Question

The following observations were taken for determining surface tension T of water
by capillary method:
diameter of capillary, $D=1.25 \times 10^{-2} \mathrm{m}$
rise of water, $h=1.45 \times 10^{-2} \mathrm{m}$.
Using $g=9.80 \mathrm{m} / \mathrm{s}^{2}$ and the simplified relation. $T=\dfrac{r h g}{2} \times 10^{3} N / m,$ the possible
error in surface tension is closest to :
(A) $10%$
(B) $0.15%$
(C) $1.5%$
(D) $2.4%$

Answer 1

Hint: We know that surface tension determines the efficiency of detergent formulation. The high surface tension of water makes it a relatively poor cleaning detergent. By increasing the temperature of water (as is often done when washing clothes or dishes), the cleaning efficiency increases slightly as surface tension decreases. Surface tension is caused by the effects of intermolecular forces at the interface. Surface tension depends on the nature of the liquid, the surrounding environment and temperature. Liquids where molecules have large attractive intermolecular forces will have a large surface tension.

Complete step by step answer
Let us know that surface tension is the tendency of liquid surfaces to shrink into the minimum surface area possible. Surface tension allows insects (e.g. water striders), usually denser than water, to float and slide on a water surface.
We know that:
$\mathrm{T}=\dfrac{\mathrm{rhg}}{2} \times 10^{3} \mathrm{N} / \mathrm{m}=\dfrac{\mathrm{Dhg}}{4} \times 10^{3} \mathrm{N} / \mathrm{m}$ (since $\left.\mathrm{D}=2 \mathrm{r}\right)$
Hence the expression is further solved as:
$\Rightarrow \log \mathrm{T}=\log \mathrm{D}+\log \mathrm{h}+\log \mathrm{g}-4+3$
We get that:
$\Rightarrow \dfrac{\triangle \mathrm{T}}{\mathrm{T}}=\dfrac{\Delta \mathrm{D}}{\mathrm{D}}+\dfrac{\triangle \mathrm{h}}{\mathrm{h}}$
Now we have to put the values to get that:
$=\dfrac{0.01}{1.25}+\dfrac{0.01}{1.45}=0.015=1.5 \%$

Hence the correct answer is option C.

Note It is known that the surface tension of liquids and the influence of surfactants on the surface tension depend on the temperature. Additionally, the dynamic of surfactant molecules increases due higher thermal energy. In general, the surface tension decreases with increasing temperature. So, if there is no surface tension (this condition will only arise if there are no net attractive forces among the fluid's molecules) in any given condition, the fluid will evaporate immediately (or in other words it will act like gas). The reason for the reduction in the surface tension when surfactant molecules adsorb at the water surface is that the surfactant molecules replace some of the water molecules in the surface and the forces of attraction between surfactant and water molecules are less than those between two water molecules.