Final Answer:
The change in the volume of water, confined in a rigid container, resulting from the application of a 31 MPa pressure can be estimated using the bulk modulus. Applying the formula ΔV/V = -ΔP/K, where ΔV is the change in volume, V is the initial volume, ΔP is the change in pressure, and K is the bulk modulus, yields an approximate change in volume of -0.014 m³.
Step-by-step explanation:
In this problem, we can use the bulk modulus of water to estimate the change in volume caused by the applied pressure. The bulk modulus (K) is a measure of the compressibility of a substance, and for water, it is around 2.2 × 10^9 Pa. The formula ΔV/V = -ΔP/K relates the change in volume (ΔV) to the change in pressure (ΔP), initial volume (V), and bulk modulus (K).
To calculate the change in volume, we substitute the given values into the formula: ΔV = -(ΔP/K) * V. In this case, ΔP is 31 MPa (converted to Pa), K is the bulk modulus of water, and V is the initial volume of 1 m³. The negative sign indicates that the volume decreases under increased pressure. After the calculation, we find that the change in volume is approximately -0.014 m³.
This negative change implies a decrease in volume due to the applied pressure, in line with the compressibility of water. The final answer, -0.014 m³, represents the estimated reduction in volume when a piston applies a pressure of 31 MPa to the water in a rigid container.