A material has a bulk modulus of 200 GPa. If the pressure on the material is increased by 10 MPa, what is the fractional change in volume?

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Q: A material has a bulk modulus of 200 GPa. If the pressure on the material is increased by 10 MPa, what is the fractional change in volume?

Solution: The fractional change in volume ΔV/V is given by ΔV/V = ΔP/B, where ΔP = 10 MPa and B = 200 GPa, resulting in 0.00005.

Steps: 6

Step 1: Understand the terms. The bulk modulus (B) is a measure of a material's resistance to uniform compression. It is given in gigapascals (GPa).
Step 2: Convert the bulk modulus from GPa to MPa for consistency. 1 GPa = 1000 MPa, so 200 GPa = 200,000 MPa.
Step 3: Identify the change in pressure (ΔP). In this case, ΔP = 10 MPa.
Step 4: Use the formula for fractional change in volume: ΔV/V = ΔP/B.
Step 5: Substitute the values into the formula: ΔV/V = 10 MPa / 200,000 MPa.
Step 6: Calculate the result: ΔV/V = 0.00005.