Name: Angle of Contact
Uploaded: 2019-07-19
Duration: 6 min 57 s
Description: What is the contact angle? Which factor does the contact angle depend on? Why does the contact angle for the same liquid on different surfaces differ? Let's...

Question

Describe the method of determination of surface tension of a liquid by capillary rise. Derive the expression used.

Accepted Answer

If a tube of very narrow bore (called capillary) is dipped in a liquid, it is found that the liquid in the capillary either ascends or descends relative to the surrounding liquid. This phenomenon is called capillarity.
The root cause of capillarity is the difference in pressures on two sides of (concave and convex) curved surface of liquid.

Examples of capillarity:

$(i)$ Ink rises in the fine pores of blotting paper leaving the paper dry.

$(i i)$ A towel soaks water.

$(i i i)$ Oil rises in the long narrow spaces between the threads of a wick.

$(i v)$ Wood swells in rainy season due to rise of moisture from air in the pores.

$(v)$ Ploughing of fields is essential for preserving moisture in the soil.

$(v i)$ Sand is drier soil than clay. This is because holes between the sand particles are not so fine as compared to that of clay, to draw up water by capillary action.

When one end of capillary tube of radius $r$ is immersed into a liquid of density $d$ which wets the sides of the capillary tube (water and capillary tube of glass), the shape of the liquid meniscus in the tube becomes concave upwards.

$R =$ radius of curvature of liquid meniscus.

$T =$ surface tension of liquid

$P =$ atmospheric pressure

Pressure at point $A = P$ , Pressure at point $B = P - \frac{2 T}{R}$

Pressure at points $C$ and $D$ just above and below the plane surface of liquid in the vessel is also $P$ (atmospheric pressure). The points $B$ and $D$ are in the same horizontal plane in the liquid but the pressure at these points is different.

In order to maintain the equilibrium the liquid level rises in the capillary tube upto height $h$ .

Pressure due to liquid column $=$ pressure difference due to surface tension

$\Rightarrow h d g = \frac{2 T}{R}$

$∴ h = \frac{2 T}{R d g} = \frac{2 T \cos θ}{r d g}$ [As $R = \frac{r}{\cos θ}$ ]

or

$T = \frac{r h d g}{2 \cos θ}$

Describe the method of determination of surface tension of a liquid by capillary rise. Derive the expression used.

Important Questions on Surface Tension

Learn and Prepare for any exam you want !