Why Do We Divide Change in Volume by Original Volume in Bulk Modulus Formula?

In summary, bulk modulus is a measure of the compression of a material. It is important because it is a property that is independent of the size of the sample.
  • #1
AakashPandita
157
0
bulk modulus = Δp/ΔV/V

Why do we need to divide change in volume by the original volume?

why is it important?
 
Physics news on Phys.org
  • #2
Say you have a spring with spring constant k that is one inch tall with no weight on it. Now say you put on top the spring a mass which compresses the spring 1/10 an inch. Now stack two such springs on top of each other and place the same mass on top of the stacked springs. It should not be too hard to convince yourself that the two springs together will now compress by 2/10 an inch. The compressive properties of the springs, k, has not changed but with more springs you get more movement. Compressive material acts like the springs, more springs stacked on top of one another you get more movement for a given force.

If we apply compressive forces to some object we want to know how much it will change shape but that depends on the size and its properties.

Does this make sense or help?
 
  • #3
Because if we used just Δp/ΔV, the bulk modulus would depend on the size of the sample. We want a quantity that is independent of the sample size.
 
  • #4
say i have 2 iron blocks. 1 is a small block and other is huge.
I need to decrease each of their volumes by 10 m^3.
would the force required in each case be the same or not?
 
  • #5
say i have 2 iron blocks. 1 is a small block and other is huge.
I need to decrease each of their volumes by 10 m^3.
would the force required in each case be the same or not?
 
  • #6
No, it would not.
What if the small block is 1 m^3 and the large one is 100 m^3?
Assume you find the force you need to decrease the volume of the large one by 1 m^3.
Will the same force decrease the volume of the first one by 10m^3? Will any force be able to do this?

Can you see what kind of problems will arise trying to define a property in terms of absolute values? Not that is not possible.
Absolute value of volume change is not a property of the material but of the specific sample.
 
  • #7
this is interesting! thanks.
 

1. What is the bulk modulus formula used for?

The bulk modulus formula is used to calculate the amount of resistance a material has to compression under a given amount of pressure. It is commonly used in engineering and materials science to determine the elasticity and strength of a material.

2. How is the bulk modulus formula derived?

The bulk modulus formula is derived from Hooke's Law, which states that the stress on a material is directly proportional to the strain applied to it. By rearranging this equation and incorporating the concept of bulk modulus, we can calculate the change in volume of a material under a given pressure.

3. What are the units of measurement for bulk modulus?

The units of measurement for bulk modulus are typically given in pascals (Pa) or newtons per square meter (N/m^2). However, depending on the context, it can also be expressed in other units such as pounds per square inch (psi) or gigapascals (GPa).

4. How is the bulk modulus formula different from the Young's modulus formula?

The bulk modulus formula measures the resistance to compression, while the Young's modulus formula measures the resistance to stretching or tension. In other words, bulk modulus is a measure of the material's response to pressure, while Young's modulus is a measure of its response to tension.

5. Can the bulk modulus formula be used for all types of materials?

No, the bulk modulus formula is specifically designed for homogeneous, isotropic materials. It is not applicable for materials that are highly anisotropic or have complex structures, such as biological tissues. Additionally, the formula assumes that the material is elastic and follows Hooke's Law, so it may not be accurate for materials that exhibit non-linear behavior under pressure.

Similar threads

B Exploring Bulk Modulus: Examining Caesium and Beyond
    • Other Physics Topics
Replies
5
Views
2K
How does bulk size impact the stability of a product during transit?
    • Materials and Chemical Engineering
Replies
4
Views
710
Determine the bulk modulus of the material
    • Engineering and Comp Sci Homework Help
Replies
10
Views
3K
Relationship of bulk modulus and fractional volume change
    • Mechanical Engineering
Replies
1
Views
1K
B Ideal gas formula not working?
    • Classical Physics
Replies
14
Views
1K
I Why volume is conserved but not the surface area?
    • Classical Physics
Replies
33
Views
2K
I want to understand this equation - Fluid Mechanics
    • Mechanics
Replies
3
Views
2K
Bulk modulus given, find change in P [Fluid Mechanics]
    • Engineering and Comp Sci Homework Help
Replies
5
Views
3K
Calculating Young's Modulus for a Cylinder with Given Pressure and Bulk Modulus
    • Engineering and Comp Sci Homework Help
Replies
2
Views
2K
Calculate the bulk modulus and Derive the mean standard deviation
    • Engineering and Comp Sci Homework Help
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top