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Bituminous coal has a heat of combustion of 31.4 MJ/kg. In the United States the average coal-burning utility producesan average of 2.2 kWh of electrical energy per kilogram of bituminous coal burned. What is the average overall efficiency of this production of electricity

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xero099

Answer:

[tex]\eta = 25.223\,\%[/tex]

Explanation:

The average overall efficiency is given by the following expression:

[tex]\eta = \frac{w}{q}\times 100 \%[/tex]

[tex]\eta = \frac{(2.2\,kWh)\cdot (\frac{3600\,kJ}{1\,kWh} )}{31.4\times 10^{3}\,\frac{kJ}{kg}} \times 100\%[/tex]

[tex]\eta = 25.223\,\%[/tex]

snehashish65

The average overall efficiency of the production of electricity is 25.22%.

Given data:

The heat of combustion produced by the coal is, [tex]Q =31.4 \;\rm MJ/kg = 31.4 \times 10^{3} \;\rm kJ/kg[/tex].

The average electric energy produced per kg is, [tex]E = 2.2 \;\rm kWh = 2.2 \times 3600 = 7920 \;\rm kJ[/tex].

The given problem is based on the concept of overall efficiency. In general, it is general defined as the ratio of the energy produced and the heat of combustion due to burning of source (coal).

Then,

[tex]\eta = \dfrac{E}{Q} \times 100 \%[/tex]

Solving as,

[tex]\eta = \dfrac{7920 \;\rm kJ}{31.4 \times 10^{3} \;\rm kJ/kg} \times 100 \%\\\\\eta = 25.22 \%[/tex]

Thus, we can conclude that the average overall efficiency of the production of electricity is 25.22%.

Learn more about the overall efficiency here:

https://brainly.com/question/8199736

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