THM-30

Mayer's relation

Ideal-gas Mayer gap.

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GoverningMayer's relation

Governing equation

c_p-c_v=R

$cv \in \left[10, 40\right]$

where

cv: cv (J/(mol·K))
cp: Mayer's relation (J/(mol·K))

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

c_p-c_v=R

$cv \in \left[10, 40\right]$

$cv = 10$ $cp = 18.31$

Along the curve

②

Domain of the variable — blue

cv_{\min} = 10,\quad cv_{\max} = 40

$cv \in \left[10, 40\right]$

$cv = 10$ $cv = 10$

Along the curve

③

Response curve — green

c_p-c_v=R

$cv \in \left[10, 40\right]$

$cv = 10$ $cp = 18.31$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}cp}{\mathrm{d}cv}

$cv \in \left[10, 40\right]$

$cv = 10.19$ $cp^{\prime} = 1$

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-30 — Mayer's relation) is the form associated with Mayer's relation. Working symbols: $cv$ $\rightarrow$ $cp$ . Ideal-gas Mayer gap. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

cp

from

cv

in Thermodynamics via

c_p-c_v=R

Ideal-gas Mayer gap. Use it when a real thermodynamics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

cv = 20.800\,\mathrm{J/(mol·K)}

, the governing relation

c_p-c_v=R

yields

cp = 29.114\,\mathrm{J/(mol·K)}

. 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

cv cv20.8 J/(mol·K)

Outputs

Mayer's relation cp29.114 J/(mol·K)

Reading speed

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Narration of this film

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

Ideal-gas Mayer gap. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube