Problem 71 - Chemistry: The Central Science in SI Units, Global Edition

Question

What type of quantity (for example, length, volume, density) do the following units indicate? (a) \(\mathrm{m}^{3},(\mathbf{b}) \mathrm{ns},\) (c) \(\mathrm{mm}\) (d) \(\mathrm{g} / \mathrm{dm}^{3}\), (e) \({ }^{\circ} \mathrm{C},\) (f) \(\mathrm{ms}^{-1}\), (g) Pa.

Step-by-Step Solution

Answer

The identified physical quantities for each unit are: (a) \(\mathrm{m}^{3}\) indicates Volume, (b) \(\mathrm{ns}\) indicates Time, (c) \(\mathrm{mm}\) indicates Length, (d) \(\frac{\mathrm{g}}{\mathrm{dm}^{3}}\) indicates Density, (e) \({ }^{\circ} \mathrm{C}\) indicates Temperature, (f) \(\mathrm{ms}^{-1}\) indicates Velocity (Speed), and (g) Pa indicates Pressure.

Step 1: Identify Quantity of m³

The unit \(\mathrm{m}^{3}\) stands for cubic meters, which is a measure of volume. So, the quantity represented by this unit is Volume.

Step 2: Identify Quantity of ns

The unit \(\mathrm{ns}\) stands for nanoseconds, which is a measure of time. So, the quantity represented by this unit is Time.

Step 3: Identify Quantity of mm

The unit \(\mathrm{mm}\) stands for millimeters, which is a measure of length. So, the quantity represented by this unit is Length.

Step 4: Identify Quantity of g/dm³

The unit \(\frac{\mathrm{g}}{\mathrm{dm}^{3}}\) stands for grams per cubic decimeters, which is a measure of mass per unit volume, i.e., density. So, the quantity represented by this unit is Density.

Step 5: Identify Quantity of °C

The unit \({ }^{\circ} \mathrm{C}\) stands for degree Celsius, which is a measure of temperature. So, the quantity represented by this unit is Temperature.

Step 6: Identify Quantity of ms⁻¹

The unit \(\mathrm{ms}^{-1}\) stands for meters per second, which is a measure of distance over time. This makes it a measure of velocity or speed. So, the quantity represented by this unit is Velocity (Speed).

Step 7: Identify Quantity of Pa

The unit Pa stands for Pascal, which is a derived SI unit of pressure. So, the quantity represented by this unit is Pressure.

Key Concepts

Volume

Volume is the amount of space an object or substance occupies. It is a three-dimensional measurement, which means it takes into account height, width, and depth. A common unit for volume is the cubic meter (\(\mathrm{m}^3\)), often used in physics and engineering.

• Think of volume as the capacity inside a box.
• Liquids and gases have their volumes typically measured in liters or milliliters.

Understanding volume is essential in many fields, from calculating how much liquid a container can hold to determining how much space an object will occupy.

Time

Time is a continuous measurement that represents the duration between events. The second is the base unit of time in the International System of Units.

• Time is measured to understand the sequence of events and the duration of processes.
• Nanoseconds (\(\mathrm{ns}\)) are often used in high-precision contexts like scientific experiments.

Time helps us organize our daily activities, and understanding it is crucial in sectors like astronomy, computing, and every form of planning.

Length

Length measures the extent of something end to end in one dimension. It is one of the most straightforward physical quantities. Millimeter (\(\mathrm{mm}\)) is a common unit for measuring small lengths.

• Think of length as how long something is, like the dimensions of a piece of paper.
• Length can be measured in other units too, such as meters or kilometers for longer distances.

It's a basic concept used not only in daily life but also in engineering and construction projects.

Density

Density is the mass per unit volume of a substance, typically measured in grams per cubic decimeter (\(\mathrm{g/dm}^3\)). It helps us understand how much matter fits in a given space.

• This concept is essential in understanding why some objects float while others sink.
• Higher density means more mass in a given volume.

Density is widely used in fields like chemistry and physics to predict how substances will behave in various scenarios.

Temperature

Temperature is the measure of thermal energy within a substance or object, essentially expressing how hot or cold it is. Measured in degrees Celsius (\(^{\circ} \mathrm{C}\)), among other units, it is crucial in daily life and scientific contexts.

• Temperature affects the state and behavior of matter.
• It's important for determining weather conditions and in cooking.

Understanding temperature is vital for various scientific experiments and industrial processes.

Velocity

Velocity describes the speed of an object in a specific direction, measured in meters per second (\(\mathrm{ms}^{-1}\)). It’s a vector quantity, which means it has both magnitude and direction.

• Unlike speed, velocity tells not just how fast something is moving, but also in which direction.
• Used extensively in physics to describe motion and predict future movement based on current trajectories.

Grasping the concept of velocity is critical for fields like aeronautics and mechanical engineering.

Pressure

Pressure is the force exerted per unit area, with common units being Pascals (Pa). It reflects how much force is being applied to a surface.

• Pressure is essential in understanding weather patterns, as it affects wind and storm systems.
• In everyday applications, think about air pressure in car tires or water pressure in plumbing systems.

It's also a vital concept in understanding how gases and fluids behave in different environments.