Question

1a. In the year 2030, it is conceivable that 20 gigawatts of electricity could be continuously generated in a single western state by coal burning power plants. At 37 percent efficiency for generating the electric power, how many tons of coal would be burned in a year? Give the answer in tons, but do not include the units.

b. In the previous problem, if the sulfur content of the coal averages 1 percent, how many tons of SO2 would be released per year?

c. Continuing with the same 20 GW of coal burning power plants, if a standard of 0.1 pounds of particulates per million Btu is adhered to, how many tons of particulates would be released in a year?

d. And as a final question about the power plants, how many tons of CO2 would be released per year, assuming that the coal is 100 percent carbon?

Answer 1

Before solving the question we must know that 1 Ton of coal equivalent gives a heat energy of = 29307600000 J

or, = 2.93076 x 10¹⁰ J

and 20 GW of electricity continuously generated by the coal power plant means output energy rate = 20 x 10⁹ W

= 20 x 10⁹ J/s

= 2 x 10¹⁰ J/s

now , if 37 % is the efficiency for the generating electric power , then total energy input into the generator to produce energy at the rate of 2 x 10¹⁰ J/s will be = output / efficiency

= 2 x 10¹⁰ J/s / 0.37

= 5.405 x 10¹⁰ J/s

so , total heat energy required for the whole year = 5.405 x 10¹⁰ x 31536000 ( since 1 year = 31536000 s)

= 1.704 x 10¹⁸ J

finally we have from 1 Ton of coal equivalent in Joule = 2.93076 x 10¹⁰ J

A) so total number of tons of coal required to burned to produce 1.704 x 10¹⁸ J of heat energy continuously =  1.704 x 10¹⁸ / 2.93076 x 10¹⁰

       = 58159685.54 Tons

B) if 1% of the total coal consumption per year is sulfur then total amount of sulfur will be = 1% of 58159685.54 Tons

= 581596.855 Tons of sulfur

but here Tons of SO₂ released in the air in 1 year need to be calculated so following the equation as:

S ( 32 u )    + O₂ ( 32 u) ------> SO₂ (64 u)

so, 32 atomic mass unit of Sulfur releases 64 amu of SO₂ , i.e double the amount of initial content

so, similarly 581596.855 Tons of sulfur will release 581596.855 x 2 = 1163193.711 Tons of SO₂ would be released per year