Carnot-efficiency

Question

Carnot-efficiency

BlackTom AI · Accepted Answer

The question as presented is incomplete: there are no answer options provided to analyze. However, we can discuss the Carnot efficiency concept and evaluate the statement that appears in the provided answer field.

Carnot efficiency is the maximum possible efficiency of a heat engine operating between two thermal reservoirs and is given by η_Carnot = 1 − Tc/Th, where Th is the absolute temperature of the hot reservoir and Tc is the absolute temperature of the cold reservoir, both measured in Kelvin.

If a statement says: 'd. Depends only from the ratio of temperatures Tmin and Tmax,' this wording attempts to describe a dependence on temperature, but it is incomplete and potentially misleading. The key points to clarify are:
- The temperatures must be absolute (Kelvin). Using Celsius or another scale without converting to Kelvin would yield incorrect results.
- The efficiency depends on the ratio Tc/Th, not on a generic 'Tmin' and 'Tmax' without specifying which temperatures they refer to, and without ensuring they are the absolute reservoir temperatures.
- In practice, Th and Tc are the reservoir temperatures, not arbitrary minima and maxima of some other variable. The ratio must be used in the form 1 − Tc/Th; any dependence on Tmin/Tmax would be inappropriate unless Tmin is Th and Tmax is Tc in the proper context and both are in Kelvins.

To evaluate the correctness of the statement in a typical exam setting:
- If Tmin and Tmax are meant to denote the cold and hot reservoir temperatures in Kelvins (Tc = Tmin, Th = Tmax), then the expression should be η = 1 − Tmin/Tmax. This would be consistent with the Carnot formula, since Tc/Th would be Tmin/Tmax. However, the naming Tmin/Tmax can be confusing and nonstandard; what matters is that the two reservoir temperatures are used in Kelvin and in the ratio Tc/Th.
- If the statement asserts dependence on a ratio but uses non-absolute temperatures or mixes scales, it would be incorrect.

With the information given, and noting that no explicit multiple-choice options are listed for direct comparison, the central misconception often lies in neglecting the requirement that temperatures be absolute and in mislabeling which temperatures belong to the reservoirs versus arbitrary extrema. The precise, standard statement is: the Carnot efficiency depends on the ratio of the absolute temperatures of the hot and cold reservoirs, η_Carnot = 1 − Tc/Th, with Th > Tc > 0 (in Kelvin).

Carnot-efficiency

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