Bulk modulus of elasticity and Compressibility

Bulk modulus of elasticity (K): It is defined as the ratio of normal stress to the volumetric strain. It is denoted by K. Its value is also different for different types of substances.

K = Normal stress/Volumetric strain  ...(i)

If V is volume of a sphere of surface area A and F be the force acting on it which causes the decrease in volume as ΔV then we have  

Normal stress = F/A ....(ii) and

Volumetric strain = -ΔV/V .....(iii)

-ve sign indicates that volume decreases on increasing pressure.

Put equations (ii) and (iii) in equation (i), then we get    K = (F/A)/(-ΔV/V)
Or                    K =  - FV/AΔV ........(iv)

Also we know that pressure i.e p = F/A

Put in (iv) equation, then we get
                         K = (- pV/ΔV)

SI unit of K is N / m² or Pascal (Pa). 

CGS unit of K is dyne/cm² and
dimensional formula K = [ML-1 T-2].

Compressibility: The reciprocal of Bulk modulus of elasticity is called compressibility the substance. It is denoted by C or σ.
Here  C = 1/K = - ΔV/pV

SI unit of C is m²/N or 1/Pascal (Pa). 

CGS unit of C is cm²/dyne and
dimensional formula K = [M-1L T2].