Surface Energy and Surface Tension — Revision Notes

⚡ 30-Second Revision

Surface Tension ($\gamma$) — Force per unit length. $N/m$. Tendency to minimize surface area.
Surface Energy ($U_s$) — Work done per unit area. $J/m^2$. Numerically $\gamma = U_s$.
Molecular Origin — Net inward pull on surface molecules due to stronger cohesive forces than adhesive forces with air.
Temperature Effect — $\gamma$ decreases with increasing temperature.
Impurities — Detergents decrease $\gamma$. Highly soluble salts slightly increase $\gamma$.
Angle of Contact ($\theta$) — Angle between liquid tangent and solid inside liquid.

- Wetting ($\theta < 90^\circ$): Adhesive > Cohesive (e.g., water on glass). - Non-wetting ($\theta > 90^\circ$): Cohesive > Adhesive (e.g., mercury on glass).

Capillary Rise/Fall (Jurin's Law) — $h = \frac{2\gamma \cos\theta}{\rho g r}$. $h \propto 1/r$.
Excess Pressure ($\Delta P$)

- Liquid Drop / Air Bubble in Liquid (1 surface): $\Delta P = \frac{2\gamma}{R}$ - Soap Bubble in Air (2 surfaces): $\Delta P = \frac{4\gamma}{R}$

Work Done in Area Change — $W = \gamma \Delta A$. For a film, $\Delta A = 2 \times \text{change in area of one side}$.
Splitting Drop — $W = 4\pi\gamma R^2 (n^{1/3} - 1)$ (for $n$ small drops from one large drop).

2-Minute Revision

Surface tension ($\gamma$) and surface energy ($U_s$) are two sides of the same coin, describing the 'elastic skin' effect on liquid surfaces. They arise because molecules at the surface experience a net inward pull, giving them higher potential energy.

This makes liquids try to minimize their surface area, leading to phenomena like spherical drops. Numerically, $\gamma = U_s$, with units $N/m$ and $J/m^2$ respectively. Temperature reduces surface tension, while detergents significantly lower it.

The angle of contact ($\theta$) dictates whether a liquid wets a solid: $\theta < 90^\circ$ for wetting (adhesive forces dominate), $\theta > 90^\circ$ for non-wetting (cohesive forces dominate). Capillary action, the rise or fall of liquid in narrow tubes, is governed by Jurin's Law, $h = \frac{2\gamma \cos\theta}{\rho g r}$, showing an inverse relationship with tube radius.

Curved liquid surfaces also exhibit excess pressure: $\Delta P = \frac{2\gamma}{R}$ for a liquid drop or air bubble (one surface), and $\Delta P = \frac{4\gamma}{R}$ for a soap bubble (two surfaces). Work done in changing surface area is $W = \gamma \Delta A$, crucial for understanding energy changes in processes like splitting drops or forming bubbles.

5-Minute Revision

Surface tension is a critical property of liquids, originating from the imbalanced intermolecular cohesive forces experienced by molecules at the liquid-air interface. These surface molecules are in a higher potential energy state, and this excess energy per unit area is termed surface energy ($U_s$).

The liquid's natural tendency to minimize this energy drives it to contract its surface area. Surface tension ($\gamma$) is the force per unit length acting tangentially along the surface, opposing this contraction.

Crucially, surface tension and surface energy per unit area are numerically equivalent: $\gamma = U_s$.

Several factors influence surface tension. It generally decreases with increasing temperature, as higher molecular kinetic energy weakens cohesive forces. Impurities like detergents drastically reduce surface tension, aiding in cleaning, while highly soluble salts might slightly increase it.

The interaction of a liquid with a solid is described by the angle of contact ($\theta$). If adhesive forces (liquid-solid) are stronger than cohesive forces (liquid-liquid), $\theta < 90^\circ$, and the liquid wets the solid (e.g., water on glass). If cohesive forces dominate, $\theta > 90^\circ$, and the liquid does not wet the solid (e.g., mercury on glass).

Capillary action is a direct consequence of surface tension and the angle of contact. In a narrow tube (capillary), a wetting liquid will rise, and a non-wetting liquid will fall. Jurin's Law quantifies this height: $h = \frac{2\gamma \cos\theta}{\rho g r}$. This formula highlights that capillary rise is inversely proportional to the tube's radius ($h \propto 1/r$).

Another important concept is excess pressure across a curved liquid surface. The pressure is always higher on the concave side. For a liquid drop or an air bubble inside a liquid (which have one liquid-air interface), the excess pressure is $\Delta P = \frac{2\gamma}{R}$. However, for a soap bubble in air (which has two liquid-air interfaces), the excess pressure is $\Delta P = \frac{4\gamma}{R}$. This distinction is vital for problem-solving, especially when dealing with connected bubbles.

Finally, the work done in changing the surface area of a liquid is $W = \gamma \Delta A$. This is applied in scenarios like forming drops or bubbles, or splitting a large drop into smaller ones. For a soap film, remember that $\Delta A$ involves two surfaces. For example, splitting a large drop of radius $R$ into $n$ smaller drops results in work done $W = 4\pi\gamma R^2 (n^{1/3} - 1)$. Mastering these formulas and their conceptual underpinnings is key for NEET success.

Prelims Revision Notes

1
Definition & Units — Surface tension ($\gamma$) is force/length ($N/m$). Surface energy ($U_s$) is energy/area ($J/m^2$). Numerically, $\gamma = U_s$. Both arise from net inward cohesive force on surface molecules.
2
Factors Affecting $\gamma$

* Temperature: $\gamma \downarrow$ as $T \uparrow$. At critical temperature, $\gamma = 0$. * Impurities: Detergents/surfactants $\gamma \downarrow$. Highly soluble salts (e.g., NaCl) slightly $\gamma \uparrow$. Insoluble impurities $\gamma \downarrow$.

1
Angle of Contact ($\theta$)

* Angle between tangent to liquid surface and solid surface, inside the liquid. * Wetting Liquids: $\theta < 90^\circ$ (e.g., water on glass). Adhesive forces > Cohesive forces. Meniscus is concave. * Non-Wetting Liquids: $\theta > 90^\circ$ (e.g., mercury on glass). Cohesive forces > Adhesive forces. Meniscus is convex. * For pure water on clean glass, $\theta \approx 0^\circ$.

1
Capillary Action (Jurin's Law)

* Rise/fall of liquid in narrow tube. * $h = \frac{2\gamma \cos\theta}{\rho g r}$ * $h \propto 1/r$. If $r$ is halved, $h$ doubles. * If $\theta < 90^\circ$, $\cos\theta > 0$, $h$ is positive (rise). * If $\theta > 90^\circ$, $\cos\theta < 0$, $h$ is negative (fall).

1
Excess Pressure ($\Delta P$)

* Pressure difference across curved surface (higher on concave side). * Liquid Drop / Air Bubble in Liquid (1 surface): $\Delta P = \frac{2\gamma}{R}$ * Soap Bubble in Air (2 surfaces): $\Delta P = \frac{4\gamma}{R}$ * For two connected bubbles, air flows from smaller (higher pressure) to larger (lower pressure) bubble.

1
Work Done / Energy Change

* Work done to increase surface area $\Delta A$: $W = \gamma \Delta A$. * For a soap film, total area is $2 \times$ area of one side. * Work done in forming a liquid drop of radius $R$: $W = 4\pi R^2 \gamma$. * Work done in forming a soap bubble of radius $R$: $W = 8\pi R^2 \gamma$. * Work done in splitting a large drop (radius $R$) into $n$ small drops (radius $r = R/n^{1/3}$): $W = 4\pi\gamma R^2 (n^{1/3} - 1)$. This work comes from cooling of the liquid.

Vyyuha Quick Recall

To remember the excess pressure formulas for drops and bubbles:

Drop has Double (2) gamma: $\Delta P = \frac{2\gamma}{R}$ Bubble has Both (2 surfaces, so 2x double) gamma: $\Delta P = \frac{4\gamma}{R}$

(Think of 'D' for Drop, 'B' for Bubble. 'D' is like 'two' in 'double', 'B' is like 'both' surfaces, so double the 'double'.)