Question

Look up today’s wholesale prices of natural gas in Texas (4.74 Dollars per thousand cubic feet) Calculate how much a kWh of electricity should cost, if it is being produced from (a) natural gas and (b) wind. You will need to worry about efficiency of combustion, energy content of natural gas, conversion of joules in kWh, etc. You will also need to figure out how to price wind, which of course blows for free.

Answer 1

Energy content of natural gas = 1037 BTU/ft³ = 1094 kJ/ft³

By definition, 1 kWh = 3600 kJ

Thus, Energy content = (1094/3600) kWh/ft³

= 0.304 kWh/ft³

Assume combustion efficiency = 95% = 0.95

Thermal Energy obtained by burning 1ft³ of gas = 0.304 * 0.95 = 0.289 kWh

Now to convert it into electricity, we'll need a generator. Assume its efficiency to be 40% or 0.4.

Therefore, electrical energy obtained by burning 1ft³ of gas = 0.289 * 0.4 = 0.116 kWh

For getting 1 kWh electricity, we'll need 1 / 0.116 ft³ of gas = 8.62 ft³

Cost of 8.62 ft³ of gas = 4.74 * 8.62 = $40.86

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For wind, since it is free, we'll only need an installation such as a wind turbine to convert it into electricity. It will be a one-time cost only. Hence, to generate 1 kWh of electricity from wind, cost will be zero.