Is the capillary rise greater in small- or large-diameter tubes? Explain with reason. 

Solution:

The capillary rise is greater in small-diameter tubes. This phenomenon is explained by the combination of capillary action and the Young-Laplace equation.

Capillary action is the ability of a liquid to flow in narrow spaces without the assistance of external forces like gravity. In a narrow tube, the adhesive forces between the liquid molecules and the tube's material, along with the cohesive forces between the liquid molecules, cause the liquid to be drawn up into the tube.

The height to which a liquid will rise in a capillary tube is given by the Young-Laplace equation:

ℎ = `2Tcos(θ)/ρgr`

where:

h is the capillary rise,

T is the surface tension of the liquid,

θ is the contact angle between the liquid and the tube,

ρ is the density of the liquid,

g is the acceleration due to gravity,

r is the radius of the capillary tube.

From the equation, it's evident that the capillary rise (h) is inversely proportional to the radius of the capillary tube (r). Therefore, in smaller-diameter tubes, the capillary rise is higher because the radius is in the denominator of the equation. The smaller the radius, the greater the capillary rise, assuming other factors remain constant.