The surface tension of water is $0.0730 \mathrm{~N} / \mathrm{m}$. What is the height of the water in a capillary tube of diameter $1.00 \mathrm{~mm}$ ?
A) $2.75 \mathrm{~cm}$
B) $2.98 \mathrm{~cm}$
C) $2.40 \mathrm{~cm}$
D) $2.55 \mathrm{~cm}$
E) $3.02 \mathrm{~cm}$

Question

Quizplus · Accepted Answer

The height $h$ of the liquid column in a capillary tube is given by the formula $h = \frac{2\gamma \cos \theta}{\rho g r}$, where $\gamma$ is the surface tension of the liquid, $\theta$ is the contact angle (which is 0 for water adhering to glass), $\rho$ is the density of the liquid (approximately $1000 \mathrm{~kg/m^3}$ for water), $g$ is the acceleration due to gravity ($9.81 \mathrm{~m/s^2}$), and $r$ is the radius of the capillary tube. Given $\gamma = 0.0730 \mathrm{~N/m}$, and the diameter of the capillary tube is $1.00 \mathrm{~mm}$, the radius $r$ is $0.5 \mathrm{~mm}$ or $0.0005 \mathrm{~m}$. Substituting these values into the formula gives a height of approximately $2.98 \mathrm{~cm}$.

The Surface Tension of Water Is 0.0730 N/m0.0730 \mathrm{~N} / \mathrm{m}0.0730 N/m What Is the Height of the Water in a

The Surface Tension of Water Is $0.0730 \mathrm{~N} / \mathrm{m}$ What Is the Height of the Water in a