If the station has a thermal efficiency of 30% and electrical efficiency of 95%, find the overall efficiency of the station.

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  1. 26.5%
  2. 27.5%
  3. 28.5%
  4. 29.5%

Answer (Detailed Solution Below)

Option 3 : 28.5%
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Detailed Solution

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Concept of Overall Efficiency:

The overall efficiency (ηoverall) of a station is the product of its thermal efficiency (ηthermal) and its electrical efficiency (ηelectrical).

The formula to calculate the overall efficiency is:

ηoverall = ηthermal × ηelectrical

Where,

  • ηthermal = Thermal efficiency (in decimal form)
  • ηelectrical = Electrical efficiency (in decimal form)

Given Data:

  • Thermal efficiency (ηthermal) = 30% = 0.30
  • Electrical efficiency (ηelectrical) = 95% = 0.95

Calculation:

Using the formula:

ηoverall = ηthermal × ηelectrical

Substituting the given values:

ηoverall = 0.30 × 0.95

ηoverall = 0.285

Converting to percentage:

ηoverall = 0.285 × 100%

ηoverall = 28.5%

Conclusion:

Hence, the overall efficiency of the station is 28.5%.

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