what is the excess of pressure inside a liquid drop?
Answers
We know that the similar molecules of a liquid attract each other by a force of coheasion and force of surface tension, tangentially to the liquid surface at restIf the liquid meniscus is horizontal there is no net force normal to the surface on the molecules lying on the upper surface as shown in the figure (i)
If the meniscus of a liquid is convex, then there exists a net downward force due to surface tension normal to the meniscus in figure (ii)
Hence it can be concluded that excess pressure is less on a convex meniscus.
Excess Pressure inside a Liquid Drop
As we know that, the force due to surface tension act normal to the surface in inward direction on the molecules of a liquid drop. For an equilibrium of the drop, these must exist excess pressure insie it.
Let R be the radius of a drop and dR be the increase in its radius by small amount due to excess pressure.
The work done by excess pressure=force×displacement
=P×A×dR
=P×4πR2×dR…(i)
Increase in the area of the drop
=4π(R+dR)2−4πR2
=4π(R2+2RdR+dR2−R2)
=8πRdR…2
dR2 can be neglected being small.
Increase in surface energy of the drop=Increase in area×Surface tension
=8πRdR×T…(iii)
Equation (i) and (iii) represents same quantity
P×4πR2×dR=8πRdR×T
P=2TR…(iv)
Pin−Pout=2TR
Excess Pressure of Air Bubble
Since the air bubble has only free surface, so the excess pressure inside is given by
P=2TR…(iv)
Pin−Pout=2TR
Excess Pressure Inside Liquid Bubble or Soap
Since a liquid bubble has two free surfaces so thee excess pressure is given by
P=2×2TR=4TR
Pin−Pout=2TR
Shape of Liquid Meniscus
The shape of a liquid meniscus depends on the result of cohesive and adhesive forces that exist on the molecules of the liquid which are in contact with the solid surface there may be three different cases of the resultant force which are described below
Let us consider a molecule A which is in contact with the solid surface and is acted upon by two forces i.e. theadhesive force Fa at right angle to the solid surface and cohesive force Fc which act along AQ at 45o to the solid surface. The angle between Fa and Fc is always 135o but their magnitude are different for different solid-liquidpairs.
Case I
If the resultant Fa and Fc lie along the solid surface then from the solid surface then from figure i
sin45o=SQAQ
SQ=AQsin45o
Fa=Fc12–√
2–√FA=Fc
Fc=2–√Fa
Case II
If the resultant of Fa and Fc lie outside the liquid and is represented by AS'
here SQ & S'Q
Fc2–√<Fa
Fc<2–√Fa…(ii)
and the meniscus will be concave
Case III
If the resultant of Fa and Fc lie within the liquid and is represented by AS'
from fig 3
SQ>S′Q
Fc2–√>Fa
Fc>2–√Fa…(iii)