What formula does the source give for the Carnot efficiency, EffC, in terms of the cold and hot reservoir temperatures Tc and Th?
AEffC = 1 - Tc/Th, with both temperatures in kelvins
BEffC = Tc/Th, with both temperatures in kelvins
CEffC = 1 - Th/Tc, with both temperatures in kelvins
DEffC = Th - Tc, with both temperatures in kelvins
Answer & Solution
Correct answer: A. EffC = 1 - Tc/Th, with both temperatures in kelvins
1. Carnot found that for a perfect heat engine, the ratio Qc/Qh equals the ratio of the absolute temperatures of the heat reservoirs, Tc/Th.
2. Substituting Qc/Qh = Tc/Th into the general efficiency formula Eff = 1 - Qc/Qh gives the Carnot efficiency EffC = 1 - Tc/Th.
3. The temperatures here must be absolute temperatures, measured in kelvins, not degrees Celsius.
4. Option B omits the 1-minus part of the formula, and option D subtracts the temperatures directly rather than taking their ratio, so neither matches the derived expression.
5. Option C inverts which temperature sits in the numerator, which would make the efficiency formula behave backward as the hot reservoir gets hotter.
_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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