The lower end of a capillary tube of radius r is dipped vertically into water, and water rises to a height h inside it. Taking d as the water density, g as gravity and J as the mechanical equivalent of heat, what is the net work done in the rise process (expressed in heat units)?

Question

Accepted Answer

-pi r² h² d g / (2J). The surface tension does work W_ST = (pi r² h d) g * h in raising the column (force balance gives the energy supplied as full weight times h). The potential energy actually stored is m*g*(h/2) = pi r² h d g * h/2, since the centre of mass rises only h/2. The remaining pi r² h² d g/2 is dissipated as heat. Expressed in heat units (dividing by J) and taken as net work done against/lost, the magnitude is pi r² h² d g/(2J). Treating the dissipated (lost) quantity as negative gives -pi r² h² d g/(2J).

The lower end of a capillary tube of radius r is dipped vertically into water, and water rises to a height h inside it. Taking d as the water density, g as gravity and J as the mechanical equivalent of heat, what is the net work done in the rise process (expressed in heat units)?

Solution

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