A reversible engine converts one-third of heat into work....

A reversible engine converts one-third of heat into work. When the temperature of the sink is reduced by $100^{\circ} \mathrm{C}$, it converts one-half of heat input into work. Calculate the temperatures of the source and the sink.

Key Concepts

Reversible Heat Engines

Reversible heat engines are idealized systems that operate on a cycle in which all processes are reversible, meaning that there is no net increase in entropy. These engines set the maximum possible efficiency limit that any real engine can achieve when operating between two heat reservoirs. The fundamental assumption of reversibility underpins the derivation of the Carnot efficiency, making these engines central to understanding the theoretical performance limits in thermodynamics.

Carnot Efficiency

Carnot efficiency is the maximum efficiency achievable by a heat engine operating between two thermal reservoirs at different absolute temperatures. It is expressed as 1 minus the ratio of the cold reservoir temperature to the hot reservoir temperature (? = 1 - T_c/T_h). This expression derives from the second law of thermodynamics and serves as a benchmark for comparing the performance of real engines to the ideal theoretical limit.

Absolute Temperature Scale

In thermodynamics, temperatures must be measured on an absolute scale, such as Kelvin, to correctly apply the formulas governing heat engine efficiency. The use of an absolute temperature scale ensures that calculations based on temperature ratios, like those in the Carnot efficiency, are physically meaningful and accurate, since degrees Celsius or Fahrenheit can lead to erroneous results when used in these contexts.

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