A material has a bulk modulus of 200 GPa. What is the change in volume when a pr
Practice Questions
Q1
A material has a bulk modulus of 200 GPa. What is the change in volume when a pressure of 50 MPa is applied?
0.0125%
0.025%
0.05%
0.1%
Questions & Step-by-Step Solutions
A material has a bulk modulus of 200 GPa. What is the change in volume when a pressure of 50 MPa is applied?
Step 1: Understand the bulk modulus (B). It is a measure of a material's resistance to uniform compression. In this case, B = 200 GPa.
Step 2: Understand the pressure (P) applied to the material. Here, P = 50 MPa.
Step 3: Convert the units of pressure to be the same. 1 GPa = 1000 MPa, so 200 GPa = 200,000 MPa.
Step 4: Use the formula for change in volume ratio: ΔV/V = P/B.
Step 5: Substitute the values into the formula: ΔV/V = 50 MPa / 200,000 MPa.
Step 6: Calculate the ratio: ΔV/V = 0.00025.
Step 7: Convert the ratio to a percentage by multiplying by 100: 0.00025 * 100 = 0.025%.
Step 8: Conclude that the change in volume is 0.025%.
Bulk Modulus – The bulk modulus is a measure of a material's resistance to uniform compression, defined as the ratio of pressure increase to the relative decrease in volume.
Pressure and Volume Change Relationship – The relationship between applied pressure and change in volume is given by the formula ΔV/V = P/B, where ΔV is the change in volume, V is the original volume, P is the applied pressure, and B is the bulk modulus.
