Surface Tension, Energy & S. Heat

1.7 Surface Tension:

A liquid, being unable to expand freely, will form an interface with a second liquid or gas.

The cohesive forces between liquid molecules are responsible for the phenomenon known as surface tension. The molecules at the surface do not have other like molecules on all sides of them and consequently they cohere more strongly to those directly associated with them on the surface. Surface tension  (pronounced upsilon) has the dimension of force per unit length (N/m) or of energy per unit area (J/m²).

In addition, Liquid droplets behave like small spherical balloons filled with the liquid, and the surface of the liquid acts like a stretched elastic membrane under tension. The pulling forces that causes this tensions acts parallel to the surface and is due to the attractive forces between the molecules of the liquid.

Pressure drop across curved interfaces due to surface tension

Pressure increase in the interior of a liquid half‐cylinder droplet of length L and radius R is, Fig a:

           Pressure droplet in the interior of a liquid half‐sphere droplet of radius R is, Fig b:

      For a full sphere droplet, e.g. soap bubble, which has two interfaces with air, the pressure increase will 

be twice:

Pressure droplet in the interior of an arbitrarily curved interface of principal radii R1 and R2, Fig c:

Contact angle  : appears when a liquid interface intersects with a solid surface.

1.8 Energy & Specific Heat:

   Potential Energy is the work required to move the system of mass m from the origin to a position against a gravity field g:

   Kinetic Energy is the work required to change the speed of the mass from zero to velocity v

  The Total Energy (E), of a substance is the sum of the internal, kinetic, and potential energies at a given state point:

        Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the temperature of a unit mass of a substance by one degree temperature.

There are two types of specific heats, constant volume C_v and constant pressure C_p.

 1.9 Capillary Effect:

           Capillary effect is the rise or fall of a liquid in a small diameter tube inserted into liquid. Capillaries is a narrow tubes or confined flow channels. The curved free surface of a liquid in a capillary tube is called meniscus.

Contact (or wetting) angle, is defined as the angle that the tangent to the liquid surface makes with the solid surface at the point of contact. Water molecules are more strongly attracted to the glass molecules than they are to other water molecules, and thus water tends to rise along the glass surface.