The Carnot cycle is an ideal heat engine cycle that shows the highest possible efficiency any engine can have between two temperature reservoirs. It matters because it sets a theoretical limit for converting heat into useful work. Engineers use this limit to judge real engines, turbines, refrigerators, and power plants.
The cycle also connects thermodynamics to clear visual tools such as PV diagrams and TS diagrams.
Key Facts
- Carnot efficiency: e = 1 - Tc/Th, where temperatures must be in kelvin.
- Net work output per cycle: Wnet = Qh - Qc.
- For a reversible Carnot engine: Qh/Th = Qc/Tc.
- Isothermal expansion at Th: the gas absorbs heat Qh while temperature stays constant.
- Isothermal compression at Tc: the gas rejects heat Qc while temperature stays constant.
- On a TS diagram, heat transfer is area: Q = T Delta S for an isothermal reversible step.
Vocabulary
- Carnot cycle
- An ideal reversible thermodynamic cycle made of two isothermal processes and two adiabatic processes.
- Heat reservoir
- A large body that can supply or absorb heat while staying at nearly constant temperature.
- Isothermal process
- A thermodynamic process in which the temperature of the working substance remains constant.
- Adiabatic process
- A thermodynamic process in which no heat is transferred into or out of the system.
- Thermal efficiency
- The fraction of absorbed heat that a heat engine converts into net work output.
Common Mistakes to Avoid
- Using Celsius in e = 1 - Tc/Th is wrong because thermodynamic temperature ratios must use kelvin.
- Assuming a Carnot engine has 100 percent efficiency is wrong because some heat must be rejected to the cold reservoir unless Tc is 0 K, which is unattainable.
- Confusing adiabatic and isothermal steps is wrong because adiabatic steps have Q = 0, while isothermal steps involve heat transfer at constant temperature.
- Thinking real engines can beat Carnot efficiency is wrong because irreversibilities such as friction, turbulence, finite temperature differences, and heat losses always reduce efficiency.
Practice Questions
- 1 A Carnot engine operates between a hot reservoir at 600 K and a cold reservoir at 300 K. What is its maximum efficiency?
- 2 A reversible Carnot engine absorbs 1200 J of heat from a 500 K reservoir and rejects heat to a 300 K reservoir. Find Qc and the net work output per cycle.
- 3 Explain why making the cold reservoir colder increases the maximum efficiency of a Carnot engine, and describe one practical reason this is difficult in a real engine.