Calculating Coal Usage for a 1000 MW Steam Power Plant

In summary, at a steam power plant, steam engines work in pairs with rejected heat from the first engine being the heat input to the second engine. The operating temperatures of the first engine are 670 C and 440 C, while the operating temperatures of the second engine are 440 C and 290 C. Assuming both engines work at 60% of their Carnot efficiency, the heat of combustion of coal is 2.8 x 10^7 J/kg. To produce a power output of 1000 MW, an expression for the amount of work performed and the efficiency of the engines must be found. Using the formula for Carnot efficiency and the given temperatures, the thermal efficiency of the engines can be calculated. With this
  • #1
physicsss
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At a steam power plant, steam engines work in pairs; the rejected heat from the first is the heat input to the second. The operating temperatures of the first are 670 C and 440 C. The operating temperatures of the second are 440 C and 290 C. Assume both engines work at 60% of their Carnot efficiency. The heat of combustion of coal is 2.8 x 10^7 J/kg. How many kg of coal must be burned per day if the power output of the plant is to be 1000 MW?

I know that the QL of the first engine is the QH of the second engine, but how do I get the actual values with only the efficiency and the ratio of the temperatures?
 
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Anyone have an idea?
 
  • #3
physicsss said:
I know that the QL of the first engine is the QH of the second engine, but how do I get the actual values with only the efficiency and the ratio of the temperatures?

You have more than just the ratio of temperatures, you have their actual values. Does this formula look familiar?

[tex]\epsilon=\frac{T_H-T_C}{T_H}[/tex]

That's the efficiency of a perfect Carnot cycle. Using this and what they gave you in the text, you should be able to figure out the efficiency of the machines themselves.

Once you have that, it's just a matter of using the definition of efficiency to get your answer. Here's another formula that might come in handy

[tex]\epsilon=\frac{|W|}{|Q_H|}[/tex]

Remember, efficiency is just the ratio of the energy you get out to what you put in.
 
  • #4
Alright, the both engines operate at 60% of their Carnot efficiency. You know this to be equal to:
[tex]\eta_{th,C}=1-\frac{T_c}{T_h}[/tex]
You know the hot and cold sink temperatures, so you can find the actual thermal efficiency of the engines by multiplying the Carnot efficiency by .6. You also know the thermal efficiency to be defined as:
[tex]\eta_{th}=\frac{w}{q_h}[/tex]
You know the power output you want to be 1000MW, which is 1000MJ in one second, or 8.64*10^7J per day. This is w. All you need to do is find an expression for the amount of work that comes from a given amount of heat input. To do this, you need to know how much energy is rejected by the first engine and put into the second. This comes from conservation of energy. It is just the difference between the heat supplied and the work performed.
 
  • #6
Astronuc said:
Supplementing what others have written -

Wtotal = W1 + W2, and

Wi = QH,i - QL,i

see also - http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/carnot.html#c1
Correction on this.

Wi = QH,i - QL,i is the ideal case with eff = 100%

if eff. < 100%, the Wi = [itex]\eta_i[/itex] (QH,i - QL,i), where [itex]\eta_i[/itex] is the efficiency.
 

FAQ: Calculating Coal Usage for a 1000 MW Steam Power Plant

How is coal usage calculated for a 1000 MW steam power plant?

The coal usage for a 1000 MW steam power plant is calculated by first determining the heat rate, or the amount of energy needed to produce one kilowatt-hour (kWh) of electricity. This is typically measured in British Thermal Units (BTUs) per kWh. The heat rate can then be used to calculate the amount of coal needed to produce 1000 MW of electricity, taking into account the efficiency of the power plant.

What factors affect the coal usage for a 1000 MW steam power plant?

The factors that affect coal usage for a 1000 MW steam power plant include the heat rate, efficiency of the power plant, and the quality of the coal being used. Other factors that may impact coal usage include the design and condition of the power plant, as well as the operating practices and maintenance procedures.

How is the efficiency of a power plant determined?

The efficiency of a power plant is determined by dividing the amount of electricity produced by the amount of energy consumed. This can be expressed as a percentage, with a higher percentage indicating a more efficient power plant. The efficiency of a power plant can also be affected by external factors such as weather conditions and demand for electricity.

Is coal the only source of energy used in a 1000 MW steam power plant?

No, coal is not the only source of energy used in a 1000 MW steam power plant. While coal is the primary source of energy for many steam power plants, some may also use other fuels such as natural gas, oil, or biomass. The type of fuel used can affect the overall efficiency and coal usage of the power plant.

How does the coal usage for a 1000 MW steam power plant impact the environment?

Burning coal for energy in a 1000 MW steam power plant can have negative environmental impacts, such as air pollution and greenhouse gas emissions. The amount of coal usage can also contribute to the depletion of natural resources and can potentially impact local ecosystems. It is important for power plants to continually improve their efficiency and explore alternative, cleaner sources of energy to mitigate these impacts.

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