Question

Calculate the volume of 100 ml when subjected to a pressure of 1.5 MPa

Answer 1

Answer on Question 62232, Physics, Molecular Physics, Thermodynamics

Question:

Calculate the volume contraction of $100\,mL$ of water when subjected to a pressure of $1.5\,MPa$. The bulk modulus of water is $2.1\,GPa$.

Solution:

Let's recall the definition of the bulk modulus. The bulk modulus, $K$, is a material property characterizing the compressibility of the fluid. The bulk modulus can be calculated as follows:

$$K = - \frac {dp}{dV / V_0},$$

here, $K = 2.1\,GPa$ is the bulk modulus of water, $dp = 1.5\,MPa$ is the pressure change that is required in order to change the volume of water by $dV$, $V_0 = 100\,mL$ is the initial volume of water.

From this formula we can find the volume contraction $dV$:

$$dV = - V_0 \frac {dp}{K} = - 100\,mL \cdot \frac {1.5 \cdot 10^6\,Pa}{2.1 \cdot 10^9\,Pa} = -0.071\,mL.$$

The sign minus indicates that an increase in pressure is accompanied by a decrease in volume.

Answer:

$$dV = -0.071\,mL.$$

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