A heat engine is a device that turns some thermal energy into useful work by operating between a hot reservoir and a cold reservoir. Examples include car engines, steam turbines, and many power plants. Heat engines matter because much of modern transportation and electricity generation depends on converting heat into motion or electrical energy.
The main question is how much of the input heat can become useful work.
Key Facts
- Energy balance for a heat engine: Qh = W + Qc
- Useful work output: W = Qh - Qc
- Thermal efficiency: e = W / Qh
- Equivalent efficiency formula: e = 1 - Qc / Qh
- Carnot maximum efficiency: emax = 1 - Tc / Th, with temperatures in kelvins
- A real heat engine must reject some heat to a cold reservoir, so Qc > 0 and e < 1
Vocabulary
- Heat engine
- A heat engine is a device that uses heat flow from a hot reservoir to a cold reservoir to produce useful work.
- Hot reservoir
- A hot reservoir is a high-temperature source that supplies heat energy Qh to the engine.
- Cold reservoir
- A cold reservoir is a lower-temperature sink that receives the rejected waste heat Qc from the engine.
- Thermal efficiency
- Thermal efficiency is the fraction of heat input that is converted into useful work.
- Carnot efficiency
- Carnot efficiency is the maximum possible efficiency of any heat engine operating between two reservoir temperatures.
Common Mistakes to Avoid
- Using Celsius in the Carnot efficiency formula, which is wrong because emax = 1 - Tc / Th requires absolute temperatures in kelvins.
- Assuming all heat input becomes work, which is wrong because the second law of thermodynamics requires some heat to be rejected to a cold reservoir.
- Confusing Qh and Qc, which leads to incorrect signs and efficiency values because Qh is heat absorbed and Qc is heat rejected.
- Reporting efficiency as W instead of W / Qh, which is wrong because efficiency is a ratio or percent, not an amount of energy.
Practice Questions
- 1 A heat engine absorbs 900 J of heat from a hot reservoir and rejects 540 J to a cold reservoir. Find the work output and the thermal efficiency.
- 2 An ideal Carnot engine operates between Th = 600 K and Tc = 300 K. What is its maximum efficiency, and how much work can it produce from 2000 J of heat input?
- 3 Explain why a heat engine cannot have 100 percent efficiency even if friction and mechanical losses are reduced to nearly zero.