Question

A certain amount of fuel contains 15x102 Btu of energy, and converted into electric energy in a power station having a 12 percent overall efficiency. The average daily (24 hours) demand on the station is 5MW. In how many days will the fuel be totally consumed?

Answer 1

4396 days

Step-by-step explanation:

1 BTU =1055.06 Joules

total energy stored in fuel = 15 *
`10^(12)` * 1055.06 = 1.58259 *
`10^(16)` J

Total energy converted is 12% of this so 0.12 * 1.58259 *
`10^(16)` J = 1.899108 *
`10^(15)` J

Daily demand = 5 MW same as 5MJ/s for 24hours (notice units are seconds)

Daily demand in terms of joules is 5 *
`10^(6)` J * 24 hours * 60 min * 60 sec = 4.32 *
`10^(11)` J

So the fuel will be consumed in 1.899108 *
`10^(15)` J / 4.32 *
`10^(11)` J = 4396.08 or 4396 days