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What is the maximum possible theoretical efficiency of a heat engine operating with a hot reservoir of gases at 2127°C, when the cooling water available is at 27°C?
  • a)
    98.8%
  • b)
    90%
  • c)
    87.5%
  • d)
    100%
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What is the maximum possible theoretical efficiency of a heat engine ...
Concept
Efficiency of heat engine (ɳ) = (TH – TL) / TH = Wout/ Qin
TH = Temperature of the hot reservoir
TL = Temperature of the cold reservoir
Qin = Heat input to the engine
Wout = Work output from the engine
Calculation:
TH = 2127°C = 2127 + 273 = 2400 K
TL = 27°C = 27 + 273 = 300 K
Efficiency will be maximum when the engine is reversible.
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Most Upvoted Answer
What is the maximum possible theoretical efficiency of a heat engine ...
To calculate the maximum theoretical efficiency of a heat engine, we can use the Carnot efficiency formula:

Efficiency = 1 - (Tc/Th)

Where:
Efficiency is the maximum possible efficiency of the heat engine.
Tc is the temperature of the cooling water (in Kelvin).
Th is the temperature of the hot reservoir (in Kelvin).

Given:
Temperature of the hot reservoir (Th) = 2127°C = 2127 + 273 = 2400 K
Temperature of the cooling water (Tc) = 27°C = 27 + 273 = 300 K

So, the efficiency is:

Efficiency = 1 - (300/2400)
= 1 - 0.125
= 0.875 or 87.5%

Therefore, the maximum possible theoretical efficiency of the heat engine, operating with a hot reservoir of gases at 2127°C and cooling water available at 27°C, is 87.5%.
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