Question

The surface tension of water at \(20^{\circ} \mathrm{C}\) is \(72.75\) dync \(\mathrm{cm}^{-1}\). Its value in SI system is (1) \(7.275 \mathrm{Nm}^{1}\) (2) \(0.7275 \mathrm{Nm}^{1}\) (3) \(0.07275 \mathrm{Nm}^{\prime}\) (4) \(72.75 \mathrm{Nm}^{\prime}\)

Short answer

The value is 0.07275 N/m, which corresponds to option (3).

Step-by-step solution

Understand the conversion

Surface tension is given in units of dyn/cm. We need to convert it into units of N/m (SI units). 1 dyn = 10^-5 N and 1 cm = 10^-2 m.

Convert dyn/cm to N/cm

Given surface tension is 72.75 dyn/cm. Converting dyn to N: \[ 72.75 \text{ dyn/cm} \times 10^{-5} \text{ N/dyn} = 0.0007275 \text{ N/cm} \]

Convert N/cm to N/m

Next, we need to convert N/cm to N/m by considering the conversion between cm and m: \[ 0.0007275 \text{ N/cm} \times 100 \text{ cm/m} = 0.07275 \text{ N/m} \]

Select the correct option

From the given options, the correct value in the SI system is 0.07275 N/m.

Key concepts

Unit Conversion

Unit conversion is a fundamental concept in both science and mathematics. It involves changing the unit of a measured quantity without altering its value. This process is crucial because different units can be used to measure the same physical quantity depending on the context or the system in use. In our example, surface tension is initially given in dynes per centimeter (dyn/cm) and needs to be converted to newtons per meter (N/m), the SI unit for surface tension.

When performing unit conversions, it's essential to know the conversion factors between the units involved. For instance, knowing that 1 dyne is equal to 10^-5 newtons and 1 centimeter is equal to 10^-2 meters can help us accurately convert the units. Always multiply the given value by the appropriate conversion factors to attain the correct result.

Surface Tension

Surface tension is a physical property of liquids that describes the elastic tendency of a fluid surface. It allows objects, such as water droplets or small insects like water striders, to remain on the surface of the liquid without sinking. Surface tension results from the cohesive forces between liquid molecules at the surface.

The unit of surface tension commonly utilized in physics and chemistry depends on the region and historical context. Although dynes per centimeter (dyn/cm) is frequently used in specific studies or older literature, the SI unit for surface tension is newtons per meter (N/m). Understanding surface tension and its units is crucial for applications in fluid mechanics, pharmaceuticals, and various engineering disciplines. Remember, these properties are measured at a specific temperature since temperature can influence the cohesion forces between molecules.

SI Units

The International System of Units (SI) is the modern form of the metric system and is the most universally accepted system of measurement. It provides a comprehensive and standardized set of units to measure various physical quantities. SI units simplify scientific communication because they are consistent and widely understood.

In the context of surface tension, the SI unit is newtons per meter (N/m). Converting to SI units ensures that measurements and calculations are compatible globally, facilitating collaboration and comparison across different scientific and engineering fields. It is important to familiarize oneself with the SI units, as they form the basis of most scientific work. Key SI units include meters (m) for length, kilograms (kg) for mass, and seconds (s) for time, among others. Each has a defined relationship with other units, allowing for straightforward conversions and consistent data representation.