A rigid container is partly filled with a liquid at 1520 kPa. The volume of the liquid is 1.232 litres. At a pressure of 3039 kPa, the volume of the liquid is 1.231 litres.
a. Calculate the average bulk modulus of elasticity of the liquid

a.The average bulk modulus of elasticity of the liquid is 1.87 GPa

b. Coefficient of compressibility 0.5437 GPa-¹

c Velocity of sound 1.87 x 10^9P

a. Bulk modulus of elasticity

ß = - ∆p/(∆V/V)

First step  is to determine ∆p

∆p = (3039 kpa - 1520 kpa)x10³

∆p  = 1519 kPa

Second step is to determine ∆V

∆V = 1231 litres - 1232 litres

∆V = -1 m³

Now let determine the Bulk modulus of elasticity

Bulk modulus of elasticity= - 1519/(-1/1232)

Bulk modulus of elasticity= 1.87x10^6 kPa

Bulk modulus of elasticity= 1.87 GPa

b. The coefficient of compressibility

Coefficient of compressibility=β =1/K

Coefficient of compressibility=β =1/1.87

β =0.5437 GPa-¹

C. Velocity of sounds  in the medium with a density of 1593 kg/m3

V=√K/ρ

V=√1.87×10^9/ 1593

V=1083m/s

V = 1.87 x 10^9P

Inconclusion:

a.The average bulk modulus of elasticity of the liquid is 1.87 GPa

b. Coefficient of compressibility 0.5437 GPa-¹

c Velocity of sound 1.87 x 10^9P

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Bulk modulus: ß = - ∆p/(∆V/V)

∆p = (3039 - 1520)x10³ = 1519 kPa

∆V = 1231 - 1232 = -1 m³

V = 1232 m³

ß = - 1519/(-1/1232) = 1.87x10^6 kPa = 1.87 GPa

Explanation:

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