Heat engines

Second Law of Thermodynamics

• States that heat energy flows spontaneously from high temperature to low temperature.

• Example: A hot cup of tea will cool down when left on a desk because heat is transferred to the surrounding environment.

• The process happens without any external work being performed.

Heat Energy Flow

• Heat energy generally transfers from a high temperature reservoir to a low temperature sink.

• This movement of heat may potentially do work if it passes through a heat engine.

• Analogous to a water wheel: water loses potential energy as it flows down, which can be converted to useful work.

Heat Engine and Work Done

• In a heat engine:

  • Heat energy from the high temperature reservoir is denoted as QH.

  • Heat energy rejected at the cold temperature sink is denoted as QC.

• Work done (W) by the engine can be calculated as:

  • W = QH - QC

Examples of Heat Engines

• Petrol Engine:

  • Burns fuel, producing hot gases that push pistons to do work. The leftover heat is expelled.

• Steam Engine:

  • Uses steam to push pistons, generating work.

• Steam Turbine:

  • Steam enters and turns turbines connected to generators to produce electricity.

Efficiency of Heat Engines

• Useful work done is expressed as:

  • Efficiency = (QH - QC) / QH = 1 - (QC / QH)

• Efficiency must always be less than 1, meaning some energy is invariably wasted.

Maximum Possible Efficiency

• Maximum efficiency is calculated by:

  • Efficiency_max = 1 - (Tc / TH)

  • Where Tc is the temperature of the cold sink, and TH is the temperature of the hot reservoir (in Kelvin).

• Greater temperature differences between the reservoir and the sink yield higher efficiencies.

Example Calculation

• For a steam turbine:

  • Steam enters at 300°C, exits at 27°C.

  • Convert to Kelvin:

    • TH = 300 + 273 = 573 K

    • Tc = 27 + 273 = 300 K

  • Calculate maximum efficiency:

    • Efficiency = 1 - (Tc / TH) = 1 - (300 / 573) ≈ 0.48

    • Thus, the maximum possible efficiency is 48%.