Capillary rise method for the determination of surface tension

The capillary rise method, also known as the capillary tube method, is used to measure the surface tension of a liquid. Here's how it works:

1. Setup: You need a thin, vertical glass tube (capillary tube) and a liquid whose surface tension you want to measure. The diameter of the tube should be small enough to observe capillary action.

2. Procedure:

   • Place the capillary tube upright into the liquid.
   • The liquid will rise or fall in the tube due to capillary action (the movement of liquid in a small space without the assistance of external forces).

3. Observation:

   • The height $h$ to which the liquid rises or falls is measured. This height depends on the liquid’s surface tension, the density of the liquid, the radius of the capillary tube, and the acceleration due to gravity.

4. Calculation: The surface tension $\gamma$ of the liquid can be calculated using the formula:

   $$\gamma =\frac{h\cdot \rho \cdot g\cdot r}{2}$$

   where:

   • $h$ is the height of the liquid column,
   • $\rho$ is the density of the liquid,
   • $g$ is the acceleration due to gravity,
   • $r$ is the radius of the capillary tube.

In summary, the capillary rise method measures how high a liquid can rise in a capillary tube due to surface tension, and this information is used to calculate the surface tension of the liquid.