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title: "A geothermal heat engine absorbs thermal energy from a hot reservoir at \\(500 \\text{ K}\\) and exhausts thermal energy to a cold reservoir at \\(300 \\text{ K}\\). Which of the following correctly identifies the maximum theoretical efficiency of this engine and provides the physical justification for why an efficiency of \\(100\\%\\) cannot be achieved?"
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url: "https://nerd-notes.com/ubq/116150/"
date_modified: "2026-08-03T11:46:01+00:00"
---

# A geothermal heat engine absorbs thermal energy from a hot reservoir at \(500 \text{ K}\) and exhausts thermal energy to a cold reservoir at \(300 \text{ K}\). Which of the following correctly identifies the maximum theoretical efficiency of this engine and provides the physical justification for why an efficiency of \(100\%\) cannot be achieved?

A geothermal heat engine absorbs thermal energy from a hot reservoir at \(500 \text{ K}\) and exhausts thermal energy to a cold reservoir at \(300 \text{ K}\). Which of the following correctly identifies the maximum theoretical efficiency of this engine and provides the physical justification for why an efficiency of \(100\%\) cannot be achieved?

- **A.** The maximum theoretical efficiency is \(60\%\) because \(60\%\) of the absorbed thermal energy must be expelled as heat to satisfy the first law of thermodynamics.
- **B.** The maximum theoretical efficiency is \(40\%\) because completing a cyclic process requires expelling some thermal energy to the lower-temperature reservoir.
- **C.** The maximum theoretical efficiency is \(40\%\) because mechanical friction between moving engine components converts a portion of useful work into internal energy.
- **D.** The maximum theoretical efficiency is \(60\%\) because completing a cyclic process requires expelling some thermal energy to the lower-temperature reservoir.

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