surface Tension =T Radius =R density =ρ Latent heat =L Let for R, small decrease on R is △R ∴ change in surface energy ∆E=[4πR2−4π(R−∆R)2]×T =4π(R−R+∆R)(R+R−4R)×T =4π⋅∆R⋅2R⋅T∴∆R≈0 =8πR⋅∆R⋅T change in mass ∆m=9∕3π(R3−(R−∆R)3)×ρ =
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π(R−R+∆R)(R2+(R−∆R)2+R(R−∆R))ρ =
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π⋅∆R(R2+R2+R2−3R∆R+(∆R)2)ρ =4⋅π⋅∆R⋅R2⋅ρ Energy for vaporization ∆V=4π∆R⋅R2⋅Lρ 8π⋅R⋅∆R⋅T=4⋅π⋅∆R⋅R2⋅L⋅ρ or 2T=RLρ or R=