THM-23

Otto efficiency

Ideal spark-ignition cycle.

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GoverningOtto efficiency

Governing equation

\eta=1-r^{1-\gamma}

$r \in \left[4, 16\right]$

where

r: r (—)
g: g (—)
eta: Otto efficiency (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\eta=1-r^{1-\gamma}

$r \in \left[4, 16\right]$

$r = 4$ $eta = 0.426$

Along the curve

②

Domain of the variable — blue

r_{\min} = 4,\quad r_{\max} = 16

$r \in \left[4, 16\right]$

$r = 4$ $r = 4$

Along the curve

③

Response curve — green

\eta=1-r^{1-\gamma}

$r \in \left[4, 16\right]$

$r = 4$ $eta = 0.426$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}eta}{\mathrm{d}r}

$r \in \left[4, 16\right]$

$r = 4.075$ $eta^{\prime} = 0.056$

Along the curve

Lecture brief

Historical brief

Carnot (1824), Clausius entropy, the first law and later van der Waals and Gibbs potentials turned heat into a state science. The sheets compute work, efficiency and vapour pressure. This sheet (THM-23 — Otto efficiency) is the form associated with Otto efficiency. Working symbols: $r$ , $g$ $\rightarrow$ $eta$ . Ideal spark-ignition cycle. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

eta

from

r

g

in Thermodynamics via

\eta=1-r^{1-\gamma}

Ideal spark-ignition cycle. Use it when a real thermodynamics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

r = 8.000\,\mathrm{—}

g = 1.400\,\mathrm{—}

, the governing relation

\eta=1-r^{1-\gamma}

yields

eta = 0.565\,\mathrm{—}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

r r8 —g g1.4 —

Outputs

Otto efficiency eta0.565 —

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Ideal spark-ignition cycle. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube