When a solid or fluid (liquid or gas) is subjected to a uniform pressure all over the surface, such that the shape remains the same, then there is a change in volume.

Then the ratio of normal stress to the volumetric strain within the elastic limits is called as Bulk modulus. This is denoted by K.

where p = increase in pressure; V = original volume; DV = change in volume

The negative sign shows that with increase in pressure p, the volume decreases by DV i.e. if p is positive, DV is negative. The reciprocal of bulk modulus is called compressibility.C = compressibility =

S.I. unit of compressibility is N^–1m² and C.G.S. unit is dyne^–1cm².

Gases have two bulk moduli, namely isothermal elasticity E_q  and adiabatic elasticity E_f .

(1) Isothermal elasticity (E_q) : Elasticity possess by a gas in isothermal condition is defined as isothermal elasticity.

For isothermal process,        PV = constant                 (Boyle’s law)

Differentiating both sides PdV + VdP = 0 Þ  PdV = – VdP

E_q = P

i.e., Isothermal elasticity is equal to pressure.

(2) Adiabatic elasticity (E_f) : Elasticity possess by a gas in adiabatic condition is defined as adiabatic elasticity.

For adiabatic process,   = constant                     (Poisson’s law)

Differentiating both sides, Þ 

E_f = g P

i.e., adiabatic elasticity is equal to g times pressure.