Question

A power station using coal as fuel has an average power output of 3000 MW. Coal is supplied by

Answer 1

The mass of coal needed is C) $1.5\cdot 10^6 kg$

Explanation:

The average output of the power station is

$P_{out}=3000 MW = 3\cdot 10^9 W$

Therefore we can find the average output energy $E_{out}$ per day using

$P_{out}=\frac{E_{out}}{t}$

where

$t=1d = 24\cdot 60\cdot 60=86,400 s$ is the duration of one day

So we get

$E_{out}=P_{out}t=(3\cdot 10^9)(86400)=2.59\cdot 10^{14} J$

The efficiency of the station in converting the energy is only 26%, so this means that the energy that must be produced in input by the coal per day is

$E_{in}=\frac{E_{out}}{0.26}=1.0\cdot 10^{15}J$

This means that the input energy per train (20 trains) is

$E=\frac{E_{in}}{20}=5.0\cdot 10^{13}J=50,000,000 MJ$

Since 1.0 kg of coal releases 33 MJ of thermal energy, we can write the following rule of three:

$\frac{1.0 kg}{33 MJ}=\frac{m}{50,000,000 J}$

where m is the amount of coal needed for each train. Solving for m,

$m=\frac{(50,000,000)(1.0)}{33}=1.5\cdot 10^6 kg$

Learn more about power and energy:

brainly.com/question/7956557

#LearnwithBrainly