A Carnot engine operates with an efficiency of 27.0 % when...

A Carnot engine operates with an efficiency of $27.0 \%$ when the temperature of its cold reservoir is $275 \mathrm{~K}$. Assuming that the temperature of the hot reservoir remains the same, what must be the temperature of the cold reservoir in order to increase the efficiency to $32.0 \% ?$

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Key Concepts

Reservoir Temperature and Its Impact

The temperatures of the hot and cold reservoirs are crucial in determining the efficiency of a heat engine. In a Carnot cycle, lowering the temperature of the cold reservoir or raising the temperature of the hot reservoir can increase the engine’s efficiency, as these temperatures directly influence the fraction of heat converted into work.

Thermal Efficiency

Thermal efficiency measures the ratio of work produced by a heat engine to the heat absorbed from the hot reservoir. In the context of a Carnot engine, this efficiency is specifically given by the formula ? = 1 - (Tc/Th), highlighting the dependence on the absolute temperatures of the reservoirs.

Carnot Engine

A Carnot engine is an idealized heat engine that operates on the Carnot cycle, representing the most efficient possible engine that any heat engine can be. It serves as a fundamental benchmark in thermodynamics for understanding the limits of energy conversion between heat and work in reversible processes.

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