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A material has a bulk modulus of 200 GPa. If the pressure applied to it is incre

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Question: 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?

Options:

  1. 0.00025
  2. 0.0005
  3. 0.0025
  4. 0.005

Correct Answer: 0.00025

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.

A material has a bulk modulus of 200 GPa. If the pressure applied to it is incre

Practice Questions

Q1
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?
  1. 0.00025
  2. 0.0005
  3. 0.0025
  4. 0.005

Questions & Step-by-Step Solutions

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?
Correct Answer: 0.00025
  • 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.
  • 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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