Power output of a coal burning power plant

In summary, the given coal power plant has an efficiency of 30% and burns 10 kilograms of coal per day. The power output of the plant is calculated to be 21 MJ/day and the rate of thermal energy being discarded is 49 MJ/day. To prevent the water temperature from increasing by more than 5°C, the rate at which water must flow away from the plant is calculated to be 1.4 L/s. The calculations for part 'a' and 'c' use 70% efficiency, while the wording states 30% which is incorrect. Discarded energy refers to the portion of energy that is not converted into useful energy. The solution for part c involves using the equation E=mcΔθ
  • #1
SeanWade
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Homework Statement


A coal power plant with 30% efficiency burns 10 kilograms of coal per day. (Take the heat of combustion of coal to be 30 MJ/kg)
a) what is the power output of the plant?
b) At what rate is thermal energy being discarded by this plant?
c) If the thermal energy is carried away by water whose temperature is not allowed to increase by more than 5°C, calculate the rate at which water must flow away from the plant.

*note: I already have the solution, I just don't understand it.*
Specifically my questions would be
1) If the efficiency is 30%, then doesn't that mean that the plant only turns 30% of the coals energy into useful energy? The answer says that 70% is converted to useful energy.
2) Is discarded energy just the amount of energy that isn't converted into useful energy?
3) Lastly (and I realize that this is a very vague request), can someone explain from start to end the solution to part c? I can make guesses as to the other parts of the problem, but this one completely baffles me.

Homework Equations



I have no idea where the equations in the answer came from. We weren't provided any in the chapter that would be specifically relevant to this problem.

The Attempt at a Solution


I attached a picture of the solution (the text wouldn't copy properly)
 

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  • #2
The calculation for part 'a' says 70% but the calculation uses 30%. So really you are correct and the actual calculation is correct, the wording is incorrect.

b) Yes, that is why they put 70% in the calculation i.e. 70% of the energy is not used.

c) From part b, you will get the rate of discarded energy in W (Pdiscarded).

The amount of energy required to raise the temperature of a substance is given by E=mcΔθ (see here for more information)

So the rate at which the energy will be transferred to the water is P=(m/t)cΔθ. Since you are transferring Pdiscarded, then P=Pdiscarded
 
  • #3
Thanks, that helped a lot!
 

What is the definition of power output in a coal burning power plant?

Power output refers to the amount of electricity that a coal burning power plant can generate and supply to the grid. It is measured in kilowatts (kW) or megawatts (MW) and is a key indicator of the plant's efficiency and capacity.

How is power output calculated in a coal burning power plant?

The power output of a coal burning power plant is calculated by multiplying the plant's heat rate (the amount of energy needed to produce one kilowatt-hour of electricity) by the amount of fuel consumed in a given time period.

What factors can affect the power output of a coal burning power plant?

The power output of a coal burning power plant can be affected by various factors, such as the quality and type of coal being burned, the efficiency of the plant's equipment, and external conditions like temperature and humidity. Maintenance and operational practices can also impact power output.

How does the power output of a coal burning power plant compare to other sources of energy?

Coal burning power plants typically have a higher power output than other sources of energy, such as wind or solar, due to the continuous combustion of coal and the ability to generate electricity on demand. However, coal is also a non-renewable and polluting source of energy.

Can the power output of a coal burning power plant be increased?

Yes, the power output of a coal burning power plant can be increased by improving the efficiency of its equipment, using higher quality coal, and implementing advanced technologies like carbon capture and storage. However, these measures may come with additional costs and environmental considerations.

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