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

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Discussion Overview

The discussion revolves around the bulk modulus formula, specifically the rationale behind dividing the change in volume by the original volume. Participants explore the implications of this division in relation to material properties and the effects of size on compressive forces.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the necessity of dividing the change in volume by the original volume in the bulk modulus formula, seeking to understand its importance.
  • Another participant uses an analogy of springs to illustrate how compressive properties can vary with the arrangement of materials, suggesting that the change in shape under compressive forces depends on the size and properties of the material.
  • It is proposed that using just the change in pressure over change in volume would make the bulk modulus dependent on the sample size, thus emphasizing the need for a size-independent quantity.
  • Two participants present a scenario involving two iron blocks of different sizes, questioning whether the force required to decrease their volumes by a specific amount would be the same.
  • A later reply asserts that the force required would not be the same, highlighting that absolute volume changes are specific to the sample and not intrinsic properties of the material.
  • One participant expresses interest in the discussion, indicating engagement with the topic.

Areas of Agreement / Disagreement

Participants express differing views on the implications of volume change and the relationship between force and sample size. There is no consensus on the specific effects of size on the bulk modulus or the force required for volume changes.

Contextual Notes

The discussion includes assumptions about material properties and the effects of size that are not fully resolved. The implications of using absolute values in defining material properties are also noted as a point of contention.

AakashPandita
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bulk modulus = Δp/ΔV/V

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

why is it important?
 
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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?
 
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.
 
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?
 
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?
 
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.
 
this is interesting! thanks.
 

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