A heat engine works in a cycle between reservoirs at 273 K and 490 K. In each cycle, the engin

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A heat engine works in a cycle between reservoirs at 273 K...

A heat engine works in a cycle between reservoirs at $273 \mathrm{~K}$ and $490 \mathrm{~K}$. In each cycle, the engine absorbs $1250 \mathrm{~J}$ of heat from the high-temperature reservoir and does $475 \mathrm{~J}$ of work. (a) What is its efficiency? (b) By how much is the entropy of the universe changed when the engine goes through one full cycle? (c) How much energy becomes unavailable for doing work when the engine goes through one full cycle?

Key Concepts

Heat Engine Cycle

A heat engine cycle is a process in which a system undergoes a series of state changes, absorbing heat from a high-temperature reservoir, doing work, and rejecting heat to a low-temperature reservoir, ultimately returning to its initial state. This cyclical operation means that the internal energy change over one complete cycle is zero, and the engine's performance is characterized by the amounts of work done and heat transferred during the cycle.

Thermodynamic Efficiency

Thermodynamic efficiency quantifies the performance of a heat engine by comparing the work output to the heat input from the high-temperature source. It is a measure of how effectively the engine converts thermal energy into mechanical work and is crucial for evaluating and comparing the practical limitations of energy conversion processes.

Entropy

Entropy is a fundamental concept in thermodynamics that measures the level of disorder or randomness within a system. It plays a key role in determining the direction and feasibility of processes, as systems tend to evolve towards states of higher entropy. The concept is also central to assessing the irreversibility of processes and the second law of thermodynamics.

Entropy Change in Cyclic Processes

While the net entropy change of the working system in a complete cycle is zero (since it returns to its initial state), the process usually results in a net increase in the entropy of the universe. This is due to the generation of waste heat and the inherent irreversibility associated with real processes, reflecting the second law of thermodynamics.

Unavailable Energy

Unavailable energy, sometimes referred to as exergy loss or waste heat, represents the portion of energy that cannot be converted into useful work due to the limitations imposed by the second law of thermodynamics. This concept highlights that not all input energy in a heat engine is available for doing work, as a significant fraction is inevitably lost to irreversibilities in the system.

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