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# The following observations were taken for determining surface tension T of waterby 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 possibleerror in surface tension is closest to :(A) $10%$(B) $0.15%$(C) $1.5%$(D) $2.4%$

Last updated date: 09th Aug 2024
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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.

$\mathrm{T}=\dfrac{\mathrm{rhg}}{2} \times 10^{3} \mathrm{N} / \mathrm{m}=\dfrac{\mathrm{Dhg}}{4} \times 10^{3} \mathrm{N} / \mathrm{m}$ (since $\left.\mathrm{D}=2 \mathrm{r}\right)$
$\Rightarrow \log \mathrm{T}=\log \mathrm{D}+\log \mathrm{h}+\log \mathrm{g}-4+3$
$\Rightarrow \dfrac{\triangle \mathrm{T}}{\mathrm{T}}=\dfrac{\Delta \mathrm{D}}{\mathrm{D}}+\dfrac{\triangle \mathrm{h}}{\mathrm{h}}$
$=\dfrac{0.01}{1.25}+\dfrac{0.01}{1.45}=0.015=1.5 \%$