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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 vaporisation.

(a) $ρ L / T$
(b) $T / ρ L$
(c) $T / ρ L$
(d) $2 T / ρ L$

Views: 5,932 students

Updated on: May 7, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2013

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Liam Discussed

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 vaporisation.

(a)

ρ L / T

(b)

T / ρ L

(c)

T / ρ L

(d)

2 T / ρ L

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

Exp. (d)
If a layer of thickness

d r

is evaporated, then Change in surface energy

=

Change in surface area

x T

= [4 π (r + d r)^{2} - 4 π r^{2}] T

= [4 π r^{2} + 4 π d r^{2} + 8 π r d r - 4 π r^{2}]

d r

is very small, so

d r^{2}

neglected.
So, change in surface energy

= 8 π r d r T

Energy required to evaporate layer of thickness

d r = (4 π r^{2} d r) ρ L

The process of evaporation just starts, if change in surface energy is just sufficient to evaporate the water layer.

∴ (4 π r^{2} d r) ρ L = (8 π r d r) T \Rightarrow

r = \frac{2 T}{ρ L}

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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 vaporisation. (a) $ρ L / T$ (b) $T / ρ L$ (c) $T / ρ L$ (d) $2 T / ρ L$
Updated On	May 7, 2023
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 4
Upvotes	415
Avg. Video Duration	8 min

Text solutionVerified

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Text solutionVerified

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