Given below are two statements:
Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.
Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water.
In the light of the above statements, choose the most appropriate from the options given below

We need to evaluate two statements about capillary rise in cold and hot water.

The height of liquid rise in a capillary tube is given by Jurin's law:

$$h = \frac{2T\cos\theta}{\rho g r}$$

where $$T$$ is the surface tension of the liquid, $$\theta$$ is the contact angle, $$\rho$$ is the liquid density, $$g$$ is acceleration due to gravity, and $$r$$ is the radius of the capillary tube.

Surface tension of a liquid decreases with increasing temperature. This is because as temperature increases, the kinetic energy of molecules increases, weakening the intermolecular attractive forces at the surface. Therefore:

$$T_{hot} < T_{cold}$$

Since $$h \propto T$$ (surface tension), and the surface tension decreases with temperature:

$$h_{hot} < h_{cold}$$

This means the height of capillary rise is smaller in hot water than in cold water.

Statement I: "The height of capillary rise will be smaller in hot water." This is TRUE, as shown above.

Statement II: "The height of capillary rise will be smaller in cold water." This is FALSE; it is the opposite of what actually happens.

The correct answer is Option (3): Statement I is true but Statement II is false.