UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Science, Engineering and Technology
⋄
FORMATIVE ASSESSMENT 3
Semester 1 — 2026
⋄
Module Code: PHY3703
Module Name: Statistical and Thermal Physics
Assignment No.: 03
Due Date: 2026
Semester: Semester 1, 2026
Submitted in partial fulfilment of the requirements for PHY3703:
Statistical and Thermal Physics at the University of South Africa.
, UNISA | PHY3703 Assessment 3 — 2026
Contents
1 Problem 5.16: Behaviour of the Specific Heat Near Tc 2
1.1 Q: Use Eq. 5.120 and m2 ≈ 3(Tc − T )/Tc to show that C(T → Tc− ) = 3k/2 . 2
1.2 Q: Hence, show that mean-field theory predicts a jump (discontinuity)
in the specific heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Problem 5.26: The One-Dimensional Ising Model 5
2.1 (a) Q: Calculate the partition function Z for a 1D Ising model with N spins
and periodic boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 (b) Q: Find the average energy ⟨E⟩ and the heat capacity C . . . . . . . 6
2.2.1 Average Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 (c) Q: Discuss why there is no phase transition for T > 0 in this model 7
3 Problem 6.1: Diffusion in a Gas 9
3.1 (a) Q: Derive an expression for the self-diffusion coefficient D in terms
of v̄ and λ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 (b) Q: Show that D ∝ T 3/2 /P . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.3 (c) Q: Estimate D for air at STP . . . . . . . . . . . . . . . . . . . . . . . . . 10
4 Problem 6.3: Thermal Conductivity 12
4.1 (a) Q: Derive an expression for the thermal conductivity K in terms of
cV , n, v̄, and λ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.2 (b) Q: Explain why K is approximately independent of density (or pres-
sure) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.3 (c) Q: Discuss the relationship between K and the viscosity η . . . . . . 13
Reference List 15
Page 1 of 15
College of Science, Engineering and Technology
⋄
FORMATIVE ASSESSMENT 3
Semester 1 — 2026
⋄
Module Code: PHY3703
Module Name: Statistical and Thermal Physics
Assignment No.: 03
Due Date: 2026
Semester: Semester 1, 2026
Submitted in partial fulfilment of the requirements for PHY3703:
Statistical and Thermal Physics at the University of South Africa.
, UNISA | PHY3703 Assessment 3 — 2026
Contents
1 Problem 5.16: Behaviour of the Specific Heat Near Tc 2
1.1 Q: Use Eq. 5.120 and m2 ≈ 3(Tc − T )/Tc to show that C(T → Tc− ) = 3k/2 . 2
1.2 Q: Hence, show that mean-field theory predicts a jump (discontinuity)
in the specific heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Problem 5.26: The One-Dimensional Ising Model 5
2.1 (a) Q: Calculate the partition function Z for a 1D Ising model with N spins
and periodic boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 (b) Q: Find the average energy ⟨E⟩ and the heat capacity C . . . . . . . 6
2.2.1 Average Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 (c) Q: Discuss why there is no phase transition for T > 0 in this model 7
3 Problem 6.1: Diffusion in a Gas 9
3.1 (a) Q: Derive an expression for the self-diffusion coefficient D in terms
of v̄ and λ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 (b) Q: Show that D ∝ T 3/2 /P . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.3 (c) Q: Estimate D for air at STP . . . . . . . . . . . . . . . . . . . . . . . . . 10
4 Problem 6.3: Thermal Conductivity 12
4.1 (a) Q: Derive an expression for the thermal conductivity K in terms of
cV , n, v̄, and λ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.2 (b) Q: Explain why K is approximately independent of density (or pres-
sure) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.3 (c) Q: Discuss the relationship between K and the viscosity η . . . . . . 13
Reference List 15
Page 1 of 15
