Question

If \( S_1 \), \( S_2 \), and \( S_3 \) are the tensions at liquid-air, solid-air and solid-liquid interfaces respectively, and \( \theta \) is the angle of contact at the solid-liquid interface, then

• A. \( S_1 \cos \theta + S_2 \sin \theta = S_3 \)
• B. \( S_1 \cos \theta + S_3 = S_2 \)
• C. \( S_2 \cos \theta + S_3 = S_1 \)
• D. \( S_3 \cos \theta + S_1 = S_2 \)

Hint:

When dealing with tensions at interfaces, remember to consider the forces in equilibrium. The angle of contact is crucial in determining how the tensions relate to each other.

Answer 1

The Correct Option is B

Step 1: The relationship between the tensions at the interfaces is governed by the forces acting at the point of contact. The tensions are related by the equilibrium condition at the solid-liquid interface. At the solid-liquid interface, the angle of contact \( \theta \) plays a crucial role in determining the relationship between the tensions. The forces acting along the surface are balanced, and the equation of equilibrium is given by: \[ S_1 \cos \theta + S_3 = S_2 \] where: - \( S_1 \) is the tension at the liquid-air interface, - \( S_2 \) is the tension at the solid-air interface, - \( S_3 \) is the tension at the solid-liquid interface, - \( \theta \) is the angle of contact at the solid-liquid interface. 

Step 2: The above equation satisfies the condition for equilibrium, where the components of the tensions along the interface balance out. Therefore, the correct relation is: \[ S_1 \cos \theta + S_3 = S_2 \]