Mercury has an angle of contact equal to 140° with soda lime glass. A narrow tube of radius 1.00 mm made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside ? Surface tension of mercury at the temperature of the experiment is 0.465 N m–1. Density of mercury = 13.6 × 103 kg m–3
Angle of contact between mercury and soda lime glass, θ=140o Radius of the narrow tube, r=1mm=1×10−3m Surface tension of mercury at the given temperature, s=0.465Nm−1 Density of mercury, ρ=13.6×103kg/m3 Dip in the height of mercury =h Acceleration due to gravity, g=9.8m/s2 Surface tension is related with the angle of contact and the dip in the height as: s=hρgr/2cosθ ∴h=2scosθ/ρgr =2×0.465×cos140o/(1×10−3×13.6×103×9.8) =−0.00534m =−5.34m Here, the negative sign shows the decreasing level of mercury. Hence, the mercury level dips by 5.34 mm.
