For which combination of working temperatures the efficiency...

For which combination of working temperatures the efficiency of Carnot's engine is highest.
(A) $80 \mathrm{~K}, 60 \mathrm{~K}$
(B) $100 \mathrm{~K}, 80 \mathrm{~K}$
(C) $60 \mathrm{~K}, 40 \mathrm{~K}$
(D) $40 \mathrm{~K}, 20 \mathrm{~K}$

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Key Concepts

Carnot Efficiency Formula

The efficiency of a Carnot engine is defined by the formula ? = 1 - (Tc/Th), where Th is the absolute temperature of the hot reservoir and Tc is the absolute temperature of the cold reservoir. This formula shows that the efficiency depends solely on the temperatures of the reservoirs and highlights the importance of using absolute temperature scales in thermodynamics.

Absolute Temperature Scale

In thermodynamic calculations involving efficiency, the temperatures must be measured on an absolute scale, such as Kelvin, because the efficiency of the Carnot engine is a function of the ratio of these temperatures. This ensures the physical relevance of the efficiency calculation, as relative temperatures might otherwise lead to incorrect conclusions.

Carnot Cycle

The Carnot cycle is an idealized thermodynamic cycle that serves as a standard of performance for heat engines. It represents a reversible cycle consisting of two isothermal processes and two adiabatic processes, making it the most efficient cycle possible between two thermal reservoirs under the constraints of the second law of thermodynamics.

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