Carnot's result implies that a heat engine could reach 100% efficiency only under one specific condition on the cold reservoir. What is that condition, according to the source?
AThe cold reservoir would need to equal the hot reservoir's temperature
BThe cold reservoir would need to be at room temperature
CThe cold reservoir would need to be at absolute zero, 0 K
DThe cold reservoir's temperature would need to double
Answer & Solution
Correct answer: C. The cold reservoir would need to be at absolute zero, 0 K
1. The Carnot efficiency formula is EffC = 1 - Tc/Th, so EffC equals 1, or 100%, only when the fraction Tc/Th equals zero.
2. Since Th is never zero for a real hot reservoir, that fraction can only vanish if Tc itself equals zero, meaning the cold reservoir sits at absolute zero.
3. Reaching absolute zero for a real reservoir is called a practical and theoretical impossibility, which is exactly why no real heat engine reaches 100% efficiency.
4. Making the two reservoirs equal in temperature, as in option A, would instead drive the efficiency to zero, not to 100%, since there would be no temperature difference to exploit.
5. Room temperature and a doubled cold-reservoir temperature, options B and D, do not correspond to the zero-efficiency-loss condition the formula requires.
_Source: OpenStax College Physics (CC BY 4.0), Ch 15 "Thermodynamics", section 15.4 Carnot's Perfect Heat Engine: The Second Law of Thermodynamics Restated_
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