Surface tension of two liquids (having same densities), 
and 
, are measured using capillary rise method utilizing two tubes with inner radii of 
and 
where 
. The measured liquid heights in these tubes are 
and 
respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights 
and 
and surfaces tensions 
and 
satisfy the relation:
and 
and 
and 
and 
Text Solution
Verified by ExpertsD
For capillary rise, the height of liquid in a tube is given by: 
, where 
is surface tension and 
is the tube radius.
For two liquids with equal density and contact angles:
and 
Taking the ratio: 
Since 
, we have 
. The capillary rise is inversely proportional to tube radius, so the smaller radius tube will have greater height. Since the liquids are measured to have heights 
and 
with 
, and they have the same density, the empirical relation shows that both liquids rise to different heights inversely proportional to their radii. For liquids with the same density measured in different tubes, if the heights and radii satisfy the capillary rise equation, the surface tensions must be equal: 
, and 
since 
.
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