Assume that liquid drop evaporates by decreasing in its surface energy so that its temperature remains unchanged. The surface tension of liquid drop is T, density of liquid is ρ and L is latent heat of vapouration of liquid. What should be the minimum radius of the drop for this to be possible

Question

Assume that liquid drop evaporates by decreasing in its surface energy so that its temperature remains unchanged. The surface tension of liquid drop is T, density of liquid is ρ and L is latent heat of vapouration of liquid. What should be the minimum radius of the drop for this to be possible

Infinity Learn · Accepted Answer

being that,T $$=$$ surface tensionthe density of the liquid: ρL $$=$$ latent heatWe know that,Decreased surface energy equals  heat required for vaporizationNow,decrease in surface energy $$=T$$×ΔA   $$=2T$$×$$(4$$$$π$$$$rdr)______(1)Now$$, the latent heat needed for $$vaporization=ML$$   $$=V$$ρL   $$=4$$$$π$$$$r2$$ρ$$L_______(2)From$$ equation $$1$$ and $$22T(4$$$$π$$$$rdr)=4$$$$π$$$$r2$$ ρL⇒$$r=2T$$ρLHence the correct answer is $$2T$$ρL.

Assume that liquid drop evaporates by decreasing in its surface energy so that its temperature remains unchanged. The surface tension of liquid drop is T, density of liquid is $ρ$ and L is latent heat of vapouration of liquid. What should be the minimum radius of the drop for this to be possible

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