Question

What type of quantity (for example, length, volume, density) do the following units indicate: (a) \(\mathrm{mL}\), (b) \(\mathrm{cm}^{2}\), (c) \(\mathrm{mm}^{3}\), (d) \(\mathrm{mg} / \mathrm{L}\), (e) \(\mathrm{ps},(\mathrm{f}) \mathrm{nm},(\mathrm{g}) \mathrm{K} ?\)

Short answer

(a) mL represents volume. (b) cm² represents area. (c) mm³ represents volume. (d) mg/L represents concentration. (e) ps represents time. (f) nm represents length or distance. (g) K represents temperature.

Step-by-step solution

(a) mL

The unit mL stands for milliliters. This is a unit for measuring volume. Specifically, 1 mL (milliliter) is equal to \(1 \times 10^{-3}\) L (liters).

(b) cm²

The unit cm² stands for square centimeters. This is a unit for measuring area. 1 cm² (square centimeter) is equal to an area enclosed by a square with sides of length 1 cm.

(c) mm³

The unit mm³ stands for cubic millimeters. This is a unit for measuring volume. Specifically, 1 mm³ (cubic millimeter) is equal to \(1 \times 10^{-9}\) m³ (cubic meters).

(d) mg/L

The unit mg/L stands for milligrams per liter. This is a unit for measuring concentration (mass per unit volume). Specifically, 1 mg/L means there are 1 milligram of a substance dissolved in one liter of solution.

(e) ps

The unit ps stands for picoseconds. This is a unit for measuring time. Specifically, 1 ps (picosecond) is equal to \(1 \times 10^{-12}\) seconds.

(f) nm

The unit nm stands for nanometers. This is a unit for measuring length or distance. Specifically, 1 nm (nanometer) is equal to \(1 \times 10^{-9}\) meters.

(g) K

The unit K stands for Kelvin. This is a unit for measuring temperature. The Kelvin scale starts at absolute zero (0 K) where all thermal motion ceases, and it has the same increments as the Celsius scale.

Key concepts

Volume

Volume is the measure of how much space an object occupies. It's often given in units like liters (L), milliliters (mL), or cubic meters (m³).
A milliliter, abbreviated as mL, is a common unit used to measure small liquid volumes. It's part of the metric system and is equivalent to one-thousandth of a liter, which can be represented as \(1 \times 10^{-3}\) L.
Another unit for volume is cubic millimeter (mm³), which is often used when precise small measurements are needed. One cubic millimeter is equal to \(1 \times 10^{-9}\) cubic meters (m³).
Volume measurements are crucial in chemistry and cooking, where precise liquid inputs are essential for reactions and recipes.

Area

Area describes the amount of space enclosed within a boundary and is measured in square units.
One common unit in the metric system for measuring area is the square centimeter (cm²).
A square centimeter is the area of a square with 1 centimeter on each side. This unit is frequently used in everyday scenarios, like measuring surfaces and materials.
For example, when you're determining how much paint you'll need for a wall, understanding the area helps in calculation. Similarly, area measurements are handy in geometry to find dimensions of shapes.

Concentration

Concentration refers to the amount of a substance present in a certain volume of a mixture. It's typically highlighted in units like mg/L (milligrams per liter).
This specific unit tells you how many milligrams of a substance can be found in one liter of a solution.

• It is widely used in science, especially in chemistry and biology, to express the concentration of solutes in solutions.
• This allows for consistent and precise communication and calculation in experiments and formulations.

Understanding concentration is crucial in various fields, from environmental science, where it might describe the pollution levels, to medicine, where it dictates drug dosages.

Time

Time is a fundamental quantity used to describe the sequence of events, and it's measured in units like seconds. A picosecond, denoted as ps, is a unit used for measuring time that is extremely short: one-trillionth of a second, or \(1 \times 10^{-12}\) seconds.
The ability to measure such small intervals of time is crucial in fields like electronics and quantum physics. These short time intervals help scientists understand rapid processes such as those found in chemical reactions or the time taken for light to travel a very short distance.

Length

Length is the measurement of distance between two points and is fundamental in describing the size of objects or distances. Nanometer (nm) is a metric unit used for exceptionally small lengths, and is equivalent to \(1 \times 10^{-9}\) meters.
This unit is particularly relevant in fields such as nanotechnology and molecular biology, where measurements at the molecular or atomic scale are required.
Understanding and accurately measuring length at such small scales is essential for advancements in technology and scientific understanding at the microscopic level.

Temperature

Temperature measures how hot or cold something is, or more scientifically, the average kinetic energy of particles in an object.
The Kelvin (K) scale is an absolute temperature scale that starts at absolute zero, where no thermal motion occurs, and uses the same increment size as the Celsius scale.

• Kelvin is often used in scientific contexts because it is an absolute measure, not reliant on changing atmospheric conditions.
• Zero Kelvin is equivalent to -273.15°C.

The Kelvin scale allows for precise scientific calculations, such as when relating temperature to energy, and is crucial in fields such as thermodynamics and astrophysics.