surface-energy-gamma-area-cross-scan - Surface Tension and Capillarity Step by Step

Surface energy is scanned across bound gamma and checked area. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Surface energy reuses a bound gamma source

The energy ledger is allowed to use gamma only by citing the checked line-force source. Area is the second independent input.

E=\gamma A=3\ \text{N/m}\cdot8\ \text{m}^{2}=24\ \text{J}

Changing gamma changes surface energy

Area is fixed in these three rows. The energy column changes only because the cited gamma source changes.

\begin{array}{c|c|c}\gamma&A&E\\2\ \text{N/m}&8\ \text{m}^{2}&16\ \text{J}\\3\ \text{N/m}&8\ \text{m}^{2}&24\ \text{J}\\4\ \text{N/m}&8\ \text{m}^{2}&32\ \text{J}\\\end{array}

Changing area also changes surface energy

Now the gamma source is fixed. The three area rows make the second input-output relationship visible.

\begin{array}{c|c|c}\gamma&A&E\\3\ \text{N/m}&4\ \text{m}^{2}&12\ \text{J}\\3\ \text{N/m}&8\ \text{m}^{2}&24\ \text{J}\\3\ \text{N/m}&12\ \text{m}^{2}&36\ \text{J}\\\end{array}