Materials Science – Dependence of Macroscopic Properties For a given engineering material, macroscopic (bulk) properties such as modulus, resistivity, permeability, thermal conductivity, and strength are measured at the continuum scale. Which statement best describes how these macroscopic quantities depend on external conditions?

Introduction / Context:
Macroscopic (bulk) properties in materials science describe how a real piece of material behaves under operating conditions. Unlike immutable constants, many measured properties vary with external variables such as temperature, pressure, stress state, frequency, humidity, and applied electromagnetic fields. Recognizing these dependencies helps engineers select materials and design components that perform reliably in service.

Given Data / Assumptions:

• Continuum description of a homogeneous material sample.
• Standard laboratory/environmental variables: temperature and pressure are commonly controlled.
• Properties of interest include mechanical, thermal, electrical, and magnetic quantities.

Concept / Approach:

Measured properties often obey constitutive relations that include explicit dependence on thermodynamic variables. For example, elastic modulus generally decreases with temperature; electrical resistivity of metals typically increases with temperature; magnetic permeability can vary with both temperature and applied stress; thermal conductivity in polymers and ceramics is temperature dependent; and density is weakly pressure dependent but this matters at high pressures. Thus, it is most accurate to view macroscopic properties as functions of state variables, prominently temperature and pressure.

Step-by-Step Solution:

Verification / Alternative check:

Material datasheets list property values at specified temperatures and sometimes pressures. Standards (e.g., ASTM, IEC) specify test temperatures and environments precisely because properties change with these variables.

Why Other Options Are Wrong:

• Absolutely constant: ignores well-known temperature and pressure effects.
• Only temperature: neglects pressure dependence observed in high-pressure physics and some engineering settings.
• Only composition: environment and loading history also matter.
• Including “other fields” is broadly true, but the question asks for the best general description with emphasis on common variables; temperature and pressure are fundamental state variables.

Common Pitfalls:

Assuming handbook values are universal constants; overlooking service temperature excursions; ignoring hydrostatic pressure or prestress effects on performance.

Final Answer:

They are functions of temperature and the applied pressure field