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Ch 11: Equilibrium & Elasticity
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 14th EditionCh 11: Equilibrium & ElasticityProblema 33
Capitolo 11, Problema 33

A specimen of oil having an initial volume of 600 cm3 is subjected to a pressure increase of 3.6×106 Pa, and the volume is found to decrease by 0.45 cm3. What is the bulk modulus of the material and the compressibility?

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1
Understand the concept of bulk modulus, which is a measure of a material's resistance to uniform compression. It is defined as the ratio of the pressure increase to the relative decrease in volume.
Use the formula for bulk modulus (B): B = -ΔP / (ΔV/V₀), where ΔP is the change in pressure, ΔV is the change in volume, and V₀ is the initial volume.
Substitute the given values into the formula: ΔP = 3.6×10^6 Pa, ΔV = -0.45 cm³ (negative because the volume decreases), and V₀ = 600 cm³.
Calculate the bulk modulus using the substituted values. Remember to keep the units consistent, especially when dealing with volume changes.
To find the compressibility (κ), which is the reciprocal of the bulk modulus, use the formula: κ = 1/B. This will give you the material's compressibility in terms of Pa⁻¹.

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Bulk Modulus

Bulk modulus is a measure of a material's resistance to uniform compression. It is defined as the ratio of the pressure increase to the relative decrease in volume. Mathematically, it is expressed as B = -ΔP / (ΔV/V), where ΔP is the change in pressure, ΔV is the change in volume, and V is the initial volume.
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02:53
Example 1

Compressibility

Compressibility is the reciprocal of the bulk modulus and indicates how much a material can be compressed under pressure. It is defined as the fractional change in volume per unit increase in pressure. A higher compressibility means the material is more easily compressed, and it is calculated as κ = 1/B.
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04:45
Additional Work to Compress Spring

Pressure-Volume Relationship

The pressure-volume relationship describes how the volume of a material changes in response to applied pressure. In the context of bulk modulus, this relationship is crucial for determining how much a material compresses when subjected to external forces, allowing for calculations of bulk modulus and compressibility.
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17:04
Pressure and Atmospheric Pressure
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