Problem 59 - A Complete Resource Book in Chemistry for JEE Main

Question

SI units of coefficient of viscosity are (a) \(\mathrm{kg} \mathrm{s}^{-1} \mathrm{~m}^{-2}\) (b) \(\mathrm{g} \mathrm{m}^{-1} \mathrm{~s}^{-1}\) (c) \(\mathrm{kg} \mathrm{m}^{-1} \mathrm{~s}^{-1}\) (d) \(\mathrm{kg} \mathrm{cm}^{-1} \mathrm{~s}^{-1}\)

Step-by-Step Solution

Answer

The SI unit of viscosity is \\( ext{kg} \cdot ext{m}^{-1} \cdot ext{s}^{-1}\\), which corresponds to option (c).

Step 1: Understand Viscosity Units

Viscosity is measured in terms of the force needed to move a fluid layer over another, and its SI unit is derived from \( ext{force} / ( ext{area} imes ext{velocity gradient}) \).

Step 2: Derive the SI Unit for Viscosity

The unit of force is \( ext{Newton (N)} \), where \( 1 ext{ N} = 1 ext{ kg} \cdot ext{m/s}^2 \). Force is applied over area, hence the unit becomes per unit area, \( ext{m}^2 \), and the velocity gradient is per unit length, \( ext{m}^{-1} \). Thus, viscosity unit becomes: \( ext{kg} \cdot ext{m}^{-1} \cdot ext{s}^{-1} \).

Step 3: Identify the Correct Option

Compare the derived SI unit \(( ext{kg} \cdot ext{m}^{-1} \cdot ext{s}^{-1})\) with the given options and determine that option (c) matches this unit.

Key Concepts

SI units

Understanding the International System of Units (SI units) is crucial for scientific communication. They provide a standard way to measure and describe physical properties. In the context of viscosity, the SI unit is essential for expressing how much force is needed to move one layer of fluid over another at a certain speed.

Simplified, SI units rely on fundamental dimensions like mass, length, and time. When it comes to viscosity, it is expressed in terms of force per area per change in velocity.

• The SI unit of force is the Newton (N), where 1 N = 1 kg·m/s².
• Area is measured in square meters (m²).
• The velocity gradient involves distance over time, which means per meter per second.

Hence, when these components combine, the viscosity's correct SI unit becomes kg·m⁻¹·s⁻¹. This shows how interconnected SI units are and how they ensure consistent measurements across various scientific fields.

viscosity measurement

Viscosity measurement is all about determining a fluid's internal resistance to flow. There are many ways to measure it, but the fundamental principle remains the assessment of how much force is required to move a specific fluid layer.

One standard method is using a viscometer. This device measures the resistance in a controlled environment, usually by observing the fluid's response to a rotating spindle or a falling ball.

• Rotational viscometers measure the torque required to turn a spindle in the fluid.
• Falling ball viscometers allow a ball to drop through the fluid, and the time taken is used to calculate viscosity.

In laboratory settings, it's important to control temperature as it can significantly affect viscosity. Generally, higher temperatures decrease viscosity. These methods aim to offer accurate and reliable viscosity measurements, ensuring that the viscous properties of fluids can be properly quantified.

force and area relationship

The relationship between force and area is key in understanding viscosity. Viscosity can be thought of as the measure of the internal friction between layers of a fluid that are in motion relative to one another.

The force applied over a certain area is what influences the fluid's movement. This is expressed in terms of stress, which is the force applied per unit area. Mathematically, stress is expressed as \[ \text{Stress} = \frac{\text{Force}}{\text{Area}} \].

• If you increase the force keeping the area constant, the stress increases.
• Conversely, increasing the area while keeping the force constant reduces stress.

This concept is particularly relevant in fluid dynamics, where understanding how fluids interact with surfaces or within the fluid itself can greatly define flow characteristics. The balance between force and area ensures that we can correctly interpret how fluids will behave under different conditions.