A material has a bulk modulus of 200 GPa. If the pressure applied to it is increased by 50 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 applied to it is increased by 50 MPa, what is the fractional change in volume?

Solution: The fractional change in volume is given by ΔV/V = ΔP/B. Here, ΔP = 50 MPa = 0.05 GPa, so ΔV/V = 0.05/200 = 0.00025.

Steps: 6

Step 1: Understand the problem. We need to find the fractional change in volume of a material when the pressure is increased.
Step 2: Identify the given values. The bulk modulus (B) is 200 GPa and the change in pressure (ΔP) is 50 MPa.
Step 3: Convert the change in pressure from MPa to GPa. Since 1 GPa = 1000 MPa, we have ΔP = 50 MPa = 0.05 GPa.
Step 4: Use the formula for fractional change in volume: ΔV/V = ΔP/B.
Step 5: Substitute the values into the formula: ΔV/V = 0.05 GPa / 200 GPa.
Step 6: Calculate the result: ΔV/V = 0.00025.