When a vertical capillary of length l with the sealed end was brought in contact with the surface of a liquid the level of this liquid rise h diameter d density p  Atm po find surface tension of liquid

 

Asked by Jayachanchal | 28th Nov, 2018, 11:00: PM

Expert Answer:

 
Figure shows the capillary rise phenomenan in the capillary tube in which one end of the tube is sealed.
 
if S is surface tension force of the liquid, then we have  pi - po = begin mathsize 12px style fraction numerator 2 S over denominator r end fraction equals space fraction numerator 2 S over denominator open parentheses begin display style bevelled d over 2 end style close parentheses end fraction cos theta space equals fraction numerator 4 S over denominator d end fraction cos theta space...................... left parenthesis 1 right parenthesis end style
where r is the radius of curvature of miniscus, d is diameter of capillary bore and θ is the angle of contact.
 
if the capillary tube has air initially at atmospheric pressure, then air is compressed, its volume decreases and
pressure slightly increased due to capillary rise. At constant temperature pressure is inversely proportional to volume
but volume of air inside capillary tube is directly proportional to length of air column.
 
Hence we have , begin mathsize 12px style p subscript i over p subscript a space equals space fraction numerator l over denominator l minus h end fraction space space.............. left parenthesis 2 right parenthesis end style
where l is length of capillary bore, h is capillary rise of liquid, pa is the atmospheric pressure and
pi is the pressure inside capillary bore after capillary rise of liquid
 
Since the pressure on the water surface outside capillary tube is same as the  inside capillary tube
at same level of water surface outside capillary tube,

we have, pa = po+ρgh .........................(3)
where ρ is density of liquid
using eqn.(1), (2) and (3) and after simplification we get,  begin mathsize 12px style fraction numerator p subscript a cross times h over denominator l minus h end fraction plus rho g h space equals space fraction numerator 4 S over denominator d end fraction cos theta end style...........................(4)
Hence from eqn.(4), using the known values of atmospheric pressure pa, height of capillary rise h, density of liquid ρ,
diameter d of capillary bore and angle of contact of the given liquid θ, we can determine the surface tension of liquid.

Answered by Thiyagarajan K | 30th Nov, 2018, 01:33: AM

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