Approximately 1 billion tons of coal are burned annually in the United States, providing 50% of the country's electricity consumption. The coal may either be moved by train from the mine to power plants near where the power is used, or the coal could be combusted near the mine mouth to generate electricity and the electricity could be transmitted over long distances to the users. As a case study of this trade-off, consider electricity use in Dallas, which is generated, in part, using coal from the Powder River Basin (PRB) in Wyoming. Power plants using PRB coal supply 6.5 billion kilowatt hours of power per year to the Dallas area, at an average conversion efficiency (energy in the generated electricity per energy in the fuel burned) of 33%. The coal mined at the PRB has a heat content of 8340 Btu/lb coal. coal (1 kWhr = 3412 BTU)

a. Determine the amount of coal required from the PRB to support consumers in Dallas.

b. If the energy required to transport coal by train is 0.0025 gallons per ton mile, and the distance from the PRB to Dallas is 1000 miles, calculate the amount of energy required to transport the coal to Texas, and the total energy consumed in combustion and transport. What fraction of the total energy is consumption is due to transport? Assume that diesel fuel has an energy content of 124,000 BTU/gal.

c. Calculate the amount of coal consumed if the electricity were generated at the mine (assume a 33% power plant efficiency) and if the transmission losses for the electricity, from the mine to Dallas were 7%.