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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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a
TpL 
b
3TpL 
c
pLT 
d
2TpL

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detailed solution

Correct option is D

being that,

T = surface tension

the density of the liquid: ρ

L = latent heat

We know that,

Decreased surface energy equals  heat required for vaporization

Now,

decrease in surface energy

 =T×ΔA   

=2T×(4πrdr)______(1)

Now, the latent heat needed for vaporization

=ML   

=VρL   

=4πr2ρL_______(2)

From equation 1 and 2

2T(4πrdr)=4πr2 ρLr=2TρL

Hence the correct answer is 2TρL.

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