Macroscopic Properties of Matter

Question 1

What is the harmonic model of bonding?

Answer 1

Bonds behave like springs with PE: u(r) = u0 + K/2(r - r0)^2 + 1/6K’*(r-r0)^3

Question 2

Why is the harmonic model insufficient?

Answer 2

Real bonds are anharmonic: asymmetrical, with third-order corrections to PE.

Question 3

Define volume thermal expansivity (β).

Answer 3

β = 1/V (∂V/∂T)P (K⁻¹)

Question 4

Define linear expansivity (α).

Answer 4

α = 1/L (∂L / ∂T) F (K⁻¹)

Question 5

What is the relation between β and α in isotropic solids?

Answer 5

β ≈ 3α

Question 6

How does ΔV relate to β and ΔT?

Answer 6

Δ𝑉 = 𝑉𝑖𝛽Δ𝑇

Question 7

What is negative thermal expansion

Answer 7

Some solids shrink when heated

Question 8

Define bulk modulus (K) and give its formula.

Answer 8

Resistance to volume change under pressure:
 
𝐾 = −𝑉 (∂𝑃/∂𝑉) 𝑇 ; units: Pa

Question 9

Define isothermal compressibility (κ)

Answer 9

𝜅 = 1/ 𝐾; units: Pa⁻¹ [1 / bulk modulus]

Question 10

Define Young’s modulus (Y)

Answer 10

Measures resistance to 1D deformation:
 
𝑌 = 𝐿/𝐴 (∂𝐹/∂𝐿) 𝑇​

Question 11

Define stress and strain in 1D.

Answer 11

Stress (σ) = Δ𝐹 / 𝐴
​
Strain (ε) = Δ𝐿 / 𝐿𝑖

∴ σ = Yε

Question 12

How does molecular potential energy relate to elasticity?

Answer 12

Elastic properties like Y arise from the curvature (slope) of interatomic PE curves around equilibrium spacing 𝑟0.

Question 13

Define shear modulus (G).

Answer 13

Resistance to shear deformation:
𝐺 = 𝜎𝑠 / 𝛾𝑠 ; units: Pa

Question 14

Define Poisson’s ratio (ν).

Answer 14

ν= −lateralstrain / axial strain =− (db/b) / (dL/L)

Question 15

How are G and Y related through ν?

Answer 15

G = Y / 2(1+ν)

Question 16

How are K and Y related through ν

Answer 16

K = Y / 3(1−2ν)

Question 17

Equation for Linear Expansivity

Answer 17

𝛼 = 1/𝐿 (∂𝐿/∂𝑇)

Question 18

Equation for Volume Thermal Expansivity

Answer 18

β = 1/V (∂V/∂T)

Question 19

Equation for Young’s Modulus

Answer 19

Y = L/A ( ∂F / ∂L)

Question 20

Equation for Bulk Modulus

Answer 20

K=−V (∂P / ∂V)

Question 21

Equation for Compressibility

Answer 21

k = 1 / Bulk Modulus

Question 22

Equation for shear modulus

Answer 22

𝐺 = 𝜎𝑠 / 𝛾𝑠

Question 23

Equation for Poissons Ratio

Answer 23

ν = − db / b / dL / L