Energy costs vary greatly with energy source: coal @ $35.00/ton, gasoline @ a pump price of $2.75/gal, and electricity @ $0.100/kW·h. Conventional practice is to put these on a common basis by expressing them in $?GJ ?1. For this purpose, assume gross heating values of 29 MJ?kg?1 for coal and 37 GJ?m?3 for gasoline.

Question

(a) Rank order the three energy sources with respect to energy cost in $?GJ ?1.
(b) Explain the large disparity in the numerical results of part (a). Discuss the advantages and disadvantages of the three energy sources.

Answer 1

a. The cost of coal per GJ is $25/ton / (907.2 kg/ton * 0.029 GJ/kg ) = $0.95 /GJ.
The cost of gasoline is $2/gal * 264.2 gal/m3 / 37 GJ/m3 = $14.30 /GJ.
The cost of electricity is $0.1 /(kW hr) / 0.0036 GJ/(kW hr) = $27.80 /GJ.
Coal is least expensive, electricity is most expensive.

b. One can explain this in a variety of ways, but the underlying factor is that energy that is more convenient and/or more efficiently usable costs more. Electricity can be converted to mechanical energy (work) with nearly 100% efficiency (at least >90% in a well designed electric motor). In contrast, a gasoline-burning internal combustion engine might have a typical efficiency of 30 to 35%. Thus, with the costs in part (a), and all other things being equal, an electric car might be more cost effective to operate than a gasoline-powered one, because the higher efficiency of energy use would more than make up for the higher cost per unit of energy input. This is what makes electric or plug-in hybrid vehicles (potentially) economical.
On the other hand, coal is inexpensive because it is very inconvenient to use. It cannot readily be used on a small scale, and is mostly consumed in large-scale industrial electricity generation and heating processes. A coal-fired power plant can convert about 1/3 of the energy of the coal into electricity. If that were the only cost of generating electricity, then with the costs in part (a), generating electricity from coal would be a very profitable business. However, the consumer electricity cost of $0.10/kW*hr reflects (along with profits) the costs of building the coal-fired power plant (although most US plants are old, and fully amortized) the cost of crushing and cleaning up the coal for combustion, the cost of pollution mitigation, and the cost of transmitting the power from the power plant . In mid- 2008, the actual average coal cost for power generation was about $2 /GJ, which leads to an electricity generation cost of something like $0.03 per kW-hr, without including transmission costs, costs of pollution/cleanup, or capital costs of building the plant.