One litre of water is subjected to an additional uniform pressure of 20 MPa. The bulk modulus of water is 2 GPa. If the decrease in volume is N mL, find N. Assume the compression is small.

Question

G1 Physics · Accepted Answer

Bulk modulus is K = −ΔP / [ΔV/V]. Therefore the magnitude of fractional volume decrease is |ΔV|/V = ΔP/K. Substitute: ΔP = 20 MPa, K = 2 GPa = 2000 MPa. Hence, |ΔV|/V = 20/2000 = 0.01. Thus the volume decreases by 1%. Initial volume: V = 1 litre = 1000 mL. Therefore, |ΔV| = 0.01×1000 = 10 mL. Hence, N = 10.