A power plant consumes 100 MJ of Energy, of which only 24 MJ are wasted heat. What is the efficiency?

Question

A power plant consumes 100 MJ of Energy, of which only 24 MJ are wasted heat.  What is the efficiency?

BlackTom AI · Accepted Answer

Efficiency is the fraction of input energy converted to useful output: efficiency = useful energy output / total input energy. Useful output here equals total input minus wasted heat.

Step-by-step reasoning and calculations:
1. Total input energy = 100 MJ.
2. Wasted heat = 24 MJ.
3. Useful energy output = total input − wasted heat = 100 MJ − 24 MJ = 76 MJ.
4. Efficiency (decimal) = useful output / total input = 76 MJ / 100 MJ.
   - The MJ units cancel: (76 MJ) / (100 MJ) = 76 / 100.
5. Compute the fraction: 76 / 100 = 0.76.
6. As a percentage: 0.76 × 100% = 76%.

Why this is correct:
- Efficiency is dimensionless because it is a ratio of energies with the same units. Using the complementary formula 1 − (wasted / input) gives the same result: 1 − (24/100) = 1 − 0.24 = 0.76.
- This shows 76% of the input energy is converted to useful work or output, while 24% is lost as waste heat.

Common mistakes (why other possible answers would be wrong):
- Reporting 0.24 (24%) would confuse wasted fraction with efficiency; waste is not the useful output.
- Using absolute MJ values without forming a ratio would not yield efficiency (which must be normalized to the input).
- Rounding errors are negligible here; 0.76 is exact given the integers.

Conclusion: The calculated efficiency is 0.76, which matches the provided correct answer.

A power plant consumes 100 MJ of Energy, of which only 24 MJ are wasted heat. What is the efficiency?Single choice

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