Bulk modulus is the ratio of volume stress to volume strain. It measures resistance to uniform compression and is written with a minus sign because compression decreases volume.
Learning Outcomes
Bulk modulus describes volume deformation.
B = −ΔPΔV/V.
The minus sign accounts for decreasing volume under increasing pressure.
The value of B is positive and its SI unit is Pa.
Intermediate Level
Volume Stress and Strain
Uniform normal force from all directions changes volume without selecting one particular length direction. Volume stress is the pressure change ΔP, while volume strain is ΔV/V.
Key equation
B=-Δ PΔ V/V
Key equation
B=-VΔ PΔ V
Physical Meaning
A large B indicates low compressibility. Solids and liquids generally have large bulk moduli; gases are much easier to compress.
Volume Compression
A pressure increase of 5.0 × 10⁶ Pa reduces a 0.020 m³ volume by 2.0 × 10⁻⁵ m³. Find B.
1
Given
ΔP = 5.0 × 10⁶ Pa
V = 0.020 m³
ΔV = −2.0 × 10⁻⁵ m³
2
Working
B = −VΔP/ΔV
3
Step 2
B = −(0.020)5.0 × 10⁶−2.0 × 10⁻⁵
Final answer:B = 5.0 × 10⁹ Pa
Textbook Material Values
Material
B (10¹⁰ Pa)
Steel
16.0
Aluminium
7.0
Copper
12.0
Iron
8.0
Brass
14.0
Common Mistakes
Use the stress and strain of the same deformation type.
Convert all data to SI units.
Modulus has the same unit as stress because strain is dimensionless.
A larger modulus means greater stiffness, not greater strain.
Short-Question Preparation
Q. Define bulk modulus.
A. The ratio of volume stress to volume strain.
Q. Why is there a negative sign?
A. Pressure increase causes volume decrease, so ΔV is negative.
Q. What does large B mean?
A. The material is difficult to compress.
Q. State its SI unit.
A. Pascal, Pa.
Sticky Notes
Bulk modulus describes volume deformation.
B = −ΔPΔV/V.
The minus sign accounts for decreasing volume under increasing pressure.
The value of B is positive and its SI unit is Pa.
60-Second Revision
Bulk modulus is the ratio of volume stress to volume strain. It measures resistance to uniform compression and is written with a minus sign because compression decreases volume.
Summary
Bulk modulus is the ratio of volume stress to volume strain. It measures resistance to uniform compression and is written with a minus sign because compression decreases volume.
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Exam preparation
Exam Focus
Important points
Bulk modulus describes volume deformation.
B = −ΔPΔV/V.
The minus sign accounts for decreasing volume under increasing pressure.
The value of B is positive and its SI unit is Pa.
Common mistakes
Match the modulus to the deformation type.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.
Bulk Modulus
Sticky Notes · Quick Revision
1.
Key Point 1
Bulk modulus describes volume deformation.
2.
Key Point 2
B = −ΔPΔV/V.
3.
Key Point 3
The minus sign accounts for decreasing volume under increasing pressure.
