Calculate the heat evolved for the rise of water when one end of the capillary tube of radius r is immeresed vartically into water. Asssume surface tension =T and density of water to be `rho`

Options

A. `(2pi S)/(rho g)`
B. `(pi S^(2))/(rho g)`
C. `(2pi S^(2))/(rho g)`
D. `(4pi S^(2))/(rho g)`

Answer

C

Explanation

Potential energy of water column,
`U = (mgh)/(2) = (2pi S^(2))/(rho g)`
The work performed by force of surface tension is
`W = 2pi rSh = (4pi S^(2))/(rho g)`
From conservation of energy the heat evolved,
`Q = W-U = (2pi S^(2))/(rho g)`