Problem

Problem

On a typical winter's day, 1.33×106 kJ1.33 \times 10^6 \text{ kJ} of energy is needed in a home. The specific energy densities and approximate empirical formulae of wood and coal and the efficiency of the heating systems are tabulated below.
FuelFormula of fuelSpecific energy / kJ g−1\text{kJ g}^{-1}Efficiency of heating / %
CoalCH3165
WoodC5H9O4\text{C}_5\text{H}_9\text{O}_42270
a. Calculate the percentage mass of carbon in the two fuels. b. Determine the carbon footprint from using the two forms of heating in terms of the mass of carbon dioxide produced by the two fuels. c. Suggest a reason why the carbon footprint calculation for wood does not give a full account of its impact on the environment.
Intuitive explanation

This problem asks you to compare two fuels by calculating how much of each you'd actually need to heat a home—the key is recognizing that useful energy delivered depends on both the fuel's energy content and the system's efficiency. You'll need to work backwards from the required energy: divide the total energy needed by the efficiency to find the chemical energy that must be released, then divide by specific energy density to get the mass of fuel. The fuel requiring less mass (or least cost/environmental impact) is the better choice.

Intuitive explanation

This problem asks you to compare two fuels by calculating how much of each you'd actually need to heat a home—the key is recognizing that useful energy delivered depends on both the fuel's energy content and the system's efficiency. You'll need to work backwards from the required energy: divide the total energy needed by the efficiency to find the chemical energy that must be released, then divide by specific energy density to get the mass of fuel. The fuel requiring less mass (or least cost/environmental impact) is the better choice.

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