Question

assume a 1000 - megawatt power plant has an overall efficiency of 33% and that on average it operates at 50% of capacity in a days operation. using coal that has an energy content of 13,000 btu per pound, what is the daily supply amounts of coal in tons? (remember 1 btu = 1055 joules and 1 watt = 1 joule/second.)

question 2

in a coal power plant the following conversion process happens in the generator

mechanical energy to electrical energy

Explanation:

Step1: Calculate the actual power output

The power - plant capacity is $P_{capacity}=1000$ MW. It operates at 50% of capacity, so the actual power output $P$ is $P = 0.5\times1000\times10^{6}\text{ W}=5\times 10^{8}\text{ W}$.

Step2: Calculate the daily energy output in joules

There are $t = 24\times3600\text{ s}$ in a day. The energy output $E_{out}$ in a day is $E_{out}=P\times t=5\times 10^{8}\text{ J/s}\times24\times3600\text{ s}=4.32\times 10^{13}\text{ J}$.

Step3: Calculate the required input energy

The overall efficiency $\eta = 0.33$. Using the efficiency formula $\eta=\frac{E_{out}}{E_{in}}$, we can find the required input energy $E_{in}=\frac{E_{out}}{\eta}=\frac{4.32\times 10^{13}\text{ J}}{0.33}\approx1.309\times 10^{14}\text{ J}$.

Step4: Convert the input energy to Btu

Since $1\text{ Btu}=1055\text{ J}$, the input energy in Btu is $E_{in - Btu}=\frac{1.309\times 10^{14}\text{ J}}{1055\text{ J/Btu}}\approx1.241\times 10^{11}\text{ Btu}$.

Step5: Calculate the mass of coal in pounds

The coal has an energy content of $13000\text{ Btu/lb}$. So the mass of coal in pounds $m_{lb}=\frac{1.241\times 10^{11}\text{ Btu}}{13000\text{ Btu/lb}}\approx9.546\times 10^{7}\text{ lb}$.

Step6: Convert the mass of coal to tons

Since $1$ ton = 2000 lb, the mass of coal in tons $m_{tons}=\frac{9.546\times 10^{7}\text{ lb}}{2000\text{ lb/ton}}\approx47730$ tons.

Answer:

47730 tons