what is dimensional formula
Answers
Dimensions formulae :-
- It is defined as the equation which represent how and which of the fundamental quantity are used to represent the dimension of quantity.
Dimension :-
- Dimension of a physical quantity is the fundamental quantities involved in the given physical quantity.
● The number of these dimensions gives the information that how many times a fundamental quantity is used.
→ Fundamental quantities are also called as base quantity
Example of Dimension formulae :-
→ Dimension formulae of Density :-
★ Density = Mass/Volume = [M]/[L^3] = [ML^-3]
Dimensional formula is an expression for the unit of a physical quantity in terms of the fundamental quantities. The fundamental quantities are mass (M), length (L), and time (T). A dimensional formula is expressed in terms of powers of M,L and T.
Dimensional formula is nothing but the representation of fundamental quantities in terms of physical quantities. And there exist Length(L), Mass(M), Time(T), Current(I), Amount of substance(n), Temperature(Θ), Luminous intensity(J).
By deeper understanding and importance of dimensional formula, let me take an example:
Suppose take a Gas constant and it has the units of J K −1 mol −1,eV K −1 mol −1, L atm K −1 mol −1,cal K−1 mol−1,kcal K−1 mol−1,erg K−1 mol−1,L kPa K−1 mol−1,m3 Pa ,K−1 mol−1,cm3 MPa K−1 mol−1,m3 bar K−1 mol−1,m3 atm K−1 mol−1,cm3 atm K−1 mol−1,m3 kgf/cm2 K−1 mol−1,L bar K−1 mol−1,L mmHg K−1 mol−1,L Torr K−1 mol−1,ft lbf K−1 g-mol−1,ft lbf °R−1 lb-mol−1,ft3 psi °R−1 lb-mol−1,ft3 atm °R−1 lb-mol−1,ft3 atm K−1 lb-mol−1,ft3 mmHg K−1 lb-mol−1,Btu lb-mol −1 °R −1.
You are supposed to calculate the volume of some mixture using the formula V=nRT/P. So, it is tough to put some units. But the dimensional formula is always [M^4LT^-1n^-1Θ^-1] . By using this you simply calculate the dimensions for volume. And never ever forgot that dimensional formula are derived from dimensions. It is simply understandable if you know the dimensions.