Carnot-efficiency

Question

Carnot-efficiency

BlackTom AI · Accepted Answer

The Carnot efficiency question asks how the maximum efficiency of a heat engine operating between two reservoirs depends on temperature.
First, note that for an ideal Carnot engine, the efficiency is defined as η = 1 − Tc/Th, where Tc is the cold reservoir temperature and Th is the hot reservoir temperature. This expression shows that the efficiency depends solely on the temperatures, and specifically on their ratio, not on other factors like the amount of heat transferred or the working substance, provided the process is reversible.
In the given item, the proposed correct statement is: 'Depends only from the ratio of temperatures Tmin and Tmax.' If Tmin corresponds to Tc and Tmax to Th, this aligns with the Carnot result, since the efficiency is determined exclusively by Tc/Th and thus by the ratio of the two temperatures. This is consistent with the idealized, reversible-Carnot framework, where no real-world irreversibilities or non-adiabatic losses are present.
Potential misconceptions to watch for:
- Saying the efficiency depends on the temperature difference (Th − Tc) would be incorrect for a Carnot engine, because while the difference is related to the amount of work that could be performed for a given heat transfer, the exact Carnot efficiency formula uses the ratio Tc/Th, not the absolute difference.
- Claiming that efficiency is independent of temperatures would be false, since the Carnot limit explicitly involves Tc and Th.
- Asserting dependence on other factors (e.g., the type of working substance or the size of the engine) would be inaccurate for the ideal Carnot case, where only the reservoir temperatures matter.
- If one interprets Tmin and Tmax as fixed constants and assumes non-ideal real-world conditions, the real engine would underperform the Carnot limit and additional irreversibilities would come into play, but the theoretical Carnot efficiency remains a function of the reservoir temperatures only.
Overall, given the standard Carnot framework, stating that efficiency depends only on the ratio of the two temperatures (Th and Tc) is the correct characterization, whereas the other common alternatives either misstate the dependence or ignore the ideal assumptions of a reversible Carnot cycle.

BH20A0720 Engineering Thermodynamics - Blended teaching 2.9.2024-15.12.2024 Quiz 6

Carnot-efficiency

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