Table of Contents

## Definition of Physical Quantity

Physical Quantity – One of the important part of the scientific work is measuring of physical quantities such as mass, volume, length, energy, temperature, etc. It is interesting to note that all these quantities can be expressed in terms of a few basic units.

For example, in everyday life, we come across a number of measurements like kilograms (for mass), liters (for volume), meters (for length measurements) etc. In addition to these common measurements we need to measure a number of other quantities as concentration, temperature, pressure, density, amount of electrical

charge etc.

“All such quantities which we come across during the Scientific studies are called physical quantities”.

A physical quantity thus refers to the result of measurement operation. It involves the comparison of the quantity to be measured with some fixed standard.

**For example**, if we are interested in Seal knowing the length of a pencil, the operations would be :

- To lay the pencil parallel to centimeter scale and
- To count the number of markings on the scale.

### Examples

- Suppose the number of markings is 9.5. This implies that the piece of paper is 9.5 times longer than one unit of measurement. It makes no sense to say that length of the paper is 9.5. However, if we attach a centimeter, a unit of length, to the numerical figure, i.e., 9.5 cm, it will become more appropriate. Thus, a measured physical quantity is expressed in two parts, a numerical coefficient, and a unit. Either of them is meaningless without the other. In the measurement of the length of the pencil, 9.5 is a numerical figure, whereas a centimeter is a unit.
- The study of experimental science thus depends upon the quantitative measurement of properties. Every measurement gives a numerical result that has three important aspects :

- Numerical magnitude.
- Accuracy or precision with which the number is expressed.
- Indicator of scale i.e., unit employed to express.

The measurement of physical quantities becomes scientifically more correct and relevant if all the three aspects as given above are reported.

## Ways To Express Physical Quantity

There are mainly two ways to express physical quantities –

### 1. Unit

“A unit may be defined as the standard of reference chosen to measure or express any physical quantity”.

Chemists measure the properties of matter using various devices or measuring tools, many of which are similar to those used in everyday life.

Rulers are used to measuring length, balances (scales) are used to measure mass (weight), and graduated cylinders or pipettes are used to measure volume.

Measurements made using these devices are expressed as quantities.

A quantity is an amount of something and consists of a number and a unit. The number tells us how many (or how much), and the unit tells us the scale of measurement.

#### For example

- When a distance is reported as “5.2 kilometers,” we know that the quantity has been expressed in units of kilometers and that the number of kilometers is 5.2.
- If you ask a friend how far he or she walks from home to school, and the friend answers “12” without specifying a unit, you do not know whether your friend walks—for example, 12 miles, 12 kilometers, 12 furlongs, or 12 yards.

Without units, a number can be meaningless, confusing, or possibly life-threatening. Suppose a doctor prescribes phenobarbital to control a patient’s seizures and states dosage of “100” without specifying units.

Not only will this be confusing to the medical professional giving the dose, but the consequences can be dire: 100 mg given three times per day can be effective as an anticonvulsant, but a single dose of 100 g is more than 10 times the lethal amount. Both a number and a unit must be included to express a quantity properly.

### 2. Scientific Notation

The study of chemistry can involve very large numbers. It can also involve very small numbers. Writing out such numbers and using them in their long form is problematic because we would spend far too much time writing zeroes, and we would probably make many mistakes! There is a solution to this problem. It is called scientific notation.

Scientific notation allows us to express very large and very small numbers using powers of 10.

**Recall that :**

10^{0} = 1, 10^{1} = 10, 10^{2} = 100

10^{3} = 1000, 10^{4} = 10000, 10^{5} = 100000

As you can see, the power to which 10 is raised is equal to the number of zeroes that follow the 1. This will be helpful for determining which exponent to use when we express numbers using scientific notation.

#### Methods to Express Scientific Notations

There are the some methods to express scientific notation of very large numbers and very small numbers

##### 1. Scientific Notation of Very Large Numbers

Let us take a very large number, 579, 000, 000, 000 and express it using scientific notation.

**Solution**

- First, we find the coefficient, which is a number between 1 and 10 that will be multiplied by 10 raised to some power.

Here the coefficient is = 5.79

- And now this number will be multiplied by 10 that is raised to some power. Now let us figure out what power that is.
- We can do this by counting the number of positions that stand between the end of the original number and the new position of the decimal point in our coefficient.

5 . 7 9 0 0 0 0 0 0 0 0 0

We can see that there are 11 positions between our decimal and the end of the original number. This means that our coefficient, 5.79, will be multiplied by 10 raised to the 11th power.

The number expressed in scientific notation is = 5.79 x 10^{11} .

##### 2. Scientific Notation of Very Sarge Numbers

You may recall that :

10^{-1} = 0.1, 10^{-2} = 0.01, 10^{-3} = 0.001

10^{-4} = 0.0001, 10^{-5} = 0.00001

The number of spaces to the right of the decimal point for our 1 is equal to the number in the exponent that is behind the negative sign. This is useful to keep in mind when we express very small numbers in scientific notation.

Let us take a very small number, 0.0000642 and express it using scientific notation.

Here the coefficient is = 6.42

- This number will be multiplied by 10 raised to some power, which will be negative. Let us figure out the correct power. We can figure this out by counting how many positions stand between the decimal point in our coefficient and the decimal point in our original number.

0 . 0 0 0 0 6 4 2

- There are 5 positions between our new decimal point and the decimal point in the original number, so our coefficient will be multiplied by 10 raised to the negative 5th power.

Therefore, the number expressed in scientific notation is = 6.42 x 10^{-5}.

You can use these methods to express any large or small number using scientific notation.

## Units For Measurement of Physical Quantity

International System of Units is used for the measurement of the physical quantities

### Definition of SI Unit

The International System of Units abbreviated SI from the French Système International D’unités, is the main system of measurement units used in science.

Since the 1960s, the International System of Units has been internationally agreed upon as the standard metric system. The SI base units are based on physical standards.

The definitions of the SI base units have been and continue to be modified, and new base units added as advancements in science are made. Stable properties of the universe describe each SI base unit except the kilogram.

### Types of SI Unit

Followings are the types of SI unit

#### 1. Mass

- The basic unit of mass in the International System of Units is the kilogram.
- A kilogram is equal to 1000 grams. A gram is a relatively small amount of mass and so larger masses are often expressed in kilograms.
- When very tiny amounts of matter are measured, we often use milligrams which are equal to 0.001 gram.
- There are numerous larger, smaller, and intermediate-mass units that may also be appropriate. At the end of the 18th century, a kilogram was the mass of a liter of water. In 1889, a new international prototype of the kilogram was made of a platinum-iridium alloy. The kilogram is equal to the mass of this international prototype, which is held in Paris, France.
- Mass and weight are not the same things. Although we often use the terms mass and weight interchangeably, each has a specific definition and usage. The mass of an object is a measure of the amount of matter in it. An object’s mass (amount of matter) remains the same regardless of where the object is placed.
**For example**, moving a brick to the moon does not cause any matter in it to disappear or be removed. - The force determines the weight of an object that gravitation exerts upon the object. The weight is equal to the mass of the object, times the local acceleration of gravity. Thus, weight is determined by the force of attraction between the object and the Earth on the Earth. Since the force of gravity is not the same at every point on the Earth’s surface, the weight of an object is not constant. The gravitational pull on the object varies depending on where the object is with respect to the Earth or other gravity-producing object.

**For example**, a man who weighs 180 pounds on Earth would weigh only 45 pounds if he were in a stationary position, 4,000 miles above the Earth’s surface. This same man would weigh only 30 pounds on the moon because the moon’s gravity is only one-sixth that of Earth.

The mass of this man, however, would be the same in each situation. For scientific experiments, it is important to measure the mass of a substance rather than the weight to retain consistency in the results regardless of where you are performing the experiment.

#### 2. Length

- The SI unit of length is the meter.
- The definition of the meter was a bar of platinum-iridium alloy stored under conditions specified by the International Bureau of Standards in 1889.
- In 1960, this definition of the standard meter was replaced by a definition based on a wavelength of krypton-86 radiation.
- In 1983, that definition was replaced by the following: the meter is the length of the path traveled by light in a vacuum during a time interval of a second.

#### 3. Temperature

When used in a scientific context, the words heat and temperature do NOT mean the same thing. Temperature represents the average kinetic energy of the particles that make up a material. Increasing the temperature of a material increases its thermal energy.

Thermal energy is the sum of the kinetic and potential energy in the particles that make up a material. Objects do not “contain” heat; rather, they contain thermal energy.

Heat is the movement of thermal energy from a warmer object to a cooler object. When thermal energy moves from one object to another, the temperature of both objects change.

- A thermometer is a device that measures temperature. The name is made up of “thermo” which means heat and “meter” which means to measure.
- The temperature of a substance is directly proportional to the average kinetic energy it contains.
- In order for the average kinetic energy and temperature of a substance to be directly proportional, it is necessary that when the temperature is zero, the average kinetic energy must also be zero.

#### 4. Time

- The SI unit for time is the second.
- The second was originally defined as a tiny fraction of the time required for the Earth to orbit the Sun. It has since been redefined several times.
- The definition of a second (established in 1967 and reaffirmed in 1997) is the duration of 9,192,631,770 periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.

#### 5. Amount

- Chemists use the term mole to represent a large number of atoms or molecules. Just as a dozen implies 12 things, a mole (mol) represents 6.022 × 10
^{23}things. - The number 6.022 × 10
^{23}, called Avogadro’s number after the 19th – century chemist Amedeo Avogadro, is used in chemistry to represent macroscopic amounts of atoms and molecules. - Thus, if we have 6.022 × 10
^{23}Oxygen atoms, we say we have 1 mol of oxygen atoms. If we have 2 mol of Na atoms, we have 2 × (6.022 × 10^{23}) Na atoms or 1.2044 × 1024 Na atoms. Similarly, if we have 0.5 mol of benzene (C_{6}H_{6}) molecules, we have 0.5 × (6.022 × 10^{23}) C_{6}H_{6}molecules or 3.011 × 10^{23}C_{6}H_{6}molecules.

### Derived SI Units

Derived units of physical quantity are combinations of SI base units. Units can be multiplied and divided, just as numbers can be multiplied and divided.

**For example**, the area of a square having a side of 2 cm is 2 cm × 2 cm, or 4 cm^{2} (read as “four centimeters squared” or “four square centimeters”). Notice that we have squared a length unit, the centimeter, to get a derived unit for area, the square centimeter.

#### Types of Derived SI Unit

##### Volume

- A Volume is an important quantity that uses a derived unit.
- Volume is the amount of space that a given substance occupies and is defined geometrically as length × width × height.
- Each distance can be expressed using the meter unit, so volume has the derived unit m × m × m, or m
^{3}(read as “meters cubed” or “cubic meters”). A cubic meter is a rather large volume, so scientists typically express volumes in terms of 1/1,000 of a cubic meter. This unit has its own name—the liter (L). A liter is a little larger than 1 US quart in volume. gives approximate equivalents for some of the units used in chemistry.). - By definition, there are 1,000 mL in 1 L, so 1 milliliter and 1 cubic centimeter represent the same volume.

##### Energy

- Energy, another important quantity in chemistry, is the ability to perform work.
- Moving a box of books from one side of a room to the other side, for example, requires energy.
- It has a derived unit of kg·m
^{2}/s^{2}. (The dot between the kg and m^{2}units implies the units are multiplied together and then the whole term is divided by s^{2}.)

Because this combination is cumbersome, this collection of units is redefined as a joule (J), which is the SI unit of energy. An older unit of energy, the calorie (cal), is also widely used. There are : **4.184 J = 1 cal**

Note that this differs from our common use of the big ‘Calorie’or ‘Cal’ listed on food packages in the United States. The big ‘Cal’ is actually a kilocalorie or kcal Note that all chemical processes or reactions occur with a simultaneous change in energy and that energy can be stored in chemical bonds.

##### Density

Density is defined as the mass of an object divided by its volume; it describes the amount of matter contained in a given amount of space.

density=mass/volume

Thus, the units of density are the units of mass divided by the units of volume: g/cm3 or g/mL (for solids and liquids, respectively), g/L (for gases), kg/m^{3}, and so forth.

**For example**, the density of water is about 1.00 g/mL, while the density of mercury is 13.6 g/mL. Mercury is over 13 times as dense as water, meaning that it contains over 13 times the amount of matter in the same amount of space.

The density of air at room temperature is about 1.3 g/L.

So this is all about physical quantity. I hope you like our article.

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