surface-energy-uses-the-same-gamma - Surface Tension and Capillarity Step by Step

Surface energy can share gamma only through a typed source chain. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Energy starts from the same gamma source

The energy check does not invent a new gamma. It points back to the line-force source before using an area.

\gamma_{\text{source}}=3\ \text{N/m}\qquad A=8\ \text{m}^{2}

More checked area stores more surface energy

Hold the cited gamma fixed. The area column alone changes the energy column.

\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}

Surface energy cites the same local gamma source

The energy ledger is allowed to share gamma only because it cites the exact line-force source by typed ref.

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