THM-25

Brayton efficiency

Ideal gas-turbine cycle.

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GoverningBrayton efficiency

Governing equation

\eta=1-r_p^{(1-\gamma)/\gamma}

$rp \in \left[4, 30\right]$

where

rp: rp (—)
g: g (—)
eta: Brayton 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_p^{(1-\gamma)/\gamma}

$rp \in \left[4, 30\right]$

$rp = 4$ $eta = 0.327$

Along the curve

②

Domain of the variable — blue

rp_{\min} = 4,\quad rp_{\max} = 30

$rp \in \left[4, 30\right]$

$rp = 4$ $rp = 4$

Along the curve

③

Response curve — green

\eta=1-r_p^{(1-\gamma)/\gamma}

$rp \in \left[4, 30\right]$

$rp = 4$ $eta = 0.327$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}eta}{\mathrm{d}rp}

$rp \in \left[4, 30\right]$

$rp = 4.164$ $eta^{\prime} = 0.046$

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-25 — Brayton efficiency) is the form associated with Brayton efficiency. Working symbols: $rp$ , $g$ $\rightarrow$ $eta$ . Ideal gas-turbine cycle. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

eta

from

rp

g

in Thermodynamics via

\eta=1-r_p^{(1-\gamma)/\gamma}

Ideal gas-turbine 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

rp = 10.000\,\mathrm{—}

g = 1.400\,\mathrm{—}

, the governing relation

\eta=1-r_p^{(1-\gamma)/\gamma}

yields

eta = 0.482\,\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

rp rp10 —g g1.4 —

Outputs

Brayton efficiency eta0.482 —

Reading speed

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Narration of this film

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

Ideal gas-turbine cycle. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube