The efficiency of a particular car engine is 25 % when the...

The efficiency of a particular car engine is $25 \%$ when the engine does $8.2 \mathrm{~kJ}$ of work per cycle. Assume the process is reversible. What are (a) the energy the engine gains per cycle as heat $Q_{\text {gain }}$ from the fuel combustion and (b) the energy the engine loses per cycle as heat $Q_{\text {lost }}$ ? If a tune-up increases the efficiency to $31 \%$, what are (c) $Q_{\text {gain }}$ and (d) $Q_{\text {lost }}$ at the same work value?

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Key Concepts

Thermal Efficiency

This concept defines the ratio of useful work output to the energy input from heat. It quantifies how effectively a system converts heat into work. Mathematically, it is expressed as net work divided by the heat input, and it serves as a critical measure in the performance evaluation of heat engines and similar systems.

Energy Balance in Heat Engines

Energy conservation in a heat engine involves accounting for the energy supplied as heat, the useful work performed, and the energy lost (often as rejected heat). The energy gained per cycle from fuel combustion is partitioned into the work output and the lost energy, ensuring that the sum equals the total heat input, in accordance with the law of conservation of energy.

Reversible Process

A reversible process is an idealized thermodynamic process that occurs infinitely slowly, ensuring that the system remains in equilibrium at all stages. In such processes, no entropy is generated, and they represent the maximum possible efficiency a system can achieve under given constraints. This idealization is often used to establish theoretical limits and to simplify the analysis of energy transfers in heat engines.

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