How much coal does a power plant need for a year if its electrical capacity is 500 MW, and 105 kg of coal

| January 12, 2021 | education

How much coal does a power plant need for a year if its electrical capacity is 500 MW, and 105 kg of coal are needed to produce each megajoule. Calculate the efficiency of the power plant.

t = 1 year = 365 days = 8760 h = 31536000 s.
N = 500 MW = 500 * 10 ^ 6 W.
Q1 = 1 MJ = 1 * 10 ^ 6 J.
m1 = 105 kg.
q = 2.7 * 10 ^ 7 J / kg.
Efficiency -?
m -?
The efficiency of the power plant is expressed by the formula: efficiency = Q1 * 100% / Q1 “, where Q1” is the amount of heat generated during the combustion of m1 = 105 kg of coal.
Q1 “= q * m1.
Q1 “= 2.7 * 10 ^ 7 J / kg * 105 kg = 2835 * 10 ^ 6 J.
Efficiency = 1 * 10 ^ 6 J * 100% / 2835 * 10 ^ 6 J = 0.035%.
Most likely, an error was made in the problem statement, since the efficiency is very low.
N = Q / t.
Q = N * t.
Efficiency = Q * 100% / Q “.
Q = Q “* efficiency / 100%.
N * t = Q “* efficiency / 100%.
Q “= q * m.
N * t = q * m * efficiency / 100%.
m = N * t * 100% / q * efficiency.
m = 500 * 10 ^ 6 W * 31536000 s * 100% / 2.7 * 10 ^ 7 J / kg * 0.035% = 16.69 * 10 ^ 11 kg.
Answer: efficiency = 0.035%, m = 16.69 * 10 ^ 11 kg.



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