Compressibility is a measure of a material’s ability to decrease in volume under pressure. It quantifies how much a substance can be compressed when subjected to an external force. Compressibility is inversely related to bulk modulus and is significant in fields like fluid dynamics and material science.
Chapter 8 Mechanical Properties of Solids examines how solid materials respond to applied forces and the resulting deformations. It introduces fundamental concepts such as stress strain elasticity and plasticity. The chapter also explores important parameters including Young’s modulus bulk modulus shear modulus and Poisson’s ratio essential for understanding material behavior in engineering contexts.
Definition of Compressibility:
Compressibility is a measure of the ability of a substance to decrease in volume under pressure. It quantifies how much a material will compress when subjected to an applied external force. The compressibility (β) of a substance is defined as the fractional change in volume per unit increase in pressure.
Mathematical Expression:
Compressibility is mathematically expressed as:
β = – (1/V) * (ΔV/ΔP)
where:
– β is the compressibility,
– V is the initial volume,
– ΔV is the change in volume,
– ΔP is the change in pressure.
Units:
The SI unit of compressibility is the reciprocal of pressure which is usually expressed in terms of:
– Pa⁻¹ (Pascal inverse) or
– N⁻¹ m² (Newton inverse per square meter).
Dimensions:
The dimensions for compressibility can be written as:
[M⁻¹ L³ T²]
Where:
M is mass,
L is length,
T is time.
In various disciplines such as fluid mechanics, material science, and engineering, it is highly relevant to know the compressibility because gases and liquids often react to varying conditions of pressure.
Click this for more solutions:
https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-8/