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STD 11 - 9.2 , surface tension — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 9.2 , surface tension4 Marks
MCQ
Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is $T$, density of liquid is $\rho$ and $L$ is its latent heat of vaporization.
  • A
    $\frac{{\rho L}}{T}$
  • B
    $\sqrt {\frac{T}{{\rho L}}} $
  • C
    $\frac{T}{{\rho L}}$
  • ✓
    $\frac{2T}{{\rho L}}$
✓

Answer

Correct option: D.
$\frac{2T}{{\rho L}}$
d
Energy for vaporization $=$ change in surface energy $\rho\left(4 \pi r^{2} \mathrm{d} r\right) L=T(8 \pi \mathbf{r d r})$

$\Rightarrow r=\frac{2 \mathrm{T}}{\rho \mathrm{L}}$

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