Dimensional formula of Surface energy

How to get the dimensional formula of surface energy

1. Start from the definition: surface energy = energy / area.
2. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
3. energy = mass × velocity², so energy is [M] × [L T^-1]² = [M L² T^-2].
4. area = length × length, so area is [L] × [L] = [L²].
5. Put in the dimension of each part: [M L² T^-2] / [L²].
6. Add the powers of each base quantity: [M T^-2].

Quantities with the dimensions [M T⁻²]

• Spring constant
• Surface tension

Equal dimensions do not make them the same quantity. Compare surface energy with the others in the full grid.

Three questions on surface energy

Related quantities

• P Pressure [M L⁻¹ T⁻²]
• dP/dx Pressure gradient [M L⁻² T⁻²]
• σ Stress [M L⁻¹ T⁻²]
• U Strain energy [M L² T⁻²]
• u Strain energy density [M L⁻¹ T⁻²]
• ε Strain [M⁰ L⁰ T⁰]