel efficiency of this car to be 450 / 15 = 30 miles / gallon.

What if these fuels are not used to power vehicles? How do we then calculate its fuel efficiency?
Enthalpy change of combustion can be calculated instead. The most efficient fuels are the most exothermic ones which are able to release the most amount of energy per mol.

Example of Calculating Fuel Efficiency through Analysis of Experiment Results
An experiment was conducted to test the effectiveness of fuels by estimating the amount of energy released from burning the fuel. The fuels tested were methanol and cyclohexane (as well as our homemade biodiesel from vegetable oil which unfortunately contained too much water to be able to burn), in which we can compare both fuels to determine the more efficient one. Although it was a pity that none of our homemade biodiesel worked, it was a lesson learnt: homemade biodiesel is tough to make!

Setup of Experiment
A retort stand was used to hold a beaker containing water at a height adjusted according to the height of the tip of the flame for each fuel.

Burning of methanol is a small flame (before adjusting of beaker according to flame height)

Burning of cyclohexane is a large flame, and beaker is already covered in soot

Results of the Experiment

	Initial Temperature / °C	Final Temperature / °C	Time Taken
Methanol	31.0	100.0	1 min
Cyclohexane	31.0	75.0	2 mins

Based on this set of results alone, it seems that Methanol might be a more efficient fuel because when burnt, it heats the water up to a higher temperature in a shorter time. Methanol, too, burns cleaner than cyclohexane in that there is less soot produced.

Calculations
Mass of Water = volume x density = (40cm³ x 0.000001)(998.2kg/m³) = 0.39928kg
∆H = mc∆T where m=mass of water, c=specific heat capacity of water and T=temperature

[Methanol]
∆H of Methanol = (0.39928kg)(4.181KJ/kg K)(100.0°C-31.0°C) = 115.19KJ (to 5sf)
Amount of Methanol used in the experiment (in kg) = (10cm³  x 0.000001)(791.30kg/m³) = 0.007913kg
Amount of Methanol used in the experiment (in mol) = (0.007913kg x 10³) / (12+4+16) = 0.24728mol (to 5 sf)
∆H of Methanol = 115.19KJ / 0.42728mol = 466 KJ/mol (to 3sf)

[Cyclohexane]
Assuming that the temperature of the water heated by the burning of cyclohexane increased linearly over 2 minutes, we can take that the change in temperature of the water heated by burning of cyclohexane in 1 minute is ∆T /2
∆H of Cyclohexane = (0.39928kg)(4.181KJ/kg K)(75.0°C-31.0°C)/2 = 36.727KJ (to 3sf)
Amount of Cyclohexane used in the experiment (in kg) = (10cm³  x 0.000001)(779kg/m³) = 0.00779kg
Amount of Cyclohexane used in the experiment (in mol) = (0.00779kg x 10³) / (12x6+14) = 0.09058mol (to 5 sf)
∆H of Cyclohexane = 36.727KJ / 0.09058mol = 405 KJ/mol (to 3sf)

As with our initial predictions, calculated enthalphy change for both fuels shows that enthalphy change is greater in methanol than in cyclohexane per mol. The above experiment thus concludes that methanol is a more efficient fuel than cyclohexane.

Sources:
http://en.wikipedia.org/wiki/Fuel_efficiency