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Assume that a drop of liquid evaporates by decrease in its sur

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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.

ρ L / T

T / ρ L

T / ρ L

2 T / ρ L

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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.

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Text solutionVerified

surface Tension

= T

Radius

= R

density

= ρ

Latent heat

= L

Let for

R,

small decrease on

R

△ R

∴

change in surface energy

Δ E = [4 π R^{2} - 4 π (R - Δ R)^{2}] \times T = 4 π (R - R + Δ R) (R + R - 4 R) \times T = 4 π \cdot Δ R \cdot 2 R \cdot T ∴ △ R \approx 0 = 8 π R \cdot Δ R \cdot T

Change in mass

Δ m = 9/3 π (R^{3} - (R - Δ R)^{3}) \times ρ = \frac{4}{3} π (R - R + Δ R) (R^{2} + (R - Δ R)^{2} + R (R - Δ R)) ρ = \frac{4}{3} π \cdot Δ R (R^{2} + R^{2} + R^{2} - 3 R Δ R + (Δ R)^{2}) ρ = 4 \cdot π \cdot Δ R \cdot R^{2} \cdot ρ

∴

Energy for vaporization

Δ V = 4 π Δ R \cdot R^{2} \cdot L ρ

8 π \cdot R \cdot Δ R \cdot T = 4 \cdot π \cdot Δ R \cdot R^{2} \cdot L \cdot ρ

or 2 T = R L ρ

or R = \frac{2 T}{ρ L}

Correct option is (D).

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Question Text	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.
Answer Type	Text solution:1
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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.

Text solutionVerified

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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.