Question

The Navajo Generating Station was a 2250 MW plant when operating at full power.

a) Assuming the plant operates at 38% efficiency and that coal has a heat content of

10,500 BTU/lb, calculate how many tons of coal are used per year if the plant

operates at full capacity (assume 24 hrs/day, 7 days/week) .

b) Calculate the area needed to replace the power generated by NGS with Si

photocells operating at 21% efficiency assuming an average solar insolation of 6

kWhr/m2. show all work

Answer 1

full power operation of Navajo Generating Station , running all time in a year, at a rate of = 2250 MW

= 2250*10⁶ W

= 2250 *10⁶ J/s

so in 1 year at full power = 2250 *10⁶ *86400 *365 ( in a day total seconds = 86400 s)

= 7.09 *10¹⁶ J

or= 7.09 *10¹³ KJ

now the unit of heat content of coal is in BTU/lb and 1 BTU/lb to KJ/Kg = 2.326 Kj/kg

since , 1 BTU/lb = 2.326 KJ/kg

so 10500 BTU/lb = 10500 *2.326

= 24423 KJ/Kg

  

∴ total amount of coal required for 1 year if the plant operates at 38% efficiency=

power generation / (heat content * efficiency)

= 7.09 *10¹³ / (24423 *0.38)

= 7639477024 Kg

or = 7639477.02 Tons of coal

B) total area required to replace to power generation with Si photocells =

actual power generation required / ( Si photocell solar insolation * efficiency)

so, actual power = 7.09 *10 ¹³ KJ

= 7.09 *10 ¹³ / 3600

= 1.97 *10¹⁰ KWh

so total area required to fulfill same power generation as of coal plant = 1.97 *10¹⁰ / ( 6 * 0.21)

= 1.56 *10¹⁰ m²