Problem 55 - A Complete Resource Book in Chemistry for JEE Main

Question

The unit of surface tension is (a) Joule \(\mathrm{m}^{-1}\) (b) \(\mathrm{N} \mathrm{m}^{-1}\) (c) \(\mathrm{erg} \mathrm{cm}^{-1}\) (d) none of these

Step-by-Step Solution

Answer

The correct unit of surface tension is (b) N/m.

Step 1: Understand Surface Tension

Surface tension is defined as the force acting on the surface of a liquid, causing it to behave as if covered by a stretched elastic membrane. It is quantitatively described as the force per unit length.

Step 2: Recognize Units of Force and Length

The SI unit for force is the newton (N), and the SI unit for length is the meter (m). Therefore, when calculating force per unit length, the derived unit is expressed in newtons per meter (N/m).

Step 3: Analyze Options for Correct Unit

Evaluate the given options: - Option (a): Joule per meter (J/m) is a unit of energy per length, not directly describing force per length. - Option (b): Newton per meter (N/m) directly describes force per length, which matches the definition of surface tension. - Option (c): Erg per centimeter (erg/cm) is a cgs (centimeter-gram-second) unit equivalent to dyne/cm, which is a possible unit but not the standard SI unit. - Option (d): None of these is incorrect as there's a correct SI unit available.

Step 4: Select the Correct Option

Based on the analysis, option (b) Newton per meter (N/m) is the correct SI unit for surface tension.

Key Concepts

SI Units in Chemistry

In chemistry, understanding the system of units used to measure different properties is crucial. The International System of Units, or SI units, is a globally agreed-upon system for measuring physical quantities.

These units provide a standard to prevent discrepancies when scientists describe measurements. For instance, the kilogram (kg) is used for mass, and the meter (m) is used for length. For force, the applicable SI unit is the newton (N). This consistency is vital in sciences such as chemistry, where precise measurements are key.

• Mass – Kilogram (kg)
• Length – Meter (m)
• Time – Second (s)
• Force – Newton (N)

For measurements involving combinations of these basic units, derived units are used. Derived units can be a combination of base units, like newtons per meter (N/m) for measuring quantities such as surface tension.

Force Per Unit Length

The concept of force per unit length is significant when discussing phenomena like surface tension. It involves measuring how much force acts along a specific length.

In simpler terms, it's how much force you apply across a set distance.

Surface tension in liquids acts this way, as if a tight invisible rubber band is stretched along the surface. The resulting measurement helps to understand how much energy is distributed across the surface of the liquid.

• To calculate: Force (N) is divided by Length (m) resulting in N/m.
• This derived unit, newton per meter, simplifies understanding of surface effects.

Surface Tension Definition

Surface tension is an interesting and observable phenomenon. It's what causes some insects to walk on water and droplets to form beads. It is defined scientifically as the force per unit length.

This means it is the force acting along the surface layer of a liquid. Due to surface tension, the liquid's surface behaves almost like an elastic sheet. The stronger the tension, the more rigid the surface appears to be.

• Surface tension results from cohesive forces between liquid molecules.
• It causes the liquid to minimize its surface area, forming a type of 'skin' effect.
• Standard unit of measurement, as per SI, is newton per meter (N/m) which effectively describes this as a force extending along a specific length.