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Bulk modulus of compressed liquid

Short answer

Pressure increase dp = 4 MN/m², volume change dV = −400 cm³, volumetric strain 400/3600 = 0.1111. Bulk modulus K = dp/(−dV/V) = 36 MN/m² (3.6×10⁷ N/m²).

A liquid compressed in a cylinder has a volume of 3600 cm³ at pressure 4 MN/m² and a volume of 3200 cm³ at pressure 8 MN/m². What is bulk modulus of elasticity?

Bulk modulus is the ratio of the increase in pressure to the resulting volumetric strain:

K=dp− dV/VK = \frac{dp}{-\,dV/V}

Given: V1=3600V_1 = 3600 cm³ at p1=4p_1 = 4 MN/m², V2=3200V_2 = 3200 cm³ at p2=8p_2 = 8 MN/m².

dp=8−4=4 MN/m2dV=3200−3600=−400 cm3−dVV=4003600=0.1111K=40.1111=36 MN/m2\begin{aligned} dp &= 8 - 4 = 4\ \text{MN/m}^2 \\ dV &= 3200 - 3600 = -400\ \text{cm}^3 \\ -\frac{dV}{V} &= \frac{400}{3600} = 0.1111 \\ K &= \frac{4}{0.1111} = 36\ \text{MN/m}^2 \end{aligned}

(The initial volume 3600 cm³ is used as the reference volume.)

Answer: K=36K = 36 MN/m² =3.6×107= 3.6 \times 10^7 N/m².

✓ Answer checked by Claude Opus 5.5 (high effort)

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