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A material has a bulk modulus of 200 GPa. If the pressure on the material is inc

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Question: 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?

Options:

  1. 0.00005
  2. 0.0001
  3. 0.0002
  4. 0.00025

Correct Answer: 0.0001

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.

A material has a bulk modulus of 200 GPa. If the pressure on the material is inc

Practice Questions

Q1
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?
  1. 0.00005
  2. 0.0001
  3. 0.0002
  4. 0.00025

Questions & Step-by-Step Solutions

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?
  • 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.
  • 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 fractional decrease in volume.
  • Fractional Change in Volume – The fractional change in volume is calculated using the formula ΔV/V = ΔP/B, where ΔP is the change in pressure and B is the bulk modulus.
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