Question

The heat evolved for the rise of water when one end of the capillary tube of radius r is immersed vertically into water is : (assume surface tension

Answer 1

radius is immersed in water
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Answer 2

Answer:

Raise of water in the capillary tube;

h = (2*T*cosθ)/(ρ*r*g)

where;

θ = angle of contact

ρ = density of water

r = radius of the capillary tube

T = Surface tension of water

When the water in the tube rises up, the surface tension do some work.

Work done = h*(2π*r* T*cosθ)

Substituting the value of 'h' in the upper relation;

Work done = (4π*T²*cos²θ) /(ρ*g)

But raise in the potential energy of water;

U = 1/2*(ρπ*r²*h)*g*h = (2π*T²*cos²θ)/(ρ*g)

So we observed from the above two relations;

Work done = 2*U

So the loss in heat = Q = (2π*T²*cos²θ)/(ρ*g)