A typical coal-fired power plant burns 310 metric tons of coal every hour to gen

Question

A typical coal-fired power plant burns 310 metric tons of coal every hour to generate 770 MW of electricity. 1 metric ton= 1000 kg. The density of coal is 1500 kg/m3 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.
A.) Suppose the coal is piled up in a 15 m × 14 m room. How tall must the pile be to operate the plant for one day?
B.) What is the power plant's thermal efficiency?
help! please show step by step process! thank you!

Explanation / Answer

mass of the coal burns per hour, m/t=310*10^3 kg/hr

electicity generate per hour E/t==770*10^6 W

and

density of the coal, rho=1500 kg/m^3

heat combution Q/m=28*10^6 J/kg

a)

volume of the coal piled room V=(15*14*h)

here, h is unknown( the height of the room)

V=(m/t)*1day/rho

V=(310*10^3*24)/(1500)

V=4960 m^3

but,

volume V=(15*14*h)

4960=(15*14*h)

==> h=23.62 m

b)

power input p=(m/t)*(Q/m)

p=(310*10^3/(60*60))*(28*10^6)

=2411.11*10^6 W

efficiency e=power out/power in

=(770*10^6)/(2411.11*10^6)

=0.319354

=31.93%

effiency e=31.93%

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