Poisson ’ s Ratio When a deforming force is applied at the free end of a suspended wire of length 1 and radius R , then its length increases by dl but its radius decreases by dR . Now two types of strains are produced by a single force .
( i ) Longitudinal strain = & DElta ; U l
( ii ) Lateral strain = – R / R ∴ Poisson ’ s Ratio ( σ ) = Lateral strain / Longitudinal strain = – R / R / ΔU l
The theoretical value of Poisson ’ s ratio lies between – 1 and 0.5 . Its practical value lies between 0 and 0.5 .
Relation Between Y , K , η and σ ( i ) Y = 3K ( 1 – 2σ )
( ii ) Y = 2 η ( 1 + σ ) ( iii ) σ = 3K – 2η / 2η + 6K ( iv ) 9 / Y = 1 / K + 3 / η or Y = 9K η / η + 3K
Important Points
Coefficient of elasticity depends upon the material , its temperature and purity but not on stress or strain .
For the same material , the three coefficients of elasticity γ , η and K have different magnitudes .
gas .
Isothermal elasticity of a gas ET = ρ where , ρ = pressure of the
Adiabatic elasticity of a gas Es = γρ
where , γ = Cp / Cv ratio of specific heats at constant pressure and at constant volume .
Ratio between isothermal elasticity and adiabatic elasticity Es /
ET = γ = Cp / Cv