Calculating Efficiency of a Coal Fired Plant - 700 MW Electrical Power

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SUMMARY

The coal-fired plant generates 700 MW of electrical power, utilizing 5.8 million kg of coal daily. With a heat combustion value of 33 million J/kg, the total energy produced from coal combustion is 1.914 * 10^9 J. The actual efficiency of the plant can be calculated as the ratio of electrical output to thermal input, yielding an efficiency of approximately 3.67%. The ideal efficiency, based on the Carnot efficiency formula, is determined by the temperatures of the steam and exhaust water, resulting in a theoretical maximum efficiency of about 66.67%.

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A coal fired plant generates 700 MW of electrical power. The plant uses 5.8 * 10^6 kg of coal each day. The heat combustion of cal is 3.3 * 10^7 J/kg. The steam that drives the turbines is at a temperature of 320 C, and the exhaust water is at 45 C. Note: 700 MW= 7.0 * 10^8 J/s = 6.0 * 10^13 J/day.

What is the actual efficiency of the plant for generating electrical power?
What is the ideal efficiency of the plant for generating electrical power?
 
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