Dimensional Formula of Volume

By carefully analysing dimensions and units we understand that there are a lot of between them.

When we speak about the dimensional formula it means that the physical quantity is measured without considering the numerical values. In comparison, we can define a unit as a way to assign a measurement its specific dimension.

So, before we understand the dimensional formula of volume in-depth, let us learn some concepts of dimensions and units properly.

Dimension is measuring a physical quantity without considering its numerical values. However, a unit is expressed when a measurement is assigned a particular dimension. 

Primarily, there are three-unit systems.

1. The English Engineering System of Units

2. The British Gravitational System of Units (BG Units)

3. The International System of Units (SI units)

Now let us understand in-depth and the derivation of the dimensional formula of volume.

Dimensional Formula of Volume

The dimensional formula of volume is

[M0 L3 T0]

Here, 

M = Mass 

L = Length 

T = Time

So now let us get into L

Volume (V) = Length x Breadth x Height……(1)

So, the dimensional formula of length= [M0 L1 T0] …… (2)

Now substituting equation (2) in equation (1) we get that 

Volume =Length x breadth x height

So, V= [M0 L1 T0] × [M0 L1 T0] × [M0 L1 T0] = [M0 L3 T0]

The Dimension of Volume

When we define volume, it is the amount of space encompassed within a closed surface. Now we can apply the dimension of volume to various substances like that solid, liquid, or plasma.

In mathematical terms, we measure volume in the SI unit, which we all know as a cubic metre. 

We can consider the volume of a container as the capacity it can hold, like that of the quantity of a fluid or gas. However, while the volume of a container may be its capacity, we cannot use it to specify the amount of space that the container will displace.

Mathematically, those shapes which possess a three-dimensional structure tend to hold a volume. 

Since you have now understood about the dimensional formula of volume, let us move on to the specific dimensional formula of volume questions.

Examples of Volume

1. Suppose there is a cube of length 8 cm. The formula of volume, which we know is V=a3, so the volume of the cube is:

V= a3

V= 83 cm3

So, V= 512 cm3

2. Suppose the volume of the cuboid if the length, breadth and height are 15 cm, 20 cm, 25 cm.

Then,

Length of the cuboid = 15 cm

Breadth of the cuboid = 20 cm

Height of the cuboid = 25 cm

So now the 

V= volume of the cuboid= length x breadth x height

V= (15 X 20 X 25) cm3= 7500 cm3 

Now let us study the different concepts of volume.

The Volume of Solid

The volume of a solid is a type of measure through which we understand how much space an object generally takes up. When the volume of two substances is combined, it is always greater than the volume of just one substance, be it liquid or gas. 

However, sometimes one substance might dissolve into the other, and the volume is not additive in such cases. 

The volume of a solid majorly depends upon its shape and is expressed in terms of cublic units like that of cubic metre, cubic feet etc 

Concept of Volume in Thermodynamics

Essentially, in thermodynamics, the volume of a particular system is a parameter for describing its thermodynamic state.

When we define a specific volume, it is a property that is intensive, and it is the system’s volume per unit. Also, it is essential to note that volume is a state function, independent of specific thermodynamic properties like that of pressure and temperature.

Volume Unit Conversion

The unit of length provides a derived SI unit of volume for, e.g., the volume of a cube has sides of a certain length given in metres.

Generally, in the International System of Units, the standard Unit of Volume is the cubic metre. In the metric system, however, the unit of volume is represented in litres hence

1 litre = 1000 cm3 = 1000 cubic centimetres = 0.001 cubic metres.

Now

1 cubic metre= 1000 litres

We can measure such small amounts of liquids in millilitres. 

Hence, 1 millilitre = 0.001 litres or 10^-6 cubic metre.

The traditional units of volume are:

1. Cubic Inch

2. Fluid Ounce

3. Cubic Foot

4. The Pint

5. The Barrel

6. The Cord

These were some of the units of volume and the different concepts of volume.

Points You Must Keep in Mind

• Generally, 3-D figures are assigned volumes. We can easily calculate the volumes of different shapes like regular, straight-edged, and circular shapes through various arithmetic formulas.

• We can calculate the volumes of certain complex shapes with the help of integral calculus if only the formula exists for the shape boundary.

Conclusion

Measuring a physical quantity without considering its numerical values gives the dimensional formula of volume. However, a unit is different from the dimensional formula of volume. It specifically means assigning a measurement or a number to a certain dimension. 

Also, we discussed the conversion formula, which we feel will help you understand the dimensional formula of volume meaning in a much better and more proactive way.