A typical coal-fired power plant burns 350 metric tons of coal every hour to gen

Question

A typical coal-fired power plant burns 350 metric tons of coal every hour to generate 710 MW of electricity. 1 metric ton = 1000 kg. The density of coal is 1500 Kg/M^3 and its heat of combustion is 28 MJ/Kg . Assume that all heat is transferred from the fuel to the boiler and that all the work done in spinning the turbine is transformed into electrical energy.
Suppose the coal is piled up in a 12 m x 9.0m room. How tall must the pile be to operate the plant for one day, and what is the plants thermal efficiency?

Explanation / Answer

I am answering only first part of question, since it is mathematics rather than physics. The plant would require 340*24 hours= 8160 MT of coal in a day. That is 8160000 kg. Volume of 1500 kg. of coal is 1m^3. Hence volume of 8160000 kg of coal will be 5440 m^3. If this much volume of coal is to be stored in an area of 11 x 11 m, then height of pile will have to be 5440/11*11 or 44.96 m. (That's pretty high, if 11 x 11 is a room. Just think where the roof will be!).

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