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

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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?

 

[russ_watters]

What have you calculated so far?

 

[quicknote]

The actual efficiency of the plant for generating electrical power can be calculated by dividing the electrical power output (7.0 * 10^8 J/s) by the total energy input, which is the heat combustion of coal (5.8 * 10^6 kg * 3.3 * 10^7 J/kg) multiplied by the number of seconds in a day (86400 seconds). This gives us an efficiency of approximately 40.4%.

The ideal efficiency of the plant for generating electrical power can be calculated using the Carnot efficiency formula, which is 1 - (T_low / T_high), where T_low is the temperature of the exhaust water and T_high is the temperature of the steam. In this case, T_low is 45 C (318 K) and T_high is 320 C (593 K), giving us an ideal efficiency of 46.3%.

It is important to note that the actual efficiency of the plant is lower than the ideal efficiency due to various factors such as energy losses during the conversion process and inefficiencies in the equipment. Improving the efficiency of the plant can help reduce its environmental impact and increase its overall productivity.