How large a pressure increase (in ATM) must be applied to water if it is to be compressed in volume by 1.0%? The bulk modulus of water is 2.0 × 10⁹ N/m² and 1 ATM = 1.0 × 10⁵ N/m². A) 50 ATM B) 100 ATM C) 1 100 ATM D) 400 ATM E) 200 ATM

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Quizplus · Accepted Answer

The bulk modulus (B) is defined as B = -ΔP / (ΔV/V), where ΔP is the change in pressure, ΔV is the change in volume, and V is the initial volume. Given that the volume change (ΔV/V) is 1.0% or 0.01, and the bulk modulus of water is 2.0 × 10^9 N/m^2, we can rearrange the formula to solve for ΔP: ΔP = -B * (ΔV/V) = -2.0 × 10^9 N/m^2 * (-0.01) = 2.0 × 10^7 N/m^2. Converting this pressure to ATM (given that 1 ATM = 1.0 × 10^5 N/m^2), we get ΔP = 2.0 × 10^7 N/m^2 / 1.0 × 10^5 N/m^2/ATM = 200 ATM.

How Large a Pressure Increase (In ATM) Must Be Applied