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 and L is its latent heat of vaporization.

Engineering

Physics

Surface Tension and Surface Energy

Question

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 $ρ$ and L is its latent heat of vaporization.

$\sqrt{T / ρL}$

T/ $ρ$ L

$ρ$ L/T

2T/ $ρ$ L

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$\frac{ΔQ}{Δt} = \frac{dm}{dt} L & \frac{dE}{dt} = 4 πT 2 R \frac{dr}{dt}$

$\frac{dm}{dt} L = 4 πT 2 R \frac{dr}{dt}$

$\frac{d}{dt} (ρ \frac{4}{3} {πr}^{3}) L = 8 πTR \frac{dr}{dt}$

$ρ \frac{4}{3} 3 r^{2} \frac{dr}{dt} L = 8 pT \frac{dr}{dt}$

$r = \frac{2 T}{ρL}$