Engine Work Fraction Three-Row Scan - Thermodynamics and Statistical Mechanics Step by Step

An engine-work-fraction scan varies the work output across three rows at fixed heat input, showing how the efficiency eta = W / Q_in moves row by row. The arithmetic is exact only for the stated work, heat, and rows in the ideal simple-engine model. Real measurements add temperature-scale error, pressure/volume calibration, thermal-equilibrium limits, gas nonideality, friction/losses, finite precision, and measurement uncertainty.

At fixed heat input, useful work raises efficiency and lowers waste. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Six joules of work is one fifth

With heat input fixed at 30 joules, useful work 6 joules leaves 24 joules as waste.

\eta=6\ \text{J}/30\ \text{J}=\tfrac{1}{5}

Twelve joules of work raises the fraction

The middle row converts 12 joules to work and rejects 18 joules. Efficiency rises to two fifths.

\eta=12\ \text{J}/30\ \text{J}=\tfrac{2}{5}

Eighteen joules of work leaves less waste

The third row converts 18 joules and leaves 12 joules. Three rows expose the useful-work fraction.

\begin{array}{c|c|c|c}Q_{\text{in}}&W&Q_{\text{waste}}&\eta\\30\ \text{J}&6\ \text{J}&24\ \text{J}&\tfrac{1}{5}\\30\ \text{J}&12\ \text{J}&18\ \text{J}&\tfrac{2}{5}\\30\ \text{J}&18\ \text{J}&12\ \text{J}&\tfrac{3}{5}\\\end{array}