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 unit of surface tension is (b) Nm^{-1}.

Step 1: Understanding Surface Tension

Surface tension is defined as the force per unit length. It's a property of the liquid's surface that makes it act like a thin stretched membrane. Commonly we see it quantified in terms of force per unit length, such as newton per meter.

Step 2: Analyzing Units

Given that surface tension is force per unit length, we identify the units. Force is measured in newtons, and length in meters. Hence, the unit of surface tension should be newton per meter, which aligns with option (b).

Step 3: Verification with Options

Now, let's verify this against the given options: - (a) Joule m^{-1} (energy per unit length, not applicable) - (b) Nm^{-1} (newton per meter, aligns with surface tension definition) - (c) erg cm^{-1} (an alternative unit, but primarily used in older texts and less common in SI units) - (d) none of these (not applicable) Thus, the correct answer is option (b).

Key Concepts

Force per Unit Length

Surface tension is an intriguing property of liquids that manifests as a force acting along the liquid's surface. To understand this better, imagine a liquid surface behaving like a stretched elastic membrane. This effect occurs because the molecules at the surface experience different forces compared to those inside the liquid.
This concept is best quantified as force per unit length. Essentially, surface tension represents how much force is acting on a segment of the liquid surface with a particular length.
In simpler terms, if you imagine a tiny "rope" lying along the liquid's surface, surface tension would be the force pulling either side of that rope.

• It's measured in units like newton per meter (N/m), showcasing the line of force present on a single meter of the liquid surface.
• This helps us understand the resistance of a liquid surface to deformation.

The notion of force per unit length explains why little insects, like water striders, can walk on water without sinking. The surface tension provides enough force to support their weight distributed over their legs, acting as a balancing tightrope.

Units of Measurement

Units are crucial in physics as they enable us to describe and calculate various quantities accurately. When considering surface tension, standard units help us convey the concept effectively.
The correct unit for surface tension comes from its definition as force per unit length. Force is typically measured in newtons (N), while length is measured in meters (m). Therefore, the SI unit of surface tension is newton per meter (N/m).
However, in some contexts or older scientific literature, you might encounter alternative units such as the erg per centimeter (erg/cm), used in the CGS (centimeter-gram-second) system. Though less common today, it illustrates the same relationship between force exerted across a unit length.

• For modern applications, SI units like N/m are preferred, due to their universal acceptance and ease of integration into various scientific calculations.
• Being consistent with units ensures clarity and prevents errors in communication, especially in scientific settings.

Understanding these units enhances our ability to compare and work with surface tension measurements effectively across different scenarios and studies.

Physics in Chemistry

The interplay between physics and chemistry offers a deep understanding of phenomena like surface tension. In chemistry, understanding molecular interactions is key. Force per unit length in surface tension originates from these interactions.
Molecules within a liquid are attracted to each other, resulting in cohesive forces. At the surface, these forces create a net inward pull, forming a 'tension.'
This seamless integration of physics and chemistry principles elucidates why liquids minimize their surface area, forming droplets.

• Surface tension impacts various chemical processes and plays a role in the behavior of bubbles, capillary action, and emulsions.
• It's essential in formulations in industries such as pharmaceuticals, where control over droplet formation and stability is crucial.

Physics principles help quantify these interactions, and chemistry explains the behavior at the molecular level, making it a fascinating study in both fields. Understanding these concepts helps in appreciating the beauty and complexity of natural phenomena and technical applications alike.