Predict/Calculate Engine A has an efficiency of 66% . Engine B absorbs the same amount of heat f

step 1 Hello everyone. This is Problem 79 from Chapter 18. It tells us that Engine A has an efficiency

Predict/Calculate Engine A has an efficiency of 66% . Engine...

Predict/Calculate Engine A has an efficiency of 66$\% .$ Engine $\mathrm{B}$ absorbs the same amount of heat from the hot reservoir and exhausts
twice as much heat to the cold reservoir. (a) Which engine has the
greater efficiency? Explain. (b) What is the efficiency of engine B?

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Key Concepts

Thermodynamic Efficiency

Thermodynamic efficiency is the ratio of the work output of an engine to the heat input from the high-temperature reservoir, often expressed as 1 minus the ratio of heat rejected to heat absorbed. This concept is fundamental for understanding how effectively a heat engine converts input energy into useful work.

Conservation of Energy in Cyclic Processes

In any heat engine cycle, the first law of thermodynamics ensures that the energy entering the system as heat is equal to the sum of the work output and the waste heat expelled. This energy conservation principle allows us to relate the amounts of heat absorbed and rejected, which directly influences an engine’s efficiency.

Heat Transfer Ratios and Efficiency Comparison

The ratio of heat rejected to heat absorbed is a crucial factor in determining efficiency. An engine that rejects a larger proportion of the absorbed energy—a higher heat transfer ratio—will have a lower efficiency. Comparing these ratios between different engines allows one to determine which engine operates more efficiently.

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