(455) HL Heat engines and Carnot cycle [IB Physics HL]

Heat Engines

• Definition: A cyclic gas process that performs useful work by converting thermal energy into mechanical work.

• Components:

  • Hot Reservoir: Contains thermal energy (QH) at temperature (T hot).

  • Cold Reservoir: Contains thermal energy (QC) at temperature (T cold).

• Energy Transfer:

  • The hot reservoir transfers energy (QH) to the engine, which then dumps the excess energy as (QC) while performing useful work.

Cyclic Gas Processes

• Definition: Processes that repeat in a cycle.

• Example: PV diagram illustrating points A, B, and C in a cyclic manner.

  • A to B: Isothermal expansion.

  • B to C: Isobaric compression.

  • C to A: Isovolumetric change.

• Key Point: The net change in internal energy (ΔU) over a complete cycle is zero.

Efficiency of Heat Engines

• Efficiency Formula:

  • Efficiency (η) = Useful Work / Input Energy

  • Important to note: Useful work is (QH - QC).

• Specific Formula: η = (QH - QC) / QH.

Carnot Cycle

• Definition: The most efficient theoretical heat engine, but not achievable in real life due to energy losses.

• Process Sequence: A to B (isothermal expansion), B to C (adiabatic expansion), C to D (isothermal compression), D to A (adiabatic compression).

• Efficiency of Carnot Cycle: Uses the formula η = 1 - (TC / TH).

  • Where: TC = Temperature of cold reservoir, TH = Temperature of hot reservoir.

• Maximizing Efficiency:

  • Minimize TC (cold temp) or maximize TH (hot temp).

Example of Carnot Engine

• Given:

  • TC in Celsius: 372°C (converted to Kelvin: 645 K).

  • TH in Celsius: 651°C (converted to Kelvin: 924 K).

• Calculation of Efficiency:

  • η = 1 - (645 / 924) = 0.31948 or approximately 30.2% efficient.

Conclusion

• Heat engine efficiency is related to the difference in thermal energy and the respective temperatures of the reservoirs.

• Understanding the operations and efficiency can aid in engineering more effective heat engines.