# A steam power station has a thermal efficiency of 30% and electrical efficiency of 90%, what is the overall efficiency of the station?

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A steam power station has a thermal efficiency of 30% and electrical efficiency of 90%, what is the overall efficiency of the station?

1. 27%
2. 33%
3. 90%
4. 30%

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Correct Answer - Option 1 : 27%

Concept:

The overall efficiency of the power plant is given as

$Overall\;Efficiency\;\; = \frac{{Electrical\;energy\;output}}{{chemical\;energy\;input}}$

Overall efficiency is also expressed as

${\eta _0} = \;\frac{{Thermal\;Energy}}{{Chemical\;Energy}} × \frac{{Mechanical\;Energy}}{{Thermal\;Energy}} × \frac{{Electrical\;Energy}}{{Mechanical\;energy}}$

So, the overall efficiency of the power plant is equal to the multiplication of the efficiencies of the boiler, turbine, and generator.

Overall Efficiency = Boiler efficiency × turbine efficiency × generator efficiency

ηpower plant = ηboiler × ηturbine × ηgenerator

Where,

Boiler efficiency = Thermal efficiency

Turbine efficiency × Generator efficiency = Electrical efficiency

∴ Overall Efficiency Thermal efficiency × Electrical efficiency

Calculation:

Given-

Thermal efficiency = 30%

Electrical Efficiency = 90%

Overall efficiency of the plant = (0.30) (0.90) = 0.27

Overall efficiency of the plant in percentages = 27%.