The following observations were take for determining surface...

The following observations were take for determining surface tension of water by capillary tube method. Diameter of capillary, $D=1.25 \times 10^{-2} \mathrm{~m}$ and rise of water in capillary, $h=1.46 \times 10^{-2} \mathrm{~m}$. Taking $g=9.80 \mathrm{~ms}^{-2}$ and using the relation $T=(r g h / 2) \times 10^{3} \mathrm{Nm}^{-1}$, what is the possible error in surface tension $T$ ? (a) $2.4 \%$ (b) $15 \%$ (c) $1.696$ (d) $0.15 \%$

The following observations were take for determining surface tension of water by capillary tube method. Diameter of capillary, $D=1.25 \times 10^{-2} \mathrm{~m}$ and rise of water in capillary, $h=1.46 \times 10^{-2} \mathrm{~m}$. Taking $g=9.80 \mathrm{~ms}^{-2}$ and using the relation $T=(r g h / 2) \times 10^{3} \mathrm{Nm}^{-1}$, what is the possible error in surface tension $T$ ?
(a) $2.4 \%$
(b) $15 \%$
(c) $1.696$
(d) $0.15 \%$

Key Concepts

Surface Tension

Surface tension is the property of a liquid that describes its tendency to minimize its surface area. It arises from the cohesive forces among the liquid’s molecules and is a critical parameter in phenomena such as capillary rise, droplet formation, and wetting. In experiments, it is often determined by balancing the gravitational forces on a liquid column with the cohesive forces at the fluid interface.

Capillary Rise Method

The capillary rise method measures the height to which a liquid ascends in a thin tube due to surface tension. This phenomenon, explained by the balance between cohesive forces (which create surface tension) and gravitational forces, is quantified using relationships such as Jurin's law. This method is widely used for determining the surface tension of liquids, particularly when direct measurement methods are impractical.

Error Propagation

Error propagation involves estimating the uncertainty in a calculated result based on the uncertainties in the measured variables. When using a formula that relates several measured parameters to compute a physical quantity, differential calculus or other approaches can be applied to determine how the individual measurement errors combine to affect the final result. This analysis is vital to provide a reliable range for the derived physical property such as surface tension.

Relative and Percentage Error

Relative error is the ratio of the absolute error in a measurement to the actual measurement value, and when expressed as a percentage, it becomes the percentage error. This metric allows scientists to assess the quality of measurements and compare uncertainties across different experiments and scales. In the context of determining surface tension by the capillary tube method, estimating the percentage error helps to understand the accuracy and reliability of the measurements and calculations.

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