Northern California is home to the largest geothermal power plant in the world.

Question

Northern California is home to the largest geothermal power plant in the world. Its heat source is water at a temperature of 200 C (note: it is under high pressure, which keeps it from vaporizing). This heat is used to create steam to drive a turbine. The excess heat is vented to the outside air at 20.0 C. Find the maximum possible efficiency for this kind of power plant. For comparison, also find the maximum possible efficiency for a power plant that uses a coal furnace, at a temperature of 1700 C, as a heat source and also vents to the outside air. NOTE: (ANSWER : 38.1% and 85.1% NEED help figuring out how to get these answers)

(THIS QUESTION GOES TO THE FIRST ONE)The coal burning power plant described in Problem 3 (question above) has an actual efficiency that is only 34 of the maximum possible. It operates continuously, producing a steady output of 800 MW. If the heat of combustion for coal is 21.0 MJ/kg, how many metric tons of coal must this power plant use per day to operate? (NOTE: ANSWER: 5150) NEED help figuring out 5150.

Explanation / Answer

1)

we know that

maxium possible efficiency is given by

max eff = ( 1 - T1 / T2) x 100

given

T1 of vent = 20 C = 20 + 273 = 293 K

T2 of source= 200 C = 200 + 273 = 473 K

so

max eff = ( 1 - 293 / 473) x 100

max eff = 38.055 %

so

the maxiumum efficiency is 38.1 %

now

given

T2 = 1700 + 273 = 1973 K

so

max eff = ( 1- 293 / 1973) x 100

max eff = 85.14 %

so

the maximum possible efficiency is 85.14 %

2)

now

given

efficiecny = 0.75 x max efficiency

so

eff = 0.75 x 85.1

eff = 63.825

now

now

efficiency = ( output / input) x 100

so

63.825 = 800 x 100 ./ input

input = 1253 MW

so

input = 1253 MJ/s

for the total day

amount of energy = input x 86400

so

amount of energy = 1253 x 86400

now

amount of coal = amount of energy / heat of combustion

so

amount of coal = 1253 x 86400/ 21

amount of coal = 5155 x 10^3 kg

so

amount of coal = 5155 metric tons

so

5155 metric tons of coal is needed

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