A reversible engine converts one-sixth of the heat input...

A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by $62^{\circ} \mathrm{C}$, the efficiency of the engine is doubled. The temperatures of the source and sink are (a) $99^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$ (b) $80^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$ (c) $95^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$ (d) $90^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$

A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by $62^{\circ} \mathrm{C}$, the efficiency of the engine is doubled. The temperatures of the source and sink are
(a) $99^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$
(b) $80^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$
(c) $95^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$
(d) $90^{\circ} \mathrm{C}, 37^{\circ} \mathrm{C}$

Key Concepts

Energy Conversion Efficiency

This concept describes the fraction of the heat input that a heat engine successfully converts into work. It is a key metric that quantifies the performance of engines and is influenced by the intrinsic thermodynamic limits imposed by reversible processes. When an engine’s efficiency is altered—such as being doubled by changes in operating temperatures—this underscores the relationship between thermal input, reservoir conditions, and work output.

Carnot Cycle Efficiency

This concept refers to the maximum efficiency achievable by any heat engine operating between two thermal reservoirs, as described by the Carnot theorem. The efficiency is given by the relation ? = 1 - (T_sink/T_source), where the temperatures are in absolute units (Kelvin). This formula is fundamental when analyzing reversible engines and establishes the theoretical upper bound for converting heat into work.

Temperature Scales and Conversions

Heat engine calculations require the use of absolute temperature scales, notably Kelvin, because the efficiency formula depends on temperature ratios. Converting temperatures from Celsius to Kelvin (by adding 273) is essential to correctly apply thermodynamic equations and obtain meaningful results in efficiency and work calculations.

Effect of Reservoir Temperature Changes

In thermodynamics, adjusting the temperatures of the heat reservoirs directly affects the engine’s efficiency. Lowering the sink temperature increases the thermal gradient, thereby improving efficiency, while changes in the source or sink temperatures shift the balance of heat exchange. In analysis problems, modifications to these temperatures can be used to investigate how performance limits scale with external conditions.

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