A heat engine receives heat from a source at 1500 K at a rate of 600 kJ / s and rejects the wa

step 1 We're told that a heat engine receives heat from a source at 1 ,500 Kelvin and at a rate of 600

A heat engine receives heat from a source at 1500 K at a...

A heat engine receives heat from a source at $1500 \mathrm{~K}$ at a rate of $600 \mathrm{~kJ} / \mathrm{s}$ and rejects the waste heat to a sink at $300 \mathrm{~K}$. If the power output of the engine is $400 \mathrm{~kW},$ the second-law efficiency of this heat engine is (a) $42 \%$ (b) $53 \%$ (c) $83 \%$ (d) $67 \%$ (e) $80 \%$

A heat engine receives heat from a source at $1500 \mathrm{~K}$ at a rate of $600 \mathrm{~kJ} / \mathrm{s}$ and rejects the waste heat to a sink at $300 \mathrm{~K}$. If the power output of the engine is $400 \mathrm{~kW},$ the second-law efficiency of this heat engine is
(a) $42 \%$
(b) $53 \%$
(c) $83 \%$
(d) $67 \%$
(e) $80 \%$

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Key Concepts

Second-Law Efficiency

Second-law efficiency compares the actual efficiency of a heat engine to the maximum possible efficiency as determined by the Carnot efficiency. It measures how well the engine performs relative to the ideal scenario, taking into account the irreversibilities present in real processes. This concept offers insight into the quality of energy conversion beyond simple energy balance.

Heat Engine Efficiency

Heat engine efficiency is a measure of how effectively a heat engine converts thermal energy into work. It is defined as the ratio of the work output to the heat input and indicates the performance of the engine based on the first law of thermodynamics.

Carnot Efficiency

Carnot efficiency represents the maximum possible efficiency that any heat engine operating between two thermal reservoirs can achieve. It is derived from the second law of thermodynamics and is given by the equation 1 - (T_cold/T_hot), where T_cold and T_hot are the absolute temperatures of the cold and hot reservoirs, respectively.

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