A heat engine receives heat from a source at 1100 K at a rate of 400 kJ / s, and it rejects th

step 1 In this question, we consider a heat engine receives a heat from source at 1 ,100 Kelvin, which

A heat engine receives heat from a source at 1100 K at a...

A heat engine receives heat from a source at $1100 \mathrm{~K}$ at a rate of $400 \mathrm{~kJ} / \mathrm{s}$, and it rejects the waste heat to a medium at $320 \mathrm{~K}$. The measured power output of the heat engine is $120 \mathrm{~kW}$, and the environment temperature is $25^{\circ} \mathrm{C}$. Determine ( $a$ ) the reversible power, $(b)$ the rate of irreversibility, and $(c)$ the second-law efficiency of this heat engine. Answers: (a) $284 \mathrm{~kW}$. (b) $164 \mathrm{~kW}$. (c) 42.3 percent.

Key Concepts

Second-Law Efficiency

Second-law efficiency is a performance metric that compares the actual performance of a heat engine to the performance of an ideal reversible engine (as characterized by the Carnot efficiency). It is defined as the ratio of the actual work output to the maximum possible (reversible) work output. This efficiency measure provides insight into how closely a real-world system approximates the ideal behavior predicted by the second law of thermodynamics.

Carnot Efficiency

Carnot efficiency is the maximum efficiency one can obtain from a heat engine operating between two thermal reservoirs. It is derived from the temperatures of the hot and cold reservoirs and sets the theoretical upper limit on how efficiently heat can be converted into work. The concept underscores the importance of temperature differences in determining the ideal performance of heat engines in a reversible cycle.

Reversible Process

A reversible process is an idealized thermodynamic process that proceeds infinitely slowly so that the system remains in equilibrium at all times, and no entropy is generated. In the context of heat engines, it represents the maximum theoretical performance (work output) that can be achieved when converting heat into work with no losses due to irreversibilities such as friction, heat transfer across finite temperature differences, or other dissipative effects.

Irreversibility

Irreversibility in a thermodynamic process quantifies the deviation from the ideal reversible process. It is directly related to the generation of entropy and corresponds to the loss of potential work. In the context of a heat engine, the rate of irreversibility is the difference between the reversible (maximum possible) power output and the actual measured power output, reflecting the efficiency losses due to non-idealities in the system.

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