A heat engine that rejects waste heat to a sink at 510 R has a thermal efficiency of 25 percent

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A heat engine that rejects waste heat to a sink at 510 R has...

A heat engine that rejects waste heat to a sink at $510 \mathrm{R}$ has a thermal efficiency of 25 percent and a second-law efficiency of 50 percent. Determine the temperature of the source that supplies heat to this engine. Answer: $1020 \mathrm{R}$.

Key Concepts

Carnot Efficiency

Carnot efficiency represents the maximum achievable efficiency for a heat engine operating between two thermal reservoirs, under the assumption of reversible processes without any irreversibility. It is calculated as 1 minus the ratio of the temperatures of the cold reservoir to the hot reservoir and sets the theoretical upper limit for the performance of any heat engine.

Second-Law Efficiency

Second-law efficiency, also known as exergetic efficiency, compares the actual performance of a heat engine to the maximum performance predicted by the second law of thermodynamics (represented by the Carnot efficiency). This metric takes into account the irreversibilities present in real processes and quantifies the deviation from ideal, reversible behavior.

Heat Engine

A heat engine is a device that converts thermal energy from a hot reservoir into mechanical work while rejecting some energy as waste heat to a lower temperature sink. Its operation is governed by the first and second laws of thermodynamics, and it serves as the fundamental concept in thermodynamic cycles and energy conversion systems.

Thermal Efficiency

Thermal efficiency is the ratio of the work output of a heat engine to the heat input it receives from the high-temperature source. This measure indicates how effectively a heat engine converts input heat into useful work, and it is inherently limited by the Carnot efficiency for any real engine.

Absolute Temperature

Absolute temperature scales, such as Kelvin or Rankine, are used in thermodynamic calculations to ensure that ratios of temperatures are dimensionally consistent and meaningful. These scales start at absolute zero, making them essential for accurately applying formulas like the Carnot efficiency equation.

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